Language Warning

In the next piece I had to discuss a particular topic. Unfortunately, I couldn’t discuss it without naming it. Therefore I apologize in advance for having to do so, and apologize to anyone offended by the sight of the name.

RINO McDaniel

As you no doubt know, RINO McDaniel got re-elected to RNC Chair Friday. I hope no one has already managed in the intervening time to suppress that memory; if so I apologize for the PTSD trigger.

RINO McDaniel isn’t the problem.

Let me be crystal clear on this, RINO McDaniel is a lower-than-whale-shit, piss guzzling ratfucking shit eating traitorous rancid syphillitic cunt. Her worth as a human being is substantially less than zero, any oxygen sucked into her lungs is wasted, and it would be, no matter what job she had.

I fear I haven’t been clear enough, but that will have to suffice.

But she is not the problem…or rather, she would not be a problem were it not for others. She’d still be as I have described, but we wouldn’t know who she is and would not care, because she could do no damage. She’d just be anonymous human refuse.

No, the real problem is the fact that a majority of the 168 top GOP people voted for her. And now that has happened five times so they cannot claim they didn’t know what she was.

In spite of the fact that under her “leadership” the party has deliberately sabotaged the will of its base, has deliberately refused to challenge blatant election fraud, had gone out of its way to ensure certain candidates do not get nominated, has diverted donor money to namby-pamby candidates who have all the electoral appeal of a puddle of dog vomit…and in general has done nothing whatsoever to help fix the problems that plague America.

However that last is to be expected; I cannot expect anyone who IS the problem to help FIX the problem.

RINO McDaniel would be powerless without an entire party leadership of the same mind as her. They want this dismal performance; they want to ignore the party base.

If she were to drop dead this instant, it would solve nothing as someone just like her would be elected by those same pustulous people.

According to Charlie Kirk, about 55 people voted against her, 10-12 wanted something different but were too chickenshit to do the right thing, and roughly 100 people voted for her enthusiastically, and even had the unmitigated gall to complain to Kirk about US. Fuck ’em. Rusty 12 gauge bore brushes would be too good for these arrogant pricks and cunts.

Every single one of those hundred is just as bad as she is. In other words, they are all worse than I described at the beginning of this piece. And no doubt those people in turn have people who supported them to be state party chairs and whateveritis they call the other two people from each state and territory who were voting.

It’s time to face up to the fact that the Republican party is effectively owned by the shit-eating RINOs. We’ve got more work to do, a lot more work, to make the GOP an instrument for the restoration of the United States of America. And that’s in addition to cleaning up our elections.

There’s no point in cleaning up elections just to elect ratfucking RINOs.

OK, hopefully now you will have some inkling of my true attitude towards RINOs. Sorry that words were inadequate to give you the full picture.

The Real Fascist is His Fraudulency Joe Biden*

*Or whoever has his hand rammed up that meat puppet’s ass.

Brandon (which I will use as a term for whoever is the power behind the Porcelain Throne) has thrown down the gauntlet…but in a way where most of America will never see it. The networks didn’t carry his tirade. CNN air brushed it (or whatever you call editing the red background) for its five viewers (who aren’t trapped in airports).

Luckily for me I live in Colorado, and therefore, despite my best efforts, I probably didn’t vote for Donald Trump.

Of course, for this purpose who I actually did try to vote for will be essential, and they undoubtedly know.

Come and get us, asswipes!

https://www.youtube.com/watch?v=3h6ZZ28QtX4

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

Small Government?

Many times conservatives (real and fake) speak of “small government” being the goal.

This sounds good, and mostly is good, but it misses the essential point. The important thing here isn’t the size, but rather the purpose, of government. We could have a cheap, small tyranny. After all our government spends most of its revenue on payments to individuals and foreign aid, neither of which is part of the tyrannical apparatus trying to keep us locked down and censored. What parts of the government would be necessary for a tyranny? It’d be a lot smaller than what we have now. We could shrink the government and nevertheless find it more tyrannical than it is today.

No, what we want is a limited government, limited not in size, but rather in scope. Limited, that is, in what it’s allowed to do. Under current circumstances, such a government would also be much smaller, but that’s a side effect. If we were in a World War II sort of war, an existential fight against nasty dictatorships on the brink of world conquest, that would be very expensive and would require a gargantuan government, but that would be what the government should be doing. That would be a large, but still limited government, since it’d be working to protect our rights.

World War II would have been the wrong time to squawk about “small government,” but it wasn’t (and never is) a bad time to demand limited government. Today would be a better time to ask for a small government–at least the job it should be doing is small today–but it misses the essential point; we want government to not do certain things. Many of those things we don’t want it doing are expensive but many of them are quite eminently doable by a smaller government than the one we have today. Small, but still exceeding proper limits.

So be careful what you ask for. You might get it and find you asked for the wrong thing.

Political Science In Summation

It’s really just a matter of people who can’t be happy unless they control others…versus those who want to be left alone. The oldest conflict within mankind. Government is necessary, but government attracts the assholes (a highly technical term for the control freaks).

A Few Things We Cannot Blame on His Fraudulency

I am pretty sure Joe Biden had nothing whatsoever to do with the 30 Years War that ran from 1618-1648 and probably killed about a third of the people then living in what is now Germany.

Nor did he cause the collapse of either Roman empire (Western, 476 CE, Eastern 1453 CE). Nor the ignominious failure of most of the Crusades. Nor the collapse of Bronze Age civilization around 1200 BCE (including the collapse of the Minoans and the blowup of Santorini).

However, my utter lack of ability to imagine how he could possibly be responsible for these things is not a valid argument against them, so I await correction if appropriate.

His Truth?

Again we saw an instance of “It might be true for Billy, but it’s not true for Bob” logic this week.

I hear this often, and it’s usually harmless. As when it’s describing differing circumstances, not different facts. “Housing is unaffordable” can be true for one person, but not for another who makes ten times as much.

But sometimes the speaker means it literally. Something like 2+2=4 is asserted to be true for Billy but not for Bob. (And when it’s literal, it’s usually Bob saying it.) And in that sense, it’s nonsense, dangerous nonsense. There is ONE reality, and it exists independent of our desires and our perceptions. It would go on existing if we weren’t here. We exist in it. It does not exist in our heads. It’s not a personal construct, and it isn’t a social construct. If there were no society, reality would continue to be what it is, it wouldn’t vanish…which it would have to do, if it were a social construct.

Now what can change from person to person is the perception of reality. We see that all the time. And people will, of course, act on those perceptions. They will vote for Trump (or try to) if their perception is close to mine, and vote against Trump (and certainly succeed at doing so) if their perception is distant from mine (and therefore, if I do say so, wrong). I have heard people say “perception is reality” and usually, that’s what they’re trying to say–your perception of reality is, as far as you know, an accurate representation of reality, or you’d change it.

But I really wish they’d say it differently. And sometimes, to get back to Billy and Bob, the person who says they have different truths is really saying they have different perceptions of reality–different worldviews. I can’t argue with the latter. But I sure wish they’d say it better. That way I’d know that someone who blabbers about two different truths is delusional and not worth my time, at least not until he passes kindergarten-level metaphysics on his umpteenth attempt.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

(Paper) Spot Prices

Kitco “Ask” prices. Last week:

Gold $1,812.50
Silver $20.86
Platinum $919.00
Palladium $1,490.00
Rhodium $11,100.00

This week, 3PM Mountain Time, markets have closed for the weekend.

Gold $1,857.50
Silver $21.35
Platinum $989.00
Palladium $1,512.00
Rhodium $10,850.00

And now, they’re going up. One could make a lot of money in this market, simply by buying low and selling high, but the trick that’s hard to learn (I never did!) is timing.

Three Bodies

So far with the occasional exception everything I’ve discussed has been “straight” Newtonian two body astrodynamics. Aside from perturbations due to irregular shapes, under these circumstances an orbit is unchanging. If something is in an elliptical orbit with such-and-such a semi-major axis (size) and eccentricity (shape) at some inclination, some longitude of the ascending node, and some argument of perigee (all discussed in the first few parts of this series), then it will stay that way, forever.

What I didn’t mention is the sixth element, which defines where on the ellipse the object is. That can be stated as some time it was at periapsis, or how long since a reference time (the epoch) it has been since it was at periapsis (“time since periapsis passage”)

Once you know that number plus the others, you can literally calculate where the satellite is at any given time…an hour from now, a billion years from now, a billion years ago (if it has been in that orbit for that long). If the epoch is midnight, 1 January 2000, and the satellite is in an orbit whose period is three hours, and at the epoch the satellite was at apoapsis, then, well that’s half an orbit, so time since periapsis passage is 1.5 hours, even for some date a billion years in the future it’s easy…in this case, because the satellite orbits exactly eight times in a day, its position at midnight any day is the same. It’s at apoapsis. (If it’s not this tidy, you can divide number of days since epoch by the orbital period…and keep the remainder.) Now there is a complicated way to turn any arbitrary time since the satellite was last at apoapsis into a position in the elliptical orbit. but the point is, it’s “closed form” and you can readily compute it for any time without being concerned with all the intervening times between epoch and that time.

Fairly routine.

Put in a third body, and all this tidiness goes right out the window. Given three bodies, in certain locations traveling at certain speeds in certain directions at some time, there is no formula to tell you where the three bodies will be…not even thirty seconds later!

There are some extremely special cases…imagine five bodies spaced equally far apart, marking the vertices of a giant pentagon in the sky. If they’re all moving in exactly the right way, you’ll simply see them all going in circles and the five points of the pentagon will simply rotate around the center of the pentagon. You can calculate positions by computing how many revolutions have occurred since your reference time. (But that has to be set up deliberately.) And there are others too.

But generally speaking…no formula.

Now given that this is the real-life case, how on (or off) Earth do we handle this?

There’s no formula to describe, say, the solar system with the sun, eight planets, and innumerable asteroids, Kuiper Belt objects, comets and so forth, but that doesn’t mean it can’t be computed (in practice they only bother with the more prominent objects).

Consider: Start with your three objects in certain positions traveling in certain directions at certain speeds.

You can compute, at that instant, the forces acting on each object, because of the other two (or more, if there are more) objects. That’s a simple matter of computing the force between the first object and each one of the other objects with Newton’s law of gravitation, then adding them up. You can turn that into accelerations, and then you can apply those accelerations to the initial positions and velocities…for a very small period of time.

It’s straightforward to compute where the objects will be after that very short period of time, and how fast they will be traveling. But now positions and speeds have shifted slightly. You have new positions and velocities. So do it again: compute new forces, and apply them to the newer situation. Compute the new situation, and repeat. Again, and again and again, until you get to the time you’re interested in trying to predict. In a way, it’s a bit like a stop-motion claymation animation.

This is called numerical integration because you’re doing computations and successively accumulating the results.

There is of course a problem: Your steps won’t be entirely accurate, because you’re assuming things don’t change during your interval. But in fact the positions, velocities and forces change continuously, not step by step. So your first computation will be a little bit off; the second one starts with a situation that’s slightly wrong, so the result of it will be a little bit more wrong because it too introduces new errors, and so on.

You can try to alleviate this by making your intervals shorter and shorter, but every time you halve the interval, you double the amount of steps you need to compute. But you can make the interval as small as you need to, to get the accuracy you want.

There are also some other tricks to make it more accurate, one called the trapezoid rule and one called the Simpson rule (and there are others); unfortunately those terms only make sense if you’re using numerical integration to approximate the area under a curve; but they apply to this much more complicated six-dimensional problem as well. (If interested: https://en.wikipedia.org/wiki/Numerical_integration. If not interested, there is still information there to read.)

Which should bring up a question in your mind. I just got through telling you we can’t compute the exact answer, so, given that numerical integration gives you an approximation, how can you tell how close the approximation is?

There are two methods. One is you experiment with decreasing step sizes. When it gets to the point where the answer doesn’t change much even if you divide the step size by (say) ten, your step size is probably so small the accumulated errors are insignificant.

Or you can apply numerical integration to a two body problem, one you know the answer to, run it for the same length of time, and cut the step size until the error is acceptable. Then you’ll have a good notion what step size will work..

I actually had to write a numerical integrator for orbital mechanics once, and I “calibrated” it by setting it to work computing a circular orbit for one period. So I just kept decreasing the step size until the spacecraft “returned” to a position less than a millimeter off from its starting point. That was good enough to attack the short-duration three body problem I was really interested in.

But as you probably noticed…you need a computer to do this.

NASA had to do this sort of thing in the 1960s when computer time was very, very expensive (and the computers were slow), so they really didn’t want to mess with it until they knew it was worthwhile. So checking out a planned probe to (say) the moon, which involved three bodies, earth, moon, and probe (and maybe–OK, definitely–include the sun too), you would want to be fairly sure what your approximate answer would be before you got started; you’d be doing this computation to get the exact answer, once you know from the approximation that the mission is possible given the rockets you have available.

So that means there had to be methods to do an approximate plan, at least one to let you know whether the mission was feasible; methods that might take a day or two with a slide rule (still cheaper than a computer back then) but not use a computer. And those methods do exist.

And that’s for a future post. But in the meantime I can leave you with some eye candy. The numerical integration method is not limited to three, or a dozen, or even a million bodies, provided you have the computing power to do it.

Our galaxy, the Milky Way, is actually traveling toward M 31, the Andromeda galaxy (or it toward us, depending on how you look at it), and in about 5 billion years they will collide. (to give you an idea of scale, the two galaxies are each roughly 100,000 light years across and they are about 2 million light years apart, so right now you can set two quarters about 20 inches apart and get a reasonably to-scale diagram of the situation,) It’s not really a big deal. The stars within a galaxy are so far apart compared to their sizes, that there might not be any collisions between the individual stars. But what will happen is that under the influence of the other galaxy’s gravity, stars will be sent flying out of their galaxy and then what is left over will coalesce into “milkdromeda.” Hundreds of billions of stars are involved. To analyze this astronomers can put a hundred thousand or a million representative stars in each galaxy (perhaps a bit more into Andromeda because it’s larger than the Milky Way) and…run the sim, for several billion years of simulation time. This is a lot of computer time, even today, but there are supercomputers that can “crunch” the numbers.

In this video, the Milky Way is on the left, and Andromeda is on the right. I’ve seen ones with longer run times, and what happens is the two “cores” eventually coalesce into one core…and about 50 percent of the stars remain to be part of the new galaxy.

Of course we will never be able to verify the accuracy of that (by the time it happens, this column will have been forgotten for 4,999,999,999.99 years), but we can find other pairs of galaxies in the process of colliding right now, and you’ll see similar looking things, like below:

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

https://youtube.com/watch?v=L3tnH4FGbd0

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

Joining The Herd Of Lemmings

I’ve had cause to consider a few things. Maybe we’re going about it the wrong way, and we need to ditch Trump

Yeah, NO

Trump all the way! Why? Because being hated by the people who hate him is a sign of impeccable character, that’s why.

The haters can go fuck themselves with rusty twelve gauge bore brushes. I’d prefer ten gauge but that’s kind of scarce, so…I’m willing to compromise.

The RINO’s Dilemma

The RINOs who who have burrowed in and taken over most GOP organizations, from the state down to local organizations, have quite a dilemma on their hands, and most of them have their heads too far up their asses to realize it.

OK, I’m not talking about the liberal in a Republican area, who knows they’re in the wrong party, but is there because it’s the only game in their town; they hope to capture a nomination someday, at which point they’re guaranteed to be elected…otherwise, they never will be. These people are a hazard in any heavily conservative area.

No, I’m talking about the guys who are a little bit conservative and want to do some good by going into politics, and they’re in a closely matched area, closely enough that they can join the party they are most aligned with and still have a chance. They think the Democrats…particularly the ones who end up running for office…are nuts.

They don’t think much better of the Deplorable types, either. A bunch of bumpkins whose hearts are in the right place, mostly…OK a bit extreme. But they think Deplorables can’t understand that first you have to get elected, then work within the system to change things…a slow process. They genuinely want many of the things Deplorables want…just not as much. The government is spending too much. Or they need to spend money on highways instead of welfare for illegal immigrants. But they want to work within the system to get these things done.

Or maybe they think things are pretty close to ideal right now, and they want to nail it in place.

The problem is, that means they don’t stand for anything in particular. And it shows. They’re about as unappetizing to the electorate as a puddle of dog vomit. The folks in the middle, who they think they are appealing to because they themselves are not extreme, would honestly prefer a clear-spoken radical to someone who qualifies everything they say to the point where they sound like they don’t believe anything at all.

The problem these “Mild RINOs” have, is they just can’t see that. And the reason they just can’t see that, is their entire sense of self-worth is tied up in not seeing that. In their minds, they’ve worked tirelessly for their party, to keep those crazy Democrats out…only to have to constantly fight with a small number of crazy Republicans–who are only liabilities if they end up as candidates. They’ve fought the good fight, and if they can just find the right candidate, someone with some charisma, they might stop the crazies…without being too beholden to the OTHER crazies. In the meantime it’s not working. What’s a responsible guy in politics to do?

They simply cannot understand that the Republicans can’t succeed as the party of nothing in particular. Not really in the past, and certainly not today when people are starting to realize that no matter what they do in the voting booth, the country is still about to fly off a precipice. If they did see it, they’d suddenly have two choices: Go away and let the GOP succeed, or stay and fight. But “go away” isn’t really an option, because what’s the point of having a party now owned by the crazies, win?

Well, they have a dilemma…and WE, therefore have a problem. And we would have that problem even IF they realized that they had a problem…that they were the problem.

No one ever thinks they are the bad guy. Even Epstein probably thought he was the good guy. Right up to the moment where he didn’t kill himself.

So if you ever wonder why these unappetizing dufuses cling on even when their fingernails are being left behind…that’s why. They don’t understand no one wants them, and can’t imagine that no one should want them. And oftentimes their greatest pride is in all the hard work they’ve done for the party. They’re not going to give that up; it’d be psychological suicide.

If you’ve worked with these people, there’s a good chance you like them and consider some of them your friends. But even if so…we’re going to have to give them a good, hard shove. Because America is more important than those milquetoasts’ egos.

Justice Must Be Done

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot (i.e., paper) Prices

Last week:

Gold $1,843.20
Silver $21.81
Platinum $930.00
Palladium $1,583.00
Rhodium $11,900.00

This week, 3PM Mountain Time, markets have closed for the weekend.

Gold $1,812.50
Silver $20.86
Platinum $919.00
Palladium $1,490.00
Rhodium $11,100.00

Industrial metals down…that’s not good news for the economy…well, actually, it’s simply not news for the economy; we all know it’s in the crapper. But gold and silver still decline, because in the foreign exchange markets the dollar is still strong (largely due to high interest rates here).

Fuck Joe B*d*n

Due to complaints about foul language, I’ve censored the most objectionable word in the title of this section.

B*d*n, you don’t even get ONE scoop of ice cream today.

(Please post this somewhere permanent, as it will continue to be true; the SOB will never deserve a scoop.)

Another Conjunction

You might recall the Great Conjunction of December 21, 2020, where Jupiter and Saturn got so close to each other in the sky (as seen from Earth) that you could literally look at both of them at the same time in a telescope. (What a boon for lazy astronomers!)

This coming Wednesday we have a similar situation with Jupiter and Venus, again in the evening sky after sunset. Similar, but by no means close enough for both of them to be in the same view in a telescope. You can still see a nice little alignment shortly after sunset looking west; Jupiter will be furthest above the horizon, and bright. Venus will be closer to the horizon, and even brighter. (There was hype about this on this last Wednesday, too, because the moon was nearby that night.) They will get within a half a degree of each other, which is less than the width of the full moon.

Venus and Jupiter are the two brightest objects in the night sky, other than the Moon.

Beyond The Simple Cases

Distributed Gravitational Mass & Tidal Forces

Orbital Mechanics VI

Thus far in talking about astrodynamics, I’ve been careful to consider only two bodies (a satellite and its primary), and I’ve been assuming they’re both point masses.

Neither of these assumptions is ever actually true. Because we live in a universe with more than two things in it, and nothing other than a black hole is a point mass–with the entire mass of the object all at one single point in space (and if we are dealing with black holes, Newton’s laws go out the window anyway, at least close in to the black hole).

However in many cases the effects from third, fourth, and other bodies are very very minor and there are actually conceivable cases where you can assume a point mass even when it isn’t.

The first one seems obvious. If other bodies are far away, they won’t have much gravitational influence. (People arguing that the positions of the planets at the moment of birth actually matters have to contend with [or more commonly, ignore] the fact that the obstetrician or midwife has more gravitational influence on the newborn than any other planet ever will.)

The second simplification, that you can sometimes pretend a large body is actually a point mass, is much less obvious.

Here is Newton’s law of universal gravitation, in mathematical form:

And if I were to translate that into plain English, it would read, “The force due to gravitation between two point masses is proportional to the product of their masses, divided by the square of the distance between them, and multiplied by the gravitational constant.”

What this form of the equation doesn’t address is the direction of the force; it’s directed from one object to the other along the straight line between them.

But there’s that awkward “point mass” thing again. What if it’s not a point mass?

What you do then, is (mentally) divide the object (let’s stick with the primary, since it’s much bigger than the satellite) up into much, much smaller pieces, then do this computation for each piece, including accounting for the direction, then add them all up. You’ll get a more precise answer the smaller you make your pieces, but you’ll also do more work because there are more pieces to do the computation for. And if you’re wondering how to add forces in different directions, that’s where vectors come into play (it’s pretty easy actually).

So let’s say you’re aboard a satellite near Earth, and you’re looking out the window at the earth. What’s the sum total of all of the gravitational attractions, of each sandgrain in the Australian outback, of every beer stein in England, of the iron at the earth’s core, and everything in between?

Hmmm, tricky. Or maybe not. Maybe we can sneak up on it.

Let’s replace the earth with a hollow sphere of, say, iron. The sphere is a perfect sphere, the iron is of uniform density, and the shell is of uniform thickness. (Imagine a very, very large ping pong ball made of iron instead of plastic.)

It turns out that under these circumstances you can do various mathematical tricks and shortcuts (these would be tricks and shortcuts that bear the name “integral calculus”) to discover that the aggregate attraction of that entire sphere is the same as another hypothetical object, a point mass at the center of that sphere, weighing the same as the entire iron shell. It makes no difference how thick that shell is, it makes no difference what it’s made out of–balsa wood, platinum, glass, whatever…as long as it’s of uniform density. It can be swapped with a point mass at the center of the shell.

[As a side note, it can also be shown that if you are inside the sphere, anywhere inside it, the net gravitational force is zero. If you’re at the very center, obviously, the mass on one side cancels the mass on the other (they’re the same, and at the same distance, but in opposite directions). But even if you’re near the shell somewhere, you have a small amount of matter close to you in one direction, and lots more matter in the other direction, but farther away…and they cancel each other out again. So the entire inside of the sphere is one big Zero Gravity zone.]

This is what you get when you divide that hollow sphere up into little pieces and add up their gravitational influences. And Newton did this…he invented calculus, in part, to be able to do this. (And yes, Leibniz was also inventing calculus about the same time, but Newton didn’t know about that, so he had to do it himself.)

Now back to talking about the earth. The earth is made up of layers, the crust, the mantle, the outer and inner cores. They’re each of fairly uniform composition, but no two layers…or even depths below ground within the same layer are quite the same. If nothing else lower spots within the same layer are denser because they’re under more compression. (The iron at the earth’s core is notably compressed and is denser than iron on the surface.)

So you can divide the earth into layers, like an onion, treat each of them like a hollow sphere, use Newton’s result above…and what you find yourself doing is adding point masses, all at the center of the earth, to get a total…which is to say, you’re going to end up with the equivalent of a point mass, as massive as the earth, at the center of the earth. Note: you don’t need to know what’s inside the earth for this to work, but you do have to assume that the density profile is the same in every direction out from the center of the earth (which is equivalent to saying that the onion layers will each be uniform).

So this is why you can treat a typical big round astronomical body as if it were a point mass.

Well, almost. In fact you can do it with objects far away. If you’re so far away from an object that it looks like a point to you, you can treat it as one.

But if you’re close to Earth, really really close, then the fact that it’s not a perfect sphere starts to tell.

Most importantly the earth rotates. Because it spins on its axis, centrifugal force makes Earth bulge a bit at the equator. (The same effect is used to make round disks of dough for pizza crusts; the pizza maker tosses a lump of dough in the air with a spin on it to get it to flatten out.)

That bulge will pull on satellites in Low Earth Orbit (LEO) and it does so quite a lot, causing orbits’ longitude of the ascending node to shift. The effect can cause the satellite to be 500 miles away from where it “should” be, in just one day. If you pick precisely the right size of orbit, you might even get the ascending node to shift through 360 degrees over the course of a year. This means that the orbit will basically always maintain the same orientation with respect to the sun; these are called “sun synchronous” orbits.

Even without the bulge, the Earth has continents and oceans, and there’s just enough difference in density between those items that even they can perturb a satellite. I talked about geostationary orbits, but in fact most locations above the equator will suffer from perturbations from the small irregularities in the shape of the earth, and a satellite in GEO will actually drift a little bit if it doesn’t use its thrusters for stationkeeping.

The moon is even more irregular; it has “mass concentrations” as if it were a gigantic lump of pudding with bowling balls rather than raisins. I remember being told when I was studying this stuff in college, that the effect of all those “mascons” was that a satellite in low lunar orbit simply wasn’t stable and would eventually crash into the moon.

So much for what happens in a close orbit when the primary is at least somewhat irregular.

What happens if the satellite is irregular?

Imagine a telephone pole in Low Earth Orbit.

Unless it is in precisely the right orientation, one end of the telephone pole will be slightly closer to the earth than the other. Because it IS slightly closer, it will feel earth’s gravity a bit more strongly than the other end. They’re physically attached to each other, and the telephone pole as a whole is moving with the center of gravity (which is what is “in orbit” around Earth). The center of gravity feels no force, because it’s responding freely to gravity. It’s in free fall. Every other spot on and within that telephone pole feels a slight force, the extra gravitational pull from being closer to earth, or the deficit from being further.

Anyhow, since the near end of the pole feels more force towards Earth, and the farther end of the pole feels less force..the whole telephone pole will eventually rotate about its center of gravity, so that it points towards/away from Earth. It’s not much, but there’s no other force to counter it, not even friction. And even after it has done that rotation, the near end and far end feel a very slight “tugging” force, as if some giant were to grab each end of the telephone pole and try to stretch it.

The name for this phenomenon might be surprising: it’s known as a tidal effect. Yes, as in ocean tides. Because they are caused by the same thing. The side of the earth closest to the moon feels more gravity; the side away from the moon feels less gravity. Water can flow freely in response to this so it tends to pile up at both ends; one end feels a net attraction to the moon, the other end feels a net repulsion.

How much is this apparent “stretching” force? Let’s say the length of the telephone pole is 2L; so the near end is L units closer to earth than the center of the pole, and the far end is L units farther away. So if, at some moment, the telephone pole is at distance a from the center of the earth, what happens? The force due to gravity of the center of mass of the telephone pole is proportional to 1/a². But the near end of the pole will feel a force that is 1/(a-L)², and the far end will feel a force that is 1/(a+L)². The apparent stretching force is the difference between these two, so it’s going to be proportional to 1/(a-L)² – 1/(a+L)². Now, doing a bunch of algebra, this will simplify to: 4aL / (a⁴-2a²L²+L⁴). Now, a is much, much larger than L, and a⁴ is much, much, much larger than L⁴, so you can approximate that gigantic mess on the bottom with just a⁴. Cancelling, the stretching force is proportional to L/a³.

So tidal effects have an inverse cube effect going on. Move your telephone pole to twice the distance (from the center of the earth), and the tidal effect is 1/8th what it was before (not one half, or even one quarter). But it’s also proportional to L; double the length of the pole, you will double the tidal effect.

OK, so imagine something like the moon. It feels a tidal effect. In fact the moon’s shape is such that tidally it should always point the same face towards earth, and it does. In the billions of years since it formed, whatever rotation it started out with has gone away under the relentless, never ending pull from the tidal effect caused by Earth.

Of course we know the moon has a tidal effect on Earth. Is it trying to pull the Earth into a situation where the Earth always presents the same face towards the moon? Yes it is, and that is one reason the Earth is, very gradually, slowing its rotation down, resulting in having to add leap seconds here and there over the years to keep our clocks synchronized with Earth’s rotation. The earth is 81 times as massive as the moon, though, so the moon has 81 times as much work to do slowing Earth down to tidally lock it. Nevertheless the loss of Earth’s rotational angular momentum is causing a rise in the Moon’s angular momentum (angular momentum is conserved, so if Earth loses it, something else must gain it), so the Moon is slowly receding from Earth. (This has been measured by bouncing lasers off reflectors the Apollo astronauts left on the moon.)

The four “big moons” (or “Galilean moons” of Jupiter are all tidally locked to Jupiter in the same way the moon is to Earth. Pluto and its satellite Charon are almost the same mass, each is tidally locked to the other. Seen from the surface of Pluto, Charon never rises nor sets; seen from the surface of Charon, Pluto never rises or sets, either; each of the two objects appears stationary from the other, just like, on the surface of the Moon, Earth does not appear to move; if it’s above the horizon to the west where you’re standing…it will stay there.

Imagine, though, if the Moon were much closer to Earth. Really close. Like, so close that when standing on that spot on the moon closest to earth, the tidal force equals the Moon’s surface gravity.

Nothing would hold you to the moon then; you could just drift off. And that would be true of the lunar soil and rocks nearby too; they would just driff off since there’s no net force holding them to the moon. (And the same would be true on the far side of the moon too, since it feels the same tidal force away from the center of the moon.)

The moon could, if it were even closer to earth, actually be disassembled, since now objects on the surface would be actively pulled away from it!

We think this is how Saturn’s rings formed. Some object got too close to Saturn and was pulled apart by the tidal forces. Or perhaps the “stuff” in orbit around Saturn when Saturn formed simply couldn’t form a moon in the first place! (But the rings themselves are slightly unstable and won’t last more than a couple of hundred million years, which argues for them being formed well after Saturn was.)

Tidal forces can get really strong. Near a black hole for instance. Since a black hole is a point mass, greater, perhaps even much, much greater than the sun’s mass, you can get very, very close to something with very strong gravity. And remember it’s an inverse qube law…getting very, very close means having a LOT of tidal force.

Even enough to rip you apart, if you get close enough. Or anything else for that matter. Astronomers call this “spaghettification” (no, I’m not joking), this alludes to the fact that anything will be stretched until it looks like a strand of spaghetti…and then it will be stretched even more.

Right now astronomers are watching a gas cloud being pulled into the black hole at the center of our galaxy and it, sure enough, is being stretched as it gets closer and closer. I can’t seem to link to the video (and it’s on msn.com so that’s just as well), but it actually labels the gas cloud as being “spaghettified.”

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

EDIT: 22:54 MT. Well let’s just say the top item didn’t age well…except perhaps for the deserved insults to Speaker Dungsmear.

I can only hope McCarthy keeps his promises.

Giving Our “Love” To the RINOs and the Dipshits Going After O’Keefe

RINOs an Endangered Species?
If Only!

(Well this is the perfect time for this to come up in the rotation!)

According to Wikipoo, et. al., the Northern White Rhinoceros (Ceratotherium simum cottoni) is a critically endangered species. Apparently two females live on a wildlife preserve in Sudan, and no males are known to be alive. So basically, this species is dead as soon as the females die of old age. Presently they are watched over by armed guards 24/7.

Biologists have been trying to cross them with the other subspecies, Southern White Rhinoceroses (Rhinoceri?) without success; and some genetic analyses suggest that perhaps they aren’t two subspecies at all, but two distinct species, which would make the whole project a lot more difficult.

I should hope if the American RINO (Parasitus rectum pseudoconservativum) is ever this endangered, there will be heroic efforts not to save the species, but rather to push the remainder off a cliff. Onto punji sticks. With feces smeared on them. Failing that a good bath in red fuming nitric acid will do.

But I’m not done ranting about RINOs.

The RINOs (if they are capable of any introspection whatsoever) probably wonder why they constantly have to deal with “populist” eruptions like the Trump-led MAGA movement. That would be because the so-called populists stand for absolutely nothing except for going along to get along. That allows the Left to drive the culture and politics.

Given the results of our most recent elections, the Left will now push harder, and the RINOs will now turn even squishier than they were before.

I well remember 1989-1990 in my state when the RINO establishment started preaching the message that a conservative simply couldn’t win in Colorado. Never mind the fact that Reagan had won the state TWICE (in 1984 bringing in a veto-proof state house and senate with him) and GHWB had won after (falsely!) assuring everyone that a vote for him was a vote for Reagan’s third term.

This is how the RINOs function. They push, push, push the line that only a “moderate” can get elected. Stomp them when they pull that shit. Tell everyone in ear shot that that’s exactly what the Left wants you to think, and oh-by-the-way-Mister-RINO if you’re in this party selling the same message as the Left…well, whythefuckexactly are you in this party, you lying piece of rancid weasel shit?

In Defense of Ranked Choice Voting

One of the biggest obstacles to direly-needed change is RINOs, and one of the weapons in their arsenal is the “Wasted Vote” argument.

Periodically a third party has arisen, trying to hold RINOs to account by putting pressure on them from outside of the party, since doing so from the inside has historically done very little good. But, even if you find a third party candidate who perfectly reflects your views, you’re likely to vote for the RINO anyway. Why? Because if you don’t, the Democrat might win, and that would be even worse. So if you vote for that third party (that few will vote for), you’re throwing your vote away and increasing the likelihood of the Democrat winning. (It’s half as much a gain for the Democrat, as actually voting for the Democrat would be. Not as much, but half as much. Because although you denied the R your vote, you did not flip your vote to the Democrat.)

The Republican Party Establishment knows you don’t love them. But they know you hate the Democrats worse, and they use that to continue to herd you into supporting them. With gritted teeth you cast your vote, but your vote counts the same whether you cast it enthusiastically. And the other alternative, pissing on the voting apparatus to express your actual feelings, is probably a felony.

But what if you could vote for that third party without increasing the chances of the Dem walking away with the prize?

This is what ranked choice voting, or instant runoff voting, can do provided it is properly implemented. (And this includes the votes, and only genuine votes, being counted honestly, of course. However, I’m going to compare it to what we have today, and pretend that is honestly done too. RCV can’t work if it’s not honestly administered, just like our current system isn’t working because it isn’t honestly administered.)

The idea behind RCV is to vote by expressing your order of preference. You could vote for the Patriot Party, then for the RINO Party as your second choice (and ignore the Democrat, the Green, the Overt Socialist Schmuckmonkey Party, etc).

What does this do? It nullifies the wasted vote argument. Your vote will be counted for the Patriot party, first, then instead of it being “wasted” when the Patriot Party loses, it ends up going to the RINO. Actually, it’s just barely possible that the Patriot Party would actually beat the RINO, if people weren’t all individually afraid to vote for it.

It’s just like the famous “Prisoner’s Dilemma” where your fear of other peoples’ actions prevents you from doing the optimal thing–and vice-versa. As long as Job Lowe is afraid to vote Patriot because he’s afraid you’ll vote RINO, you’ll have to vote RINO because you fear that Job Lowe will, because he fears you will.

So on the whole I like RCV. It gives you a no-risk way to vote against the RINO scum, and in favor of someone who deserves your vote.

The problem is, as done here in the US, it comes packaged with a “jungle primary.” A bunch of candidates get to put their name out there, and the top four (or so) candidates get onto the “main” ballot. This gives party establishments their way around the threat of a good third party bumping them off. Because they know that few people bother with primaries, and third parties don’t have the resources to run in a primary…so they throw two or three establishment hacks into the primary and they will probably beat the third party. The result is the RINOs end up with two of the four slots in the general election, and the Dems get the other two. Now there’s suddenly no third party candidate on the ballot at all.

If we were to combine RCV with the present system where each party could nominate exactly one candidate to appear on the November ballot, or at the very least, ensure minor parties could get onto the ballot with at least one candidate regardless of the primary, we would be getting somewhere, but the establishment is smarter than we like to give them credit for. They will support the jungle primary + RCV “solution” rather than the more appropriate one-candidate-per-party + RCV solution.

It’s not RCV that is the problem, it’s the primary structure grafted onto it.

Justice

It says “Justice” on the picture.

And I’m sure someone will post the standard joke about what the fish thinks about the situation.

But what is it?

Here’s a take, from a different context: It’s about how you do justice, not the justice that must be done to our massively corrupt government and media. You must properly identify the nature of a person, before you can do him justice.

Ayn Rand, On Justice (speaking through her character John Galt, in Atlas Shrugged):

Justice is the recognition of the fact that you cannot fake the character of men as you cannot fake the character of nature, that you must judge all men as conscientiously as you judge inanimate objects, with the same respect for truth, with the same incorruptible vision, by as pure and as rational a process of identification—that every man must be judged for what he is and treated accordingly, that just as you do not pay a higher price for a rusty chunk of scrap than for a piece of shining metal, so you do not value a rotter above a hero—that your moral appraisal is the coin paying men for their virtues or vices, and this payment demands of you as scrupulous an honor as you bring to financial transactions—that to withhold your contempt from men’s vices is an act of moral counterfeiting, and to withhold your admiration from their virtues is an act of moral embezzlement—that to place any other concern higher than justice is to devaluate your moral currency and defraud the good in favor of the evil, since only the good can lose by a default of justice and only the evil can profit—and that the bottom of the pit at the end of that road, the act of moral bankruptcy, is to punish men for their virtues and reward them for their vices, that that is the collapse to full depravity, the Black Mass of the worship of death, the dedication of your consciousness to the destruction of existence.

Ayn Rand identified seven virtues, chief among them rationality. The other six, including justice, she considered subsidiary because they are essentially different aspects and applications of rationality.

—Ayn Rand Lexicon (aynrandlexicon.com)

Justice Must Be Done.

Trump, it is supposed, had some documents.

Biden and company stole the country.

I’m sure enough of this that I put my money where my mouth is.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system. (This doesn’t necessarily include deposing Joe and Hoe and putting Trump where he belongs, but it would certainly be a lot easier to fix our broken electoral system with the right people in charge.)

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is pointless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud in the system is not part of the plan, you have no plan.

This will necessarily be piecemeal, state by state, which is why I am encouraged by those states working to change their laws to alleviate the fraud both via computer and via bogus voters. If enough states do that we might end up with a working majority in Congress and that would be something Trump never really had.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot Prices

Last week:

Gold $1,865.30
Silver $22.41
Platinum $983.00
Palladium $1,703.00
Rhodium $12,500.00

This week, 3 PM MT on Friday, markets closed for the weekend

Gold $1,866.50
Silver $22.08
Platinum $956.00
Palladium $1,614.00
Rhodium $12,950.00

Little significant change…the biggest being palladium which is dropping. Since that gets used in catalytic converters this might be a sign car manufacturing is declining.

Escape

Thus far I’ve been monologuing almost entirely about the typical two body problem, a small satellite orbiting a massive primary, and below escape velocity. The orbits end up being ellipses (or possibly a perfect circle, if the satellite is traveling at the circular velocity, in a “horizontal” direction, at exactly the right distance from the primary.

Ellipses have eccentricities of 0 through 0.9999… (keep writing 9s forever), with zero being a circular orbit (considered a special case of the ellipse). That ellipse with an eccentricity of just below 1 is extremely narrow compared to its length.

I brought up the concept of escape velocity last time, too. That represents a spacecraft traveling in an orbit with an eccentricity of exactly 1.

Such an orbit is a parabola. And I’d better step back and talk just a little bit about conic sections.

Conic sections are the shapes you get when you slice a cone. And here is the paradigmatic diagram:

Slicing perpendicular to the centerline of the cone, you get a circle…you see the one in red, and because they cut the cone off at the bottom of the diagram (technically, it should extend to infinity), there’s another (unlabeled) circle there too.

Slicing at a shallow angle gives you some sort of an ellipse.

But notice the blue (purple) shape. You get that from slicing the cone at exactly the angle of the cone itself. The center line of that purple shape is parallel to the side of the cone to the left.

That is a parabola, and you can also get a parabola by graphing something like y=x². You can multiply the x² by some number, the y by some number, or add a constant to either side. You can even add x (or some multiple) to either side. It makes no difference, you get a parabola. Multiplying will change the size of the parabola, but it will not change the shape. (It’s always possible to rotate and zoom in/out on a parabola and make it identical to another parabola.)

If you cut at an even steeper angle, you get a hyperbola, just like shown in the diagram.

Ahem. No, that’s not quite true. I said the cone is supposed to extend to infinity earlier, and that’s true in both directions.

Here’s the correct diagram:

Notice the cone is now what we’d think of as a double cone (but technically, that’s what a cone is). Number 3 is the parabola. Because that plane is parallel to the top half of the cone, it never will cut through the top half of the cone. But in diagram 4 the cut is vertical, and the plane does cut through both halves of the cone. (It will also do so for any slant higher than the one shown in diagram 3.) That two-piece shape is called a hyperbola, and…well, we’ll get to it, I promise. (Evil laugh.)

If you imagine the cones and the plane extending to infinity, you’ll realize that neither the parabola or hyperbola are actually closed curves; they don’t loop back on themselves.

And if something is moving at escape velocity, it never comes back. So it makes sense that the parabola is the escape trajectory.

(Provided that the smaller body is moving precisely at escape velocity. If it’s moving faster, it’s in a hyperbolic orbit.)

OK, so where is the primary? In an ellipse it sits at one focus; where does it sit in a parabola?

Another way to define a parabola is shown below.

Draw a line like the one on the left, called the directrix. Pick a point not on the directrix, like the one near the c=a in the diagram, where the bottom of the red line is. This is the focus.

The parabola is the curve, such that every single point on the curve, is the same distance from the focus as it is from the directrix.

(This is similar, sort of, to the ellipse, where you can pick two foci, and every point on the ellipse is the same total distance to the two foci. It’s just that here one of the foci is replaced by the directrix.)

Notice that the distance from the focus to the “base” of the parabola is a, and the distance from the base to the directrix is also a.

It’s a just like the semi-major axis of the ellipse was a, and in orbital mechanics this a means exactly the same thing; it’s the size of the orbit. If a is big the parabola is big and therefore not as sharply curved; that represents the trajectory not being bent as much because the spacecraft never gets really close to the primary.

Does this actually correspond to anything in the real world?

Almost.

About a light year away from the Sun, we believe there are vast numbers of small, icy “snowballs” in orbit about the Sun; that grouping is called the Oort cloud. That’s far, far away (260,000 AU, or 260,000 or so times as far from the sun as Earth is), so things aren’t moving too fast out there.

That’s far enough away that every once in a while another star will pass close enough to perturb these bodies, and some of them might be brought to a dead halt in its orbit. It starts to drop toward the sun.

It is so far away, that the orbit is almost exactly a parabola. If it’s dropping almost directly into the sun, it will be a nice tight parabola with the nearest point inside the orbit of Mercury (so a which is the minimum distance to the sun could equal 0.3 AUs or less); if it still has some “sideways” motion the snowball won’t get too close to the sun; it will be a very open parabola, very large in size, a might be about 5 if it gets only as close as Jupiter; it might be much higher than that.

If it is that far away it’s extremely hard to detect. But if it gets close to the sun, the ices in the snowball will heat up, and boil off, and the snowball will grow a tail. It will be a comet.

Most comets come from the Oort cloud, and effectively, we’ll only see the comet once, because it’s just under escape velocity. Sure, it will be back…millions of years from now! The recent “green” comet has a smaller (but still not small) elliptical orbit; it’s expected to come back in 50,000 years. Most famously, though Halley’s comet has an eccentricity of 0.96658; a is 17.737 AUs, and its closest distance to the sun is 0.59278 AUs, so it gets closer to the sun than Venus (roughly 0.7 AUs), but not closer than Mercury (roughly 0.4 AU).

Halley’s comet probably started out as a visitor from the Oort cloud, but it passed too close to one of the outer planets and its orbit was bent into a (still fairly large) ellipse.

How fast does an Oort cloud comet travel? Well, that’s simple: Figure out how far it is from the Sun and then calculate escape velocity at that distance.

Circular orbital velocity at some distance r, (i.e., how fast an object in a circular orbit must be traveling) is:

while escape velocity at that same distance is:

Notice that the difference is a 2 under the radical so the escape velocity is sqrt(2) times the circular velocity. sqrt(2) is roughly 1.414. Speed the earth up in its orbit 41.5 percent and we’re going away and never coming back. (It’s cold out there!)

So let’s see what happens if an Oort cloud comet hits Earth. Earth moves around the sun at 29.78 kilometers every second (yowza!); the comet must be moving at 1.414 times this speed or roughly 42 kilometers per second.

Now this could be a head on collision, if the comet’s a is 1 AU just like ours is, and it happens to be closest to the sun where Earth is and is traveling the other direction. Which makes a 72 kilometer per second head-on collision. Or it could be traveling in the same direction as earth, in which case the difference is “only” 12 kilometers per second.

Either way that impact would hurt. But far more likely is the comet heading almost directly into the sun, and therefore cutting across Earth’s orbit at almost a right angle. By the time you get done playing with vectors, that works out to very roughly 51 kilometers per second collision speed.

That’s damned fast. We don’t want to be hit by a comet; asteroids are bad enough.

But I would like to send a lot of Uniparty hacks on an escape trajectory out of here, someday. I might even be generous and seal the spacecraft so it holds air…for a while.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

To conclude: My standard Public Service Announcement. We don’t want to forget this!!!

Remember Hong Kong!!!

https://youtube.com/watch?v=L3tnH4FGbd0

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

News Flash

Today, it is still the case that Joe Biden didn’t Win.

I realize that to some readers, this might be a shock; surely at some point things must change and Biden will have actually won.

But the past cannot actually be changed.

It will always and forever be the case that Joe Biden didn’t win.

And if you, Leftist Lurker, want to dismiss it as dead white cis-male logic…well, you can call it what you want, but then please just go fuck off. No one here buys that bullshit–logic is logic and facts are facts regardless of skin color–and if you gave it a moment’s rational thought, you wouldn’t either. Of course your worthless education never included being able to actually reason–or detect problems with false reasoning–so I don’t imagine you’ll actually wake up as opposed to being woke.

As Ayn Rand would sometimes point out: Yes, you are free to evade reality. What you cannot do is evade the consequences of evading reality. Or to put it concretely: You can ignore the Mack truck bearing down on you as you play in the middle of the street, you won’t be able to ignore the consequences of ignoring the Mack truck.

And Ayn Rand also pointed out that existence (i.e., the sum total of everything that exists) precedes consciousness–our consciousnesses are a part of existence, not outside of it–therefore reality cannot be a “social construct” as so many of you fucked-up-in-the-head people seem to think.

So much for Leftist douchebag lurkers. For the rest of you, the regular readers and those lurkers who understand such things: I continue to carry the banner once also carried by Wheatie. His Fraudulency didn’t win.

Let’s Go, Brandon!!

Hey China!

Or rather, “Hey Chinese Communist Party and your entire array of servitors, ass-wipers, and fellators!”

You’re not even worth my time this week. When you decide to act like civilized people, maybe I’ll give you a lesson or two in how non-barbarians behave.

Hey BiteMe!
(Or, Whoever Has Their Hand Rammed Up That Putrefying Meat Puppet’s Ass)

[Language warning]

You and yours have caused a lot of injury. Literal injury with your war on people who don’t want to take an untested vaccine. When people die in an emergency room because a hospital won’t admit them because they haven’t had their clot shot, that’s a crime.

I’m going to address here the insult on top of the injury, because I am among the insulted. I still have my health but apparently you want me to live under the 8th Street Bridge (which actually isn’t on 8th Street, but whatever, that’s what the I-25 overpass over Cimarron is called), so maybe if you have your way that won’t be true for long. Dreadful time of year to become homeless.

No, you’re just trying to make me unemployed, because I won’t take your fucking shots.

Well, that threat is NOT going to work. I. Won’t. Take. Your. Fucking. Shots.

And it looks like enough people agree, that you’re having to back down, you worthless asswipe.

You’re LOSING.

You LOSER.

You Chinese-bought ratfucking traitor.

I would love to see you die an agonizing, humiliating death. (This isn’t a threat, because I am not threatening to cause that death. I am just announcing my intention to party if it happens.) It would be just recompense for the way you’re killing America…and millions of Americans.

His Fraudulency

Joe Biteme, properly styled His Fraudulency, continues to infest the White House, we haven’t heard much from the person who should have been declared the victor, and hopium is still being dispensed even as our military appears to have joined the political establishment in knuckling under to the fraud.

One can hope that all is not as it seems.

I’d love to feast on that crow.

(I’d like to add, I find it entirely plausible, even likely, that His Fraudulency is also His Figureheadedness. (Apparently that wasn’t a word; it got a red underline. Well it is now.) Where I differ with the hopium addicts is on the subject of who is really in charge. It ain’t anyone we like.)

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot Prices.

Kitco Ask. Last week:

Gold $1,928.50
Silver $23.69
Platinum $1,021.00
Palladium $1,696.00
Rhodium $12,550.00

This week, markets closed as of 3PM MT.

Gold $1,865.30
Silver $22.41
Platinum $983.00
Palladium $1,703.00
Rhodium $12,500.00

WOW. Major drops in everything just today. Gold was around 1950 on Wednesday, dropped a bit Thursday and went down almost 50 bucks today. Silver went down $1.14 today..

More Stupid Orbit Tricks (Orbital Mechanics Part 3)

Well, this is a bit embarrassing. This is one subject that I actually have some formal background in, albeit from over thirty years ago, and I flubbed something in the first column.

[Math note: Take the velocity vector for the satellite. Normalize it, so its length is 1. Take the cross product of it and the z axis unit vector. Take the magnitude of that product. You now have the sine of the inclination angle. For those of you who didn’t understand that, be assured that it’s dead damn easy and you don’t have to watch the satellite in orbit to figure out its inclination, so long as your velocity measurement is accurate.]

Me being slightly stupid two weeks ago

You can certainly do this. It works as described. But it’s vastly better to take the dot product of the normalized vector with the z axis unit vector, and treat that as the cosine of the inclination angle. Why? Two reasons. First, the cosine could be anything from 1 down to -1, and those correspond to angles of 0-180 degrees, the exact range of angles an inclination can be. Second…to take that dot product, just grab the z component of the normalized velocity vector; no need to actually do the dot product, (v_x, v_y, v_z) (0, 0, 1) is a no-brainer.

OK with that out of the way, we can pick up where we left off last week. I gave you the formula for the period of an elliptical orbit of a certain semi-major axis (a), and used the special case of a circular orbit where a is the radius of the circle, to figure out the radius of a geostationary orbit. Here’s the formula once again:

(Last week, the one I found had GM where this one has μ; they’re the same thing, the gravitational parameter of the object being orbited, which is the mass of that object multiplied by the gravitational constant.)

It’s really easy to get from here to the speed the object is traveling at in its orbit. The orbit will have a total length of 2πa. (The circumference is 2π times the radius.) Divide that length by the period. Both of the 2πs cancel, and you’re left with a / sqrt of a³/μ, but that’s just the square root of μ/a.

Yes, this one has r instead of a. (This is what I get for copying and pasting formula graphics from Wikipoo; it’s not being consistent about using μ instead of GM, and the point I am about to make is obscured by using r instead of a.)

So does this mean that if you’re at a certain distance from the center of the object, a, and you’re traveling at speed v, you’re in a circular orbit?

Not necessarily. You’ll notice I said “speed” not “velocity.”

It is true that if you are at that distance, and traveling at that speed, your orbit will have a semi-major axis of a, but it won’t necessarily be a circular orbit; it could be an ellipse. The direction you are moving in at that distance matters. Draw a line from you to the center of the primary. That line defines “down” (even though you don’t feel weight while in orbit). Perpendicular to “down” you are moving “horizontally.” See the following very fancy (and stolen) diagram, where v is always in a horizontal direction:

If that is the direction you’re moving, and you are at the proper speed, you will be in a circular orbit. Otherwise, if you’re at the proper speed but not moving “horizontally” you are in an elliptical orbit whose semi major axis happens to match your distance from the primary. The more eccentric the orbit it, the farther away you will get from the primary at apoapsis…but the closer you will be at periapsis.

And this is where clean theory departs from actual practice. The theory pretends the entire mass of the primary is located at a point at one focus of the ellipse (or the center of the circular orbit). The fact of the matter is, the primary has a size, a radius, and if periapsis is less than that number, your time in orbit ends when you smack into the surface of the primary.

If you are in an elliptical orbit, then of course your speed at apoapsis is less than the speed we just computed, and your speed at periapsis is greater than that speed–unless it’s zero because you smacked into the surface of the primary. This formula is only good when your distance from the center of the primary is the same as the semi-major axis of your orbit. (Always true in a circular orbit, true at exactly two points of an elliptical orbit.)

Surely there’s a better formula useful in other circumstances!

Stop calling me Shirley, and yes, there is. It’s called the vis viva equation:

a is your semi major axis, and r is the distance from the center of the primary. Notice that you do not need to know the orbit’s eccentricity. More importantly, notice r and a don’t have to be the same.

(Also notice that if they are the same, things cancel and you get the circular orbit formula above. And notice also that if r is more than 2 times a, you get a negative sign under the radical. But that makes sense, it’s physically impossible no matter how eccentric an elliptical orbit gets, for you to be more than 2a away from the center of the primary, because the orbit itself is 2a in length, measured the long way.)

And now we have the background needed for today’s stupid orbit tricks.

Escape Velocity

If you set the semi-major axis a to infinity in the vis viva equation, you’re now thinking, basically, about an ellipse with apoapsis at infinity, which is to say, you’re not ever going to get to it, so you’re never coming back. Plugging that in to vis viva, the 1/a term becomes zero, and so escape velocity (at any given distance r from the primary) is:

(And now we’re back to GM.) You don’t have to be in orbit for this to work. So at the surface of the earth, 6,378 km from the center, escape velocity is roughly 11 km/s.

(And again, now reality crowds into theory. In reality there is more than just the earth and your spacecraft, there’s also the sun. You’ll get away from earth, but not from the sun…so you won’t travel infinitely far from the earth. To get away from the sun, you need 42 km/s (yes, even 150 million kilometers away from the sun). The earth’s orbital velocity of 26 km/s can help you with that, if you launch in the right direction; just add 16 km/s to get to 42 km/sec. This is how New Horizons was launched to–and past–Pluto.)

Note that the formula has a “greater than or equal to” sign; any velocity greater than this is also good for escaping, with some left over of course.

Changing Orbits

How do you change from one orbit to another?

If you’re in orbit you need some source of thrust, and the most common and obvious one is a rocket.

But here is the key thing…if you want to change from one orbit to another, you apply thrust where the two orbits–the one you’re in and the one you want to be in–cross each other. Because what you change with thrust is not position (not at the time you thrust, but of course later on your position will be different than it otherwise would be), but rather velocity. So the position before you thrust will be the same as your position after the thrust, but your velocity will differ.

Let’s go back to the eccentricity diagram.

Let’s say you’re in the red orbit and want to go into the green orbit. What you do is wait until you’re at one of the two points where the two orbits intersect–let’s pick the bottom one for this example, fire up your rocket, and change your velocity so that you’re now travelling on the green ellipse instead of the red circle.

But–and this is key–I said velocity not speed. The speed remains the same (remember, from above, that when those other orbits cross the red orbit, they’re at the same radius r and the orbits all have the same semi-major axis, a, so they have the same speed, just in different directions.

Velocity is defined both by speed and a direction of motion. In this case, you need to change the direction without changing the speed. This is a job for vectors! Just eyeballing it, at the bottom of the diagram where the red and green orbits intersect, you’ll want to point your rocket almost directly at the thing you’re orbiting, and thrust for a bit. That will result in your velocity shifting a bit downwards on the diagram, and you’ll be moving on the green ellipse instead of the red circle.

Remember what I said about being able to change velocity but not position, with thrust?

There was an egregious misunderstanding of this in a certain Star Trek: The Next Generation episode, Deja Q (from the third season). A certain planet was facing disaster, because its moon, formerly in a nice tidy circular orbit, was starting to drop inwards. With every orbit, the periapsis was getting closer and closer to the planet; eventually it’d hit the planet.

The Enterprise was going to try to pull the moon back into its proper orbit with the tractor beam.

But the Hollywood effects people were utterly ignorant of what I was just telling you. If you want to move the moon from that elliptical orbit back into its circular orbit, what do you do? You go to where the two orbits touch, at 3 o’clock in the diagram…and give it a good shove there. (You will want to speed it up at that moment; same direction, but make it go faster.)

Instead they depicted the enterprise waiting until the moon was at periapsis (9 oclock on that elliptical orbit) then pushing from there. Luckily they didn’t succeed, otherwise that moon would have ended up in a different orbit than what they wanted, quite possibly a very eccentric ellipse that would collide with the planet…oops!

Now a real starship crew would know this (unless they slept through orbital mechanics at Starfleet Academy), but Hollywood writers and producers? Nope. And either their “technical consultant” didn’t know Jacques Schiff about orbital mechanics (which, let’s face it, is an arcane specialty for people on Earth, though if we ever migrate into space in a big way, people up there will have to know it), or the Hollywood weenies decided not to listen to him.

(And let’s leave aside the fact that there’s simply no reason for a moon to suddenly have a shrinking orbit like this, in the first place! The only way it could happen, in reality, is if someone applied a small thrust to it at 3 o’clock, every time it was there, to slow it down and get the other side of the orbit to drop. I can’t think of a natural process that would do that. Once, yes, but every single time it’s at the same spot in its orbit?)

So there you go, an orbit change…and even an application (and you get to laugh at Hollywood too).

Hohmann Transfers

But what if the two orbits don’t touch? The short and glib answer is, then you use a transfer orbit; pick one that touches both orbits.

Hohmann transfers get used a lot by NASA for interplanetery probes. The orbits of Earth and (say) Mars are in very nearly the same plane, so you just pick an ellipse that touches both orbits, sort of like the way that wayward moon’s new orbit was touching the old one at 3 o’clock.

But it gets used for satellites too.

Imagine we have a satellite in a very low, circular orbit, say, 222 km above the earth’s surface or 6600 km from the center of the earth. And we want to put it into a geostationary orbit, which is at 42,164 km from the center of the earth.

We need a transfer orbit.

Like this one:

Our two circular orbits are connected by an elliptical orbit. (And yes my low special effects budget is in play here….the diagram is again stolen from Wikipedia, and it’s for the sun and two planets, clearly. Just imagine that’s Earth at the center instead of the sun.)

When you change an object from one orbit to another, its position doesn’t change, its speed does change. So what has to happen is the satellite, when it reaches 6 o’clock in orbit 1, has to change its speed to be appropriate for that elliptical orbit, at its closest distance, so now it’s in orbit 2. Then it will have to change speed again when it gets to 12 o’clock in orbit 2, to put itself in orbit 3. Needless to say, there’s a rocket attached to the satellite for doing this.

We know a for orbits 1 and 3, but we don’t know it for orbit 2. But look at it. The semi major axis of 2 is half of the long distance across the ellipse, and it should be pretty obvious that the long distance the sum of a for orbits 1 and 3. Because the top end of ellipse 2 is at the same distance as a for orbit 3, and the bottom end is at the same distance as a for orbit 1. Add them together to get the total distance, and divide by 2. A for the transfer orbit is 24,382 km.

Orbital velocity at 6600 km comes from . Using μ=3.986 x 10⁵ we get v = 7.771 km/second.

Orbital velocity at 42,164 km comes from the same formula and is 3.075 km/sec.

So now we need to use vis viva twice, once for r=6600 km in an a=24,382 km orbit, and another for r=42,164km in a 24,382 km orbit (the same orbit, two different distances). At 6600km, to be in that orbit, the spacecraft must be moving at 10.22 km/second (not that much below escape velocity!) and at 42,164 km it will be moving at 1.600 km/sec (it’s 1.59968 but I am rounding everything to four significant figures).

So at the point where orbits 1 and 2 touch, the spacecraft is moving at 7.771 km/second and has to speed up to 10,22 km.sec, which is a change of 2.448 km/second.

And at the point where orbits 2 and 3 touch, the spacecraft will arrive moving at 1.600 km/sec but needs to speed up to 3.075 km/sec to go into the circular geostationary orbit, which is a change of 1.475 km/sec.

As I said this is done with a rocket attached to the spacecraft. This rocket must be able to change the velocity of the spacecraft 2.448+1.475 = 3.923 km/second.

With that, and the mass of the satellite and of the rocket with empty fuel tanks, and the characteristics of the rocket fuel, you can use the “rocket equation” to compute exactly how much fuel that booster needs to do the two “burns” it has to do, in order to move the satellite to geostationary earth orbit (GEO).

The rocket equation sounds like a good thing to talk about in a future Saturday daily, assuming anyone in my audience still has eyeballs that haven’t turned into glass.

But in the meantime, you at least have some notion of how to send the GOPe to its most appropriate next convention site.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!