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.

Physics?

Part 1 was last week. I intended to do Part 2 this week, but both of my drafts are an utter mess. I’m going to keep plugging away at it, though, so hopefully next week.

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.)

(Paper) Spot Prices

Last week:

Gold $1778.20
Silver $26.07
Platinum $1236.00
Palladium $2914.00
Rhodium $28,000.00

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

Gold $1768.60
Silver $25.97
Platinum $1205.00
Palladium $2996.00
Rhodium $29,000.00

(Be advised that if you want to go buy some gold, you will have to pay at least $200 over these spot prices. They represent “paper” gold, not “physical” gold, a lump you can hold in your hand. Incidentally, if you do have a lump of some size, doesn’t it give you a nice warm feeling to heft it?)

Of these, palladium continues its steady climb. In fact, on Thursday it had closed at $3012, above three thousand dollars for at least the second time in the last week.

I did, long, long ago, buy some palladium, not a huge amount. (But I can drop it on my foot. I won’t hurt if I do so, because, like I said, not a huge amount.) I even told the guy I was buying it because it had gone over 900 bucks earlier (which at the time was higher than gold had ever been), maybe it would do so again. He scoffed, and explained that was due to a temporary supply interruption from Russia, unlikely to ever happen again. But now, it’s worth well over ten times what I paid for it. In fairness, I had to hold onto it for over 20 years for it to finally do what I wanted it to do, so this isn’t the short of thing that is a “short term” play.

I knew someone who, about the same time, wanted to find a way to get into rhodium, but back then there was no such thing as a rhodium one ounce bar. I don’t know if he managed to find a way to do it, but if he did, he has done very, very well, even if it took a couple of decades for it to finally move.

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 !!!

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 $1777.50
Silver $26.05
Platinum $1207.00
Palladium $2834.00
Rhodium $28,200.00

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

Gold $1778.20
Silver $26.07
Platinum $1236.00
Palladium $2914.00
Rhodium $28,000.00

Unfortunately, when looking at the prices only on Friday, you lose some things. It looks like gold has barely moved, but the fact of the matter is, it almost blooped up above $1800 earlier in the week. A far cry from the situation just a few weeks ago when it would drop below $1700 and then popped back up again, two or three times.

To really get a feel for what is going on, you should look at a chart.

Here is what gold has done this past year:

http://www.dailymetalprice.com/metalpricecharts.php?c=au&u=oz&d=240

The price is moving up and down, but the overall trend is down, imagine a series of sawtooths (sawteeth?). And if you look at the recent rise, it’s still consistent with just being an upward movement in the overall down trend; you can sort of eyeball a straight line through all those peaks, sloping down and to the right, and the price of gold hasn’t broken through that line, not yet it hasn’t. A trader would likely expect it to reverse and drop again.

Palladium on the other hand, is in a slow upward trend, again as seen in a graph for the past year:

http://www.dailymetalprice.com/metalpricecharts.php?c=pd&u=oz&d=240

And so I would expect it to continue to climb, for now. Here’s rhodium:

http://www.dailymetalprice.com/metalpricecharts.php?c=rh&u=oz&d=240

Note that it has gone from below $10,000 to almost $30,000 just since last June. Also note at the far right the price is moving up and down, but the height of the oscillations is decreasing. This may be what the technical traders call a “flag,” if so when it reaches its “point” the commodity often breaks out, either up or down, in a big way.

Here’s iridium:

http://www.dailymetalprice.com/metalpricecharts.php?c=ir&u=oz&d=240

And it probably shows the most stark behavior. Dead flat for months, then suddenly it starts climbing, and climbing, and climbing! That line almost looks like the profile of the Grand Canyon, in fact, complete with the vertical faces and then lines sloping upward to the next vertical face.

Mass (Part I of a Long Series)

Introduction

Having run out of precious metals to babble about, I’m going to change tacks. If you’ve been here a while, you might remember two postings I did on stars. These were independent posts, having nothing to do with politics (poly = many, ticks = blood sucking bugs) and at least some people enjoyed them. I wanted to go to the opposite end of the scale and talk about a certain sub-atomic particle, but then I realized that the best way to do that would be a very, very, very long post. (And yes, it’s a subatomic particle, but it has a lot to do with stars.) A huge part of it would be explaining where physics stood in 1895, and how four discoveries in the next four years basically overturned things, and eventually led to that subatomic particle, the real star (ahem) of the whole series.

So I decided to break this story up into pieces. And this is the first of those pieces.

And here is the caveat: I will be explaining, at first, what the scientific consensus was in 1895. So much of what I have to say is out of date, and I know it…but going past it would be a spoiler. So I’d appreciate not being “corrected” in the comments when I say things like “mass is conserved.” I know that that isn’t considered true any more, but the point is in 1895 we didn’t know that. I will get there in due time. (On the other hand, if I do misrepresent the state of understanding as it was in 1895, I do want to know it.)

Also, to avoid getting bogged down in Spockian numbers specified to nine decimal places, I’m going to round a lot of things off. I use 9.8, below, for a number that’s actually closer to 9.80665, for instance, similarly for the number 32.

OK so without further ado, mass.

What Mass Is, and Isn’t

Mass is not the same thing as weight, at least not when scientists are using the terms.

But the distinction between mass and weight didn’t become clear until Isaac Newton came along. He tried to imagine what objects would behave like if there were no gravity, and no friction. And he realized that an object under those circumstances would stay at rest unless a force acted on it, or, if were already moving, would continue to move in the same direction at the same speed, unless a force acted on it. It has inertia. But that doesn’t match what we actually see. You let go of an object that’s not on the ground, it falls (or if it’s a balloon, it might rise). An object that’s moving on a flat surface slows down and stops.

But the reason why we see things fall faster and faster, is that gravity exerts a force on them, a downward force, and the reason things moving horizontally slow down is friction, and that, too is a force.

For clarity, we have to ignore friction. Imagine these objects are wet ice on a hockey rink–or cars sliding on ice (yikes!). Or air hockey pucks. There’s still some friction in all of these cases, but not a whole lot. You can imagine, after watching these sorts of things, what it would be like with no friction.

Largely building upon what Galileo discovered (when he wasn’t looking through a telescope), Newton essentially defined the concept of inertia. It’s basically the resistance of an object to being shoved. And mass is essentially a measure of that. If object A is twice as massive as object B, it’s twice as hard to shove around and get the same effect. You need to exert twice as much force.

On the other hand, if you stick with the same object, and apply twice as much force, it reacts twice as much.

You can state this a little more precisely as, acceleration, a, is proportional to the force, F, and inversely proportional to the mass, m. You can increase or decrease any of the three items, decrease or increase one of the other two, and you will see the third item increase or decrease exactly in proportion.

Or to be even more concise, you can write the following:

a ∝ F/m.

That little Jesus fish like thing means “is proportional to” and basically, it means that if you double one side, you double the other side, but they’re not equal.

You can rearrange to get:

F ∝ ma.

And this is the form you usually see this in, it’s Newton’s second law of motion. Well almost. There’s something we can do to get rid of that Jesus fishy thing and replace it with an equals sign. More on that shortly.

Mass is considered to be the ultimate measure of “how much matter” is in an object. Twice as much matter, will have twice as much inertia. And some object, say one of the big weights off of a weightlifting set, will have the same inertia even on the moon.

But the weight of the objects will change on the Moon, because weight is actually force. And the Moon’s gravity will pull on the same objects, with less force than on Earth.

The kilogram is actually a unit of mass. A chunk of metal massing a kilogram (think of it as a one kilogram gold bar if that will put a smile on your face) will still mass a kilogram on the moon, pick it up and swing it around, you will feel the same tugs as you would feel on earth, because now you are playing with its inertia, which doesn’t change–it will take the same force to keep the bar from flying out of your hand as it did on Earth.

But pounds are (usually) a unit of force. That kilogram of gold will weigh about 2.2 pounds here on Earth. That means that the earth’s gravity pulls on it with that amount of force. But take it to the moon, and it weighs about 5.9 ounces, that’s how much force the moon exerts on that one kilogram mass.

[Or–let’s be frank here–for me, and for most of you, it weighs exactly zero both on Earth and the Moon because your kilogram bar of gold doesn’t exist at all except in your dreams. Oh, OK, never mind, forget I said this and return to smiling.]

The one force we can’t get away from in our daily is gravity, and as such in the English system a lot of things are defined with respect to the amount of gravity Earth has. But when you’re doing engineering you have to deal with a lot of forces–the force exerted by a pile driver, the thrust of a jet engine, and so on. So you need a unit of force and a unit of mass, so you can figure out how much your masses will respond to your forces, or alternatively, how much force you’ll have to exert to make that mass move the way you want it to.

The metric system, which starts with unit of mass, has to derive a unit of force, and the English system which starts with a unit of force, has to derive a unit of mass. Metric invented a unit of force called the Newton–the amount of force needed to accelerate a kilogram, one meter per second, for every second it’s applied, and yes, it’s named after Sir Isaac. And the English system retro-invented the slug–it’s the amount of mass that, when acted upon by one pound of force, will accelerate one foot per second, every second.

Once you’ve defined your units, you can change that proportionality constant to an equals sign. But you may need a fudge factor, which I will call k. F = kma. (And yes, Biden can kma.) In metric, as long as you stick to meters, kilograms, and meters per second squared, the fudge factor is 1. The Newton was deliberately defined that way. And in the English system, as long as you stick to feet, slugs, and feet per second squared, the fudge factor is also 1. 1 will disappear if it’s in an algebraic multiplication, so now we’re dealing with

F = ma

Drop a kilogram of gold–it will accelerate at 9.8 meters per second per second, a = 9.8, and m is one. Plug it into the formula above. That means it’s being acted on by a force of 9.8 newtons.

Galileo showed that heaver objects fall at exactly the same rate as lighter ones (once you account for air resistance, which is a force and partially cancels out gravity). So a two kilogram mass of gold, falling at the same rate, which we call g, gives you F = 2 x 9.8 = 19.6 Newtons.

Switch to the English system now. Drop a pound of something else–bananas, say–it will accelerate at 32 feet per second, every second. (That’s the English equivalent of 9.8 meters per second per second…we’re just using a different measuring stick.) But this time we have a weight, not a mass, F, and we have a and are looking for m, so we need to do a bit of beginner’s algebra and come up with:

m = F/a

But this time F is 1 pound, and a is 32 feet per second squared. So our mass is 1/32. And indeed, if our answer is supposed to be in slugs, that’s the right answer. A slug, as it turns out, weighs 32 pounds here on earth, and 1/32 of a slug weighs one pound.

Engineers find it so useful to have a unit of mass, the ones working in the English system (poor sods) actually invented a “pound mass,” the mass of something that weighs a pound here on earth. But when they use the “pound mass” in their formulas they have to put a fudge factor of 32 in. With mass in pound mass, the formula becomes

m = 32 F/a

Or rearranging to the usual form

F = ma / 32

A pound mass will respond to a force 32 times as much as a slug would to the same force, as you can see when you solve for the acceleration (response), a = 32 Fm. Failure to properly account for this has doomed more than one rocket. Metric is cleaner, a kilogram is mass, and only mass.

I got my STEM education entirely in metric, that’s what I’m comfortable with, that’s what I’m going to use from here on out.

OK, so mass and weight are different. How do you measure them? If they are different things, you need different methods to measure them.

A force can be measured with a spring. Your typical bathroom scale, or your kitchen scale, will have a spring inside; the amount the spring is compressed by the stuff you put on the scale is a measure of the force exerted on the spring. Drag your kilogram of gold to the moon and bring your scale with it, it will push on the spring less and therefore weigh less.

A mass is best measured by a balance scale. Your doctor’s scale, for instance, is a balance scale. Take it to the moon, and if it read 100 kg on earth, it will read 100 kg on the moon.

But it’s probably marked off in pounds. If you weighed a hundred pounds on earth…that scale will read 100 pounds on the moon. It’s actually measuring your mass but is calibrated in pounds actually pounds mass. So it only looks like it’s measuring your weight.

A kilogram (mass) weighs 2.2 pounds on earth, the object that exerts a force of 2.2 pounds on earth, has a mass of one kilogram. That 2.2 will change on every different planet, however, since most of us never leave earth, we simply think of a kilogram as equaling or being the same as 2.2 pounds, when it really isn’t. It isn’t the same thing, any more than a gallon is the same as 8.33 pounds. (It weighs that much if it’s water and we’re on earth, but that doesn’t make a gallon the same thing as 8.33 pounds in any fundamental sense.)

With me still? I hope so.

Conservation of Mass

OK, I’ve shown you Newton’s Second Law by way of introducing you to the distinction between weight and mass. It’s called a “Law” not because some politician decreed it, but because the universe works this way.

F = ma

Always.

And when you have to use a fudge factor, the fudge factor is a constant. It’s a constant 1 in the case of metric and English slugs.

One could ask what would happen if the fudge factor were to change, and the answer is a bit surprising. Since the Newton is defined as being the force necessary to accelerate a kilogram at one meter per second per second, if it suddenly, tomorrow, took twice as much force to do that, the Newton would simply get twice as big.

Since it’s awkward having your units of measure change (for exactly the same reason that inflation sucks), the fact that scientists set things up that way should be evidence enough that they are sure the fudge factor never changes.

How do we know that? It is an induction, not a deduction. It has always been true, we assume it’s just the way the universe works, until we find an exception, and believe me, people are always looking for the exception. And also for just outright blatant violation of the rule; such as objects suddenly and inexplicably changing their velocity. That would be an a without an F, or perhaps the m taking a vacation and reducing to almost nothing momentarily.

Our whole view of the universe wouldn’t make sense if Newton’s second law weren’t true. Car collisions on icy roads, air hockey…if someone made an animated movie where this rule were blatantly violated, it would look fake to us. Of course if the movie were almost spot on, with maybe the fudge factor changing by 1 percent at random, we’d have a hard time seeing it, but this has been measured in laboratories, and it’s always true. And the fudge factor doesn’t change.

One other thing turns out to be true, at least as of 1895. Mass never disappears into nothing, and it never appears from nowhere, either.

Sure, the mass of an object can change. It could decrease. But that mass always goes somewhere else, it never gets destroyed. Or similarly, if the mass of an object increases, that mass came from somewhere else.

This is one of those realizations that turned science into a form of bookkeeping. The books have to balance, the mass in has to equal the mass out.

Set a two kilogram log on fire. Weigh the ashes afterwards, they mass out to maybe 600 grams. Did the other 1400 grams just disappear? Nope. It can’t, it’s not allowed to. So that tells the scientists they didn’t account for something. In this case, they didn’t capture and weigh the smoke and the carbon dioxide given off by the burning log (whilst upsetting leftists). So if you add that in, are you okay?

Nope, because now the mass after is more than the mass before. That’s not allowed either; you can go back to the bench and re-run the experiment.

This time, count not just the wood, but also the oxygen used to burn the wood.

Once you do that, your mass before matches your mass after. Life is good.

The books balance.

And this was another thing that (as of 1895) was considered to be always true. Every time it had been tested, it was true. And a test isn’t just an explicit lab exercise like I just described, but literally everything done in a lab implicitly follows this rule.

In this case simple arithmetic is enough to do the bookkeeping. And nothing of negative mass has ever been seen, so you will see addition and subtraction, but never a negative result. Real accountants would find this dead easy. The trick, of course, is to account for everything, and measure carefully.

Gravity

There is one other thing about mass, though, that was (and still is) an important feature of the universe. And that is gravitation. I’ve mostly talked about gravity as something that exerts a force on a mass, so far, but I’ve not mentioned yet that mass actually exerts gravity. Every mass, exerts a force on every other mass. If you double the mass of the object, it exerts twice as much force. If you double the distance between the objects, however, you divide the force by 4. This is the square of the distance, and you’re dividing by it, so it’s called an inverse square relation. But one more thing. If you double the mass of the other object, the force you exert on it doubles too, and it responds with the same acceleration.

You are exerting a tiny gravitational force on the Andromeda galaxy. And vice versa. In fact, it’s the same amount of force in both directions.

The law of gravitation was also first noted by Sir Isaac Newton.

You can write this law as follows, at least as a first cut.

F = m₁ m₂ / d ²

Multiply your masses together, divide by the square of the distances, and you get F.

Except, no you can’t. Meters, kilograms, seconds, and Newtons go together with F=ma, but they don’t go together in this equation. Two masses 1 kilogram each, at one meter’s distance? That equation says the force should be one Newton. It’s not. It’s a lot less. You need to plug in a fudge factor, and this one is named G. The law of gravitation properly reads

F = G m₁ m₂ / d ²

And G is a very small number, because in Newton’s day you couldn’t even measure what F was. Without being able to measure F, we couldn’t figure out what G was. And for any scenario where we could measure F, we either couldn’t measure one of the masses, or d, or both. Either way, G was unmeasurable.

But even without that, Newton could see the law was good, because he could check the responses of things to earth’s gravity. An apple, and the moon.

To start this out, in fact, let’s assume we want to measure the acceleration, not the force. Both sides of the equation above are a force, dividing by the mass of one of the objects, the one we want to watch, gives:

a = G m₂ / d ²

And you can substitute mass of the earth, m_e, for m₂. So the acceleration of, say, an apple dropped, is:

a = G m_e / d ²

And if you’re standing on the surface of the earth, d is the radius of the earth. (You can treat the earth as if its entire mass were at the center, so long as it’s radially symmetrical (which it almost is). That’s one of many things Newton proved. He had to invent calculus to do that.)

In this particular case, we knew a, and we knew d, but we knew neither G or m_e. But we knew what their product had to be! This is called the earth’s gravitational parameter, and is usually written μ_e. (Greek letter mu, usually pronounced as “mew” in English, though logically it should be “moo.”) This is very handy, in fact, it’s so handy that even today people who work with orbital motion just use gravitational parameters; it saves them the bother of multiplying the same numbers over and over again.

a = μ_e / d ²

Newton had pretty good information on how far away the moon was. He could compute how much it was accelerating as it orbits the earth (always downward, as if it were on a string being whirled around the earth), and his equation and the data matched. The moon responded to Earth’s gravitation exactly the same way as the apple did. This was the first time we had ever shown that something “up there” follows the same physical laws as something “down here.” And that’s why it’s called the universal law of gravitation.

So Newton knew the earth’s gravitational parameter, and the distance to the moon was known before his time. But what about the rest of the solar system? Well, life was rough for astronomers working out the solar system back then. Because we didn’t know the actual distance between the sun and any of the planets, nor between other planets and their moons. We did know the relative distances; we knew, for instance that Jupiter’s distance to the sun was 5.2 times that of Earth’s. Kepler had figured that out in the late 1500s. We could also see that the inverse square law worked: The acceleration Jupiter experienced was about 1/27th that of earth, though we couldn’t tell what it was because we didn’t know the scale. Newton, in fact, showed mathematically that any inverse square force will cause things to orbit in ellipses, thereby vindicating and strengthening Kepler, and using Kepler as evidence that an inverse square law was involved.

Measuring the Solar System, Massing the Earth

So astronomers didn’t know the gravitational parameter of the sun, much less G and the mass of the sun. And they didn’t know d, in this context the distance from anything to the sun, much less the earth-sun difference (but they named it: It’s an astronomical unit, and is still called that to this day). But if they could figure out what d was for Earth, they’d know it for everything else in the solar system, because we knew the proportions. And if they knew d, they could figure out the Sun’s gravitational parameter, because you can figure out the acceleration directly from d and the length of the year.

Astronomers got the first intimations of d when we were able to triangulate on Venus as it crossed between earth and the Sun, in 1761 and 1769. We could plot its motion and position on the sun’s disk from multiple places on earth, see how different it was, and determine how far away it was, just like when you move your head from side to side, a near object will move against the horizon more than a distant one will. If you measure that apparent shift, and know how much you moved your head, you can compute how far away it is. Multiple parties went to different places on earth, just to measure these transits, the more measurements the better. It was one of the first major examples of international scientific cooperation.

Similarly we now had a good number for the distance to Venus, and because we knew the proportions of the solar system, we instantly had the distance from earth to the sun. We therefore knew a, and…now we had the gravitational parameter of the sun, because it was equal to a times d ².

The gravitational parameter of the sun is 333,000 times the amount of the gravitational parameter of the earth. Since both numbers are G times the mass, you can see that the sun’s mass, whatever it is, must be 333,000 times that of Earth. Whatever that is. We still didn’t know.

But even better. We now knew the exact distance to Jupiter. And we could therefore watch how far the moons of Jupiter got from it in the night sky, do a quick calculation and get their orbit sizes…and now we could figure out the gravitational parameter of Jupiter! It is 317.8 times that of the earth, so its mass is also 317.8 times ours (again, whatever that is). Saturn has moons, and we could do the same thing for it. Mars has moons too, but they hadn’t been discovered yet.

Then in 1781 the planet Uranus was discovered. And in 1787, two moons were discovered. Shazaam! We knew how many earth masses Uranus was, and six years earlier we hadn’t even known Uranus existed. And we eventually figured it out for Mars, when we finally did discover its moons a century later.

But Venus and Mercury don’t have moons, and we could only make educated guess at their masses…until the 1960s and 1970s when we sent probes to them and could see how they interacted with those planets.

One last piece of the puzzle. Henry Cavendish (1731–1810) was actually able to measure the force of gravity between two heavy lead balls in his laboratory in 1798. This was painstaking work, but he now had a situation where he knew every term in the law of gravity except for G; he had the force, the distance, and the masses. So from that he was able to compute the value of G, and (in metric) it is: 6.67 x 10^-11.

Now that we had that number, we could go back to every gravitational parameter we knew, divide by G and get the masses.

Now we knew the mass of the Earth. It’s 5.972×10²⁴ kilograms. And everything else proportionately.

We did this, but we did not have to go “out there” and weigh anything.

Problems with the Law of Gravitation?

The law of gravitation worked really, really well. We never saw anything inconsistent with it…well, almost!

When we tracked Uranus in its orbit about the sun, it was clear it was not following the law, not quite. Was something wrong with the law of gravitation? The law was so useful everywhere else, and I mean everywhere else, that it would make no sense for it to be broken here, so instead of assuming the law was broken, we figured that there was something unknown out there, pulling on Uranus. It was complicated work, but Le Verrier in France and John Couch Adams in England both did the calculations in 1845, and when they told Galle, another astronomer, one who used a telescope rather than being a theorist, where to look…well, Galle found the planet Neptune almost immediately.

Far from it being a problem for the theory of gravitation, the discrepancy with Uranus’ orbital motion turned into a triumph, for the theory of gravity had been used to discover a planet, and had predicted it so well that it took someone who knew where to look less than an hour to find it.

That gives you a really strong feeling that this is the truth!

But I mentioned two problems. What was the other one?

The other was the orbit of Mercury. It’s an elliptical orbit, and if Mercury and the Sun were alone in the universe, that ellipse would never, ever move. But it does move, the long axis shifts 574 arc seconds every century. And of course Mercury and the Sun aren’t alone in the universe. So what we should be able to see is that the planets–and the sun’s slight oblateness–explain Mercury’s orbit precessing.

But when you add up all those effects, there’s still a discrepancy. They don’t add up. There’s still 43 arcsecond per century left over. And this bothered scientists.

But really, this probably isn’t a problem. We know what the answer has to be. There’s an unknown planet pulling on Mercury, one so close to the sun we just couldn’t see it in all the glare. The same Le Verrier that predicted Neptune predicted this planet. We even gave it a name, Vulcan; a perfect name because he was the Roman god of the forge and it gets hot near forges and near the Sun. But despite what you may have heard, scientists usually want to square things away, they want to see that planet, then they’ll be confident they know why Mercury is misbehaving.

But Vulcan was never found, and in 1895, it remained an open question. They expected to find it, they just hadn’t, yet. In truth, it really would be hard to see something like that; it can only be done during solar eclipses.

Conclusion

Well, this turned out to be pretty long. And maybe hard to follow (I hope not). But as I wrote it I realized how much “hung off” the concept of mass, and the law of gravitation, and how much we were able to learn about the solar system and our own Earth, each bit of knowledge building on the prior, with theory used as a framework. And you saw some limitations…we could only estimate the mass of bodies with no moons. This wasn’t even where I wanted to go with this, but it was too good to pass up. (Next week we continue towards our final destination.)

But hopefully you saw some notion of how science is supposed to function. It’s full of humans with their own foibles, of course, but in the end the truth does out. It’s nice when you can use a theory to predict something unexpected; it gives you a very warm fuzzy sense that the theory is correct. But at the same time, there are implicit assumptions; that the generalizations we see will continue to hold true. Sometimes we discover otherwise, and have to adjust; usually when that happens it turns out that the generalization was true under certain circumstances and is still useful, under those circumstances, but that you have to scrap it under others. (At the risk of a spoiler, you’ll see that Newtonian gravity is one of those cases.)

And in so many cases, if we seem to see far, it is because we stand on the shoulders of giants, the men who preceded us, and they stand on the shoulders of the men who preceded them. None of this could happen if we weren’t willing to use information gathered by others and build on it, and in turn that’s a testament to the power of being able to write things down so that knowledge outlives us.

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 !!!

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.

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 $1734.30
Silver $25.13
Platinum $1192.00
Palladium $2748.00
Rhodium $25,000.00

This week–markets closed 3PM Thursday for Good Friday (or April Fools, depending)

Gold $1731.80
Silver $25.01
Platinum $1216.00
Palladium $2736.00
Rhodium $26,800.00

What I am seeing here is precious metals trading within a pretty well defined range. Gold has dropped down into the 1680s twice but then immediately bounced up. Which implies (to some) that it might be prepping to go up again. Silver seems to be in the doldrums right now; I don’t know whether it’s going up or down (does anyone really ever know about these things?) and won’t even hazard a guess.

Note: Last week’s gold and platinum prices are almost identical to the prices from five weeks ago! Five weeks ago:

Gold $1735.60
Silver $26.80
Platinum $1191.00
Palladium $2379.00
Rhodium $26,000.00

Iridium: The Smoke From The Smoking Gun

4.567 billion years ago, our solar system began to “condense” from the nebula. Clumps of dust particles began to come together, part of a poorly-understood process that eventually led to the planets. The nebula had a potpourri of “stuff” in it. Mostly elements up to iron, with a heavy leavening of ones after iron, created in supernovas or even neutron star collisions. (Most gold is believed to have come out of neutron star collisions…next time you admire that gold coin or your wedding band…think about where that stuff has been! Any of it not from a collision got blasted out of a supernova at 70,000,000 miles per hour.)

Very large bodies, moon sized and larger certainly, would heat up as they formed, from the potential energy of infalling stuff, and also from the fact that this dust had a lot of radioactive stuff in it. Many isotopes with very short half lives, like aluminum 26, were common then; we have no trouble seeing their traces in meteorites today. But back then they were a source of intense heat. Even today, much of the heat of the earth’s interior comes from radioactive decay of uranium, thorium, and even potassium (which has one fairly uncommon radioactive isotope).

Those large bodies became molten, and the heavy stuff sank towards the center. Iron was quite common in the nebula, and iron is heavier than the sorts of things that became typical rocks, and so we today have planets with iron cores.

A lot of good stuff went down into the core with the iron, including gold, the platinum group metals, and silver. Some gold hung around with the lighter slag since gold likes quartz. That resulted in gold being relatively more common than the PGMs in the earth’s crust.

But a lot of things in the solar nebula got big, but not big enough to melt. They became asteroids, and they are relatively rich in PGMs as compared with the earth’s crust. (If we can ever start mining those suckers…PGM prices will go down, and gold will go down somewhat…remember it’s relatively common in the earth’s crust, but that means it won’t become as common, proportionately to where it is today, when we go after asteroids.)

So one sure-fire sign of a meteorite is extra PGMs.

There was once an asteroid the size of Mount Everest. It probably hung out in the asteroid belt for about 4.5 billion years; in fact, it hung out, wherever it hung out, for almost exactly 4.5 billion years.

Then something happened to alter its orbit. And then, sometime after that, perhaps within a million years, it chanced to encounter Earth.

It plunged through the atmosphere–which rapidly raised its surface temperature. Then it slammed into the ocean, at a point just off the coast of what we today know as the Mexican State of Yucatan. The rocks it hit were the worst possible thing it could find…sulfur-rich gypsum, calcium sulfate. The meteorite vaporized in an instant. And so did a lot of that gypsum.

The tsunami in the Gulf probably reached as far inland as Illinois.

The sky was filled with sulfur trioxide, which became sulfuric acid and rained out over the next few days. And the amount of sunlight reaching the surface of the earth was cut, both by the sulfuric crud and just ordinary dust ejected into the stratosphere by the impact, putting another challenge on plant life. Which is at the root of the food chain. Fewer plants, fewer herbivores, fewer herbivores, fewer carnivores.

There’s good reason to believe life was already under stress from massive volcanic eruptions in what is now the Deccan traps, in India. This was just exactly what wasn’t needed for icing on the cake. (Alternatively, the Deccan eruptions may have been triggered by the impact. Yes, even though they were almost on the other side of the world!)

75 percent of species died out, including almost all of the dinosaurs. Some of the ones that had taken to the air and had feathers and warm blood survived the next five years of darkness. And of course many of those little mammals survived too.

Thus ended the Cretaceous Period and the Mesozoic Era (which included the Triassic, Jurassic, and Cretaceous).

The Cretaceous Period had lasted some 80 million years–note, longer than everything since. If you were to go back in time halfway to the beginning of the Cretaceous, you’d be in the Cretaceous.

65.6 million years later, give or take 300,000 years, a couple of geologists were investigating exposed rock near Raton, New Mexico (less than two hours away from me). They knew from fossil evidence that this little thin white stripe in the rock separated Cretaceous from Paleogene (which used to be called the “Tertiary”). Below the line, many kinds of dinosaurs were alive when the rock was deposited. Above it, only the birds.

They analyzed the white stripe. It had 100 times as much iridium as the rock above and below it. Still not a lot (a hundred times almost, almost nothing is still almost nothing), but it was the smoke that showed the smoking gun was an asteroid.

An asteroid almost certainly killed the big “Jurassic Park” dinosaurs.

Many have read this story and come away thinking the asteroid was made out of iridium. No, no more than the gun found at the crime scene is made out of fingerprint oil. Iridium was along for the ride, but the sulfur the asteroid found at its destination probably did as much as anything to kill almost every large animal on earth.

So what is this “iridium” anyway? It’s element #77, with 77 protons in the nucleus, tucked in between osmium and platinum. It was discovered alongside osmium in 1803/4 by Smithson Tennant, a story I told last week. It’s almost as dense–the difference is so small you wouldn’t be able to perceive it. And it’s another one of those bothersome high-melting point elements…six hundred kelvins below osmium but still 2400K. But it does not form iridium tetroxide and kill people. In fact, it may be the most chemically inert metal known, the noblest metal. It is not attacked even by aqua regia, a mixture of acids that will make short work of gold.

What I didn’t mention last week was that iridium tended to be the major impurity in those Russian platinum coins. It could be detected while processing the platinum, because at one point during that processing, some of the aqueous solutions would be orange or even red if any iridium were present, rather than yellow. And indeed when analyzed today iridium and iron are the major impurities in those coins.

Today, iridium can be rendered a solid, with some work. This video is well worth watching! Osmium is rarely made into big solid objects. Iridium, on the other hand…

The professor mentioned the price of iridium. It’s now running six thousand dollars an ounce. Back in early December it was $1700, before that it was fairly stable, the ten year chart shows a few years of $1000/oz and even $600/oz iridium, before it blooped up to $1500 in 2018, slowly rose to $1700, and then went bananas. http://www.dailymetalprice.com/metalpricecharts.php?c=ir&u=oz&d=2400

And now for a link to the story of a man who had two kilograms of iridium powder, and decided to go get it melted. Some of you expressed interest in just how it works with these super-high-melting elements; there’s detail here for you.

https://theodoregray.com/PeriodicTable/Stories/077.x3/

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 !!!

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.

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

Last week:

Gold $1746.90
Silver $26.33
Platinum $1198.00
Palladium $2688.00
Rhodium $29,000.00

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

Gold $1734.30
Silver $25.13
Platinum $1192.00
Palladium $2748.00
Rhodium $25,000.00

Gold and platinum are fairly stable, silver took a fairly big hit, Palladium took a healthy jump, and rhodium seems to have dropped 4000 bucks, however, it did so a couple of weeks before and bounced right back up again. I think rhodium has found a range, a wide one…for now.

Osmium. This One Can Kill You.

Someone last week made snarky comments about writing about precious metals, so I figured I’d respond the only way I could: by continuing to do so. In fact, I was thinking about combining osmium and iridium, and now I know I shouldn’t!

Osmium is one of the Platinum Group Metals. In fact, it’s the one directly “below” last week’s metal, ruthenium, in the periodic table.

It’s famous for one thing. It is the densest stable element, bar none. In other words, it’s the most efficient paperweight. It packs more weight into a smaller volume than anything else, bar none…well, at least until you start spooning up pieces of white dwarf or neutron stars. It comes in at 22.59 grams per cubic centimeter–just a shade more than iridium, which we’ll get to in due course.

It also tends to have a slight bluish cast, not unlike zinc (which is neither dense nor valuable). And it’s very hard (Mohs 7.0) and almost completely incompressible.

Provided, of course, that you can get it in bulk. It generally is marketed as a finely-divided powder, and even if you buy melted beads, the beads will often have voids on the inside, because of the same issues that arise when melting any of the refractory metals. That will make the beads lighter than one might expect.

The melting point is a whopping 3306 K, 5491 F, with rhenium and tungsten the only metals with higher melting points. That’s difficult to attain, even in a black car with black interior parked in Phoenix.

Osmium and iridium both were discovered in 1803 as part of the investigation of platinum by Wollaston and Tennant in England. Smithson Tennant gets the credit for osmium and iridium, while Wollaston gets the credit for rhodium and palladium. Tennant found osmium and irididum by studying the black residue left over after dissolving what they thought was pure platinum in aqua regia.

Aqua regia (royal water) is actually a mixture of hydrochloric and nitric acids; unlike other acids, gold will be attacked by aqua regia, and so will platinum. But even after dissolving the platinum, there was this black residue, which (after a lot of trial and error with various chemical reactions) proved to contain two new metals, osmium and iridium.

Osmium proved to have an oxide, OsO₄,. And that’s where the “kill” comes from. Osmium tetroxide is a solid that readily sublimates, turning directly to vapor like dry ice, and it stinks. Hence the name osmium, from osme, “a smell.” Worse: osmium tetroxide is poisonous, and if it doesn’t kill you, it’s liable to damage your eyes.

And if you open a container of powdered osmium, it can catch fire spontaneously, reacting with the air to form osmium tetroxide. This makes it difficult to machine…imagine lathe turnings catching fire and killing or blinding the lathe operator.

Quoting from wikipedia regarding osmium tetroxide:

OsO₄ is highly poisonous. In particular, inhalation at concentrations well below those at which a smell can be perceived can lead to pulmonary edema and subsequent death. Noticeable symptoms can take hours to appear after exposure.

OsO₄ will irreversibly stain the human cornea, which can lead to blindness. The permissible exposure limit for osmium(VIII) oxide (8 hour time-weighted average) is 2 µg/m³.^[7] Osmium(VIII) oxide can penetrate plastics and food packaging, and therefore must be stored in glass under refrigeration.^[14]“

wikipedia

Based on this…you can die from it even if you can’t smell it.

When the Russians made that platinum coinage I talked about a few weeks ago, part of their purification process involved dealing with the osmium they were extracting from the raw platinum in a way that was safe; fairly sophisticated stuff for the early-mid 1800s.

There is good news: even though the powder can kill you, osmium is completely safe (and practically impervious to anything) in bulk form. (It might start to form osmium tetroxide if heated to 400 C.)

Depending on who you ask, osmium is the least common stable element in the earth’s crust…averaging fifty parts per trillion by mass (weight).

Osmium is found with platinum, but also turns up as a by product of copper and nickel mining. Perhaps that is why its price hasn’t gone bananas like some of the other PGMs, whose production depends on platinum mining.

It’s mainly used in alloys, to harden them (rather than as a catalyst). Osmiridium and iridosmine, for instance (you can guess what they are mixtures of). Osmium and its alloys were once used as fountain point pen tips, and still see use as instrument pivots,electrical contacts. Osmium was also used for phonograph needles. Ballpoint pen balls sometimes contain a tiny bit of osmium, too.

Total world production is very hard to nail down, but in 1971 the US produced about 60 Kg as byproduct of copper mining. We import about twice that much, on average, every year. 120 Kg, by the way, is very roughly a gallon and a half of this stuff. (And we are talking about over 250 grocery pounds here. heavy stuff!!) I found in one place a claim that only one or two metric tons is produced per year world wide. (That would be a slab a meter on a side and about four inches thick, tops.)

The “spot” price is hard to nail down on something so thinly traded, but it seems to be about $400 an ounce (and has sat there for years). On the other hand, I’ve also found a site that claims it’s 1200 euros per gram which would make it something like 36000 euros an ounce–probably about 40,000 dollars an ounce. (That flat out doesn’t seem right to me.) If you do find it close to the spot price, it will be in powder form, in a container you had better not break the seal on.

I can’t really recommend it as an investment, the market for it is so small.

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 !!!