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 !!!