This is the sixth in a series. The first one can be found at http://sigma5.blogspot.com/2012/07/50-years-of-science-part-1.html. Part 2 can be found in the August 2012 section of this blog. Parts 3 and 4 can be found in the September 2012 section. Part 5 can be found in the March 2016 section. I take the Isaac Asimov book "The Intelligent Man's Guide to the Physical Sciences" as my baseline for the state of science as it was when he wrote the book (1959 - 1960). More than 50 years have now passed but I am going to stick with the original title anyhow even though it is now slightly inaccurate. In these posts I am reviewing what he reported and examining what has changed since. For this post I am starting with the chapter Asimov titled "The Birth of the Solar System" and then moving to "Of Shape and Size". Both chapters are in his "The Earth" section.
The first chapter under discussion doesn't even mention the Earth. It reviews various theories about the formation of the Solar System. If you want to know what science looks like when Science has only a vague idea of what it is talking about this is a good chapter. This chapter was written at the dawn of the space age. I have talked about the best device for studying the heavens at that time, the 200" Hale telescope, elsewhere. Frankly it was not up to the task of studying the Solar System in the detail necessary to understand it the way we do now. Scientists of that time knew the size and orbital parameters of all the planets. Asimov lists some very important observations that scientists had picked up on by that time.
Nearly all the planets had circular orbits. (Pluto, the only exception, had not yet been demoted from planet-hood back then.) All the planets orbited in a counterclockwise direction (when looking down from a great height above the Earth's North Pole). Nearly all the planets and nearly all the moons known at the time rotated in a counterclockwise direction around axes that were roughly vertical. (There were a few exceptions but they could be explained away as "exceptions that proved the rule"). And with each planet (again excepting Pluto), the ratio between the size of adjacent orbits fell in or near pleasant ratios.
There seemed to be a system to the Solar System. But scientists were pretty much stumped as to what that system was. The best theory at that time was one by Weizsacker. His 1944 theory had serious problems but it was the best anyone had come up with. So what, in the most general sense, was the problem?
There were two problems. The obvious one is the one I have already alluded to. They didn't have much data. The Hale telescope was better than nothing but not that good at making the necessary precision measurements. There were a few satellites in orbit but none of them had a telescope or other good instruments for studying the Solar System. There may have been probes launched toward Venus or Mars (I didn't check) but, if so, they were very primitive fly-by missions. And pretty much nothing was known about the gas giant planets. The first great exploration missions to them, Voyager I and II, would not even launch until 1977. The same was true for missions to the rocky inner planets (Mercury, Venus, and Mars). And the greatest instrument of them all, the Hubble Space Telescope, did not launch until 1990 and it took a couple of years more to fix it. So scientists lacked data.
They also lacked analytical tools. There were some computers around in 1960 but they were small and slow by modern measures, and also few and far between. I personally own three desktop computers. Any one of them was more powerful in terms of speed, RAM, and disk space than all the computers in existence in 1960. This meant that scientists were stuck with literally not much more than the back of an envelope when it came to thoroughly investigating a theory or trying to assess its ramifications.
A good thing to use as an illustration is the orbital spacing I mentioned above. The spacing of the orbits of the planets was known to a medium degree of accuracy. But the idea of "resonance" was not well understood. Imagine two bodies orbiting the same larger body. And imagine their orbits are such that one takes exactly twice as long as the other. This means that over the course of one of the slower orbits each and every combination of relative position will happen exactly twice because the faster body will have orbited twice around and both bodies will end up exactly where they started with respect to each other. Now imagine that there is a certain configuration where the bodies tug on each other, pulling each other in one direction. It turns out because of the complete symmetry of the situation that there is another configuration where they pull in exactly the opposite direction. So over the course of one slow orbit everything exactly balances out. This is called a 2:1 resonance.
Now assume the resonance is slightly more than or less than 2:1. Then a net pull can develop over the course of a complete slow orbit that slows one planet down a little or speeds it up a little. This means that over time the planets will be pulled a little closer together or a little farther apart. In other words, in our 2:1 resonance case the orbits are stable (they don't change at all over time) but in the other case they evolve. Now there are other resonances like 3:2 or 4:3 or whatever. With lots of cheap computer power astronomers are now able run sophisticated long running simulations to discover exactly how things would evolve. The current state of the art now permits very complicated situations to be thoroughly analyzed and understood.
And with this ability astronomers found that there were only a few stable resonances. The rest of the time the planets (or moons) get pulled around, often in complicated ways that could not have been predicted by looking at the equations and doing some simple analysis. The simulations showed that they kept getting pulled around until they hit a stable resonance point, a point that may only have been arrived at after the simulation had covered millions of simulated years. And guess what? The current orbits of the planets are predicted by this resonance point analysis. It was literally impossible to do this kind of analysis before abundant computer power was available cheaply.
The other problem is data. As we sent space missions like Voyager out we were able to gather tons of data that was much more accurate and complete than that available in 1960. This was the information needed to do the resonance point analysis with enough accuracy to give meaningful results. It was literally impossible to make the kinds of detailed calculations necessary unless the parameters put into the simulation were known to a very high degree of accuracy. Those highly accurate values were not known until we had sent spacecraft out exploring.
And this led directly to one of the things that astronomers got wrong at the time. That was the question of the origin of the asteroid belt. The asteroid belt (there are actually several but I am going to concentrate on the main one) consists of a bunch of sub-planet-sized rocks. The leading theory of the time was that something had torn up a small planet. We now know that the asteroid belt is a side effect of these resonances. But the reason we now know this is because we have a lot more data and the data is of much higher quality. We can also simulate the creation or destruction of a single larger body. The simulations can't be made to produce the outcome we now see. But a simulation of a bunch of rocks shows them drifting into the area now occupied by the asteroid belt then getting stuck there.
It wouldn't work if it was just one rock of whatever size. A single rock would be pulled either toward Jupiter or toward Saturn. But a flock of rocks can be stable over long periods of time. At any one time some rocks are pulled in and others are pulled out. But on average and over time, they just stay within the band that is the belt. The average can maintain a behavior (stability) that no individual component is capable of. Individually their orbits are all slightly unstable but this leads to stability at the group level.
And now we have the instruments to study the individual asteroids in the asteroid belt in considerable detail. NASA has recently inserted a space probe directly into the middle of things. The Dawn mission put a spacecraft into orbit around Vesta, a large asteroid. After studying Vesta for several months the probe was moved to Ceres, the largest asteroid. Dawn has returned a massive amount of data about the asteroid belt to supplement what earlier probes discovered.
A couple of decades after 1960 scientists thought they had a good handle on the formation of the Solar System. The idea was that the Sun condensed out of a cloud of gas. This happened precisely 4.567 billion years ago. (They have good reason to believe they know the Sun's age that accurately.) They also think the rest of the Solar System formed a very quickly and a very short time later. It only took a hundred million years, give or take. They are very certain that it was very quick but exactly how quick is not nailed down very well.
And they had a theory which sounded very good about why the various planets with their various compositions ended up where they were and with the composition they did. The theory was that the planets formed in roughly the locations you now see them. The heat of the Sun's radiation was enough to blow the gas out of the inner solar system and into the outer solar system. So you had rocky planets (Mercury, Venus, Earth, Mars) in the inner solar system and gas giants (Jupiter, Saturn, Neptune, Uranus) in the outer solar system. Pluto was assumed to be an asteroid-like thing that got knocked around until it ended up where it ended up. This theory sounded reasonable to everybody and seemed to work very well.
Then it became possible to discover exo-planets, planets orbiting some star other than our Sun. The Kepler spacecraft has found literally thousands of them. And the solar systems around these other suns don't look at all like our solar system does. There are gas giants in the inner solar system all over the place. Lots of gas giants have been found with orbits that are smaller even than Mercury's. What astronomers now know for sure is that don't know.
The common theory for the moment is a hybrid one. Planets formed in their traditional locations. Rocky planets formed close in (they are hard to see if they are orbiting another start so it is no surprise that very few have been discovered). Gas giants formed further out. Then the gas giants migrated (see the discussion of resonance above) into the inner solar system of these other stars. In this theory the fate of the rocky inner planets is unknown. But frankly this is a theory like the ones discussed in this chapter of Asimov's book. It has problems but it is the best scientists currently have. This means scientists expect the theory to undergo drastic modification or even be discarded completely for a quite different one.
"Of Shape and Size" starts with a discussion of the shape of the Earth. It has been known to be roughly spherical for several hundred years now. But some noticed evidence supporting the idea of a spherical shape much further back. But for a long time their evidence did not carry the day. By Newton's time (400 years ago) it was generally accepted that the Earth was spherical in shape. But Newton calculated that gravitational effects should distort it into an oblate spheroid. The French in the 1800s tried and eventually succeeded in confirming Newton's idea. The best number for exactly how far out of round the Earth was in 1960 was 26.7 miles. That is not far off the current number.
We now have much more accurate ways of measuring distance. So we can very accurately measure the distance from a fixed point on the Earth to a satellite. A bunch of these measurements yields a very accurate description of the exact shape of the Earth. It is an oblate spheroid with a number of lumps and bumps on it. The actual shape, even after you smooth out mountains and oceans, is very complicated and I am not going to go into it. And, of course, we have turned the whole "satellite distance" thing around to create the GPS system. GPS satellites need, among other things, a mathematical model of the shape of the Earth. They use a moderately sophisticated one that works well enough to keep our navigation systems on track almost all of the time.
One of the things the French effort brought out, Asimov tells us, is the fact that at the time there was no agreed upon standard of length. Everybody knew approximately how long a yard was but no one knew precisely how long it was. This led to the creation of the "Meter" (French spelling: Metre). It was the distance between two very precisely marked lines on a specific piece of metal. Eventually the "Metric standard" was adopted around the world. Now even the Yard is defined in terms of the Meter. An "Inch" is one 39.34th of a Meter. A "Yard" is 36 inches. It's clumsy but it works.
And this "two marks on a piece of metal" definition of the Meter worked well for more than a hundred years. But scientists kept getting better and better at accurately measuring distances. Soon a more precise specification was required. The laser made it possible to measure the properties of light very precisely. And Einstein said "the speed of light is always and everywhere the same". In 1983 scientists took advantage of this to define a Meter as a certain specific number of oscillations of a certain kind of light as measured under certain very specific conditions. Now a properly equipped laboratory can measure a Meter far more accurately than was possible at any time during the "Meter bar" era.
And this idea of very precisely specifying all the basic units like those of time, weight (actually mass), etc. caught on. The French developed an entire "Metric" system with seconds (a carry over from the old system), Kilograms (a replacement for the pound), etc. Now there is a complex system called the "International System of Units". It is abbreviated as SI based on the French terminology. It also includes things like Volts, Watts, Ohms, etc. for electricity, Joules, Newtons, etc. for forces and work (to replace things like "pounds force", horsepower, etc.), Celsius (originally Centigrade - to replace Fahrenheit degrees of temperature), and so on.
Returning to the problem with the shape of the earth. A trick used then and still in use now was to observe a pendulum. In this case it was used to accurately measure gravity. If gravity was stronger than normal the pendulum would swing too fast. If gravity was weaker than normal the pendulum would swing too slow. This made it possible to measure and map "gravitational anomalies". We are using instruments that can do the job far more accurately now but the mapping of gravitational anomalies is a booming business these days. Geologists can tell a lot from gravitational anomalies (i.e. where there's oil) but there are numerous other applications I am going to skip getting into.
Asimov ends this particular portion of the discussion by noting that prior to 1960 the distance between New York and London was only known to within plus or minus a mile. The techniques I mentioned above (measuring the locations of satellites) was just coming into use as a "by hand" version of GPS. And at the time a lot of the results of this procedure were classified. Why?
After the USSR fell in 1989 it turned out that popular maps issued by the Communists showed the locations of their major cities incorrectly. A typical "error" was say 25 miles. It was not that they were bad at making accurate maps. It was thought instead that they had purposely introduced the errors as an attempt to throw off the aim of western ICBM missiles. Of course, the US had long since switched to the "GPS by hand" method described above, for deciding where to point their ICBMs.
Asimov then moves on to related problems. If you know the precise shape of the Earth you can accurately calculate its volume. Then, if you know its weight (or, more correctly mass) you can calculate its density. But the problem is figuring out its weight. And here is a good time to explain why scientists use mass instead of weight.
If you stand on a scale what is actually being measured is force. A certain amount of force bends a spring a certain amount and that can be used to turn a meter a certain distance. But it is the force that is being measured. But the force depends on how strong gravity is pulling. Scientists wanted to get gravity out of the process. So they decided that matter has an inherent property called "mass". The force generated in a specific gravitational field depends on the mass and on the strength of the field. This let scientists split things into a question of the amount of mass, an amount that is independent of what gravity is or isn't doing, and gravitational force, something that is independent of mass and only depends on what is happening with gravity.
If you are standing still on the surface of the earth then weight and mass can seem like pretty much the same thing. But let's say you are in a car and you haven't fastened your seat belt and your car crashes into a brick wall. Lots of force is involved and it is likely to get you killed if you aren't extremely lucky. But this force has nothing to do with gravity. It has to do with two things. One of them is how fast you are slammed to a stop (very fast). The other is your mass. Remember gravity is not part of the process so "weight" is irrelevant. But mass is mass is mass. It can be accelerated by being operated on by the force gravity, which varies depending on altitude, gravitational anomalies, etc. Or by a car being forced to come to a stop extremely quickly using a process that doesn't involve gravity at all. By going with mass, which is the same no matter what else is going on (I'm ignoring relativity here) scientists can plug the right number for mass on the one hand and force on the other hand into their calculations and end up with the right result.
Back to the mass (or, for civilians, weight) of the earth. The problem is that gravity is everywhere. How do you get outside it so you can measure it? Newton came up with a formula that looked helpful. f = ( G * m-1 * m-2) / d**2. If you knew the value of "f", a force and "d", a distance and if you knew the value of "G", the "gravitational constant" and if you knew the value of m-1 (the mass of one object, say the moon), you could calculate the value of m-2 (the mass of another object, say the earth). This does not look promising. We don't seem to know the value of several of those things. But the formula applies everywhere. So let's go into the laboratory. Here we can measure force ("f") using a spring scale. We can use a ruler to measure distance ("d"). And we can just weigh m-1 and m-2 and use that to calculate the mass of each. That leaves just "G". But the formula then lets us calculate its value. The problem is that "G" turns out to be a very small number. There is so little gravitational force to measure between two normal objects you can find in a laboratory that it seems impossible to do so.
The first one to make a serious and successful run at the problem was Henry Cavendish. If we take a thin wire that is say a foot long and fasten one end to the ceiling we can twist the other end and measure the amount of force involved to twist it say 30 degrees. It's not much but if we use a sensitive spring balance we can measure it. Now it turns out that if we instead use a 30 foot long piece of the same wire it takes only a thirtieth as much force to twist it the same 30 degrees. That's the basic idea.
Cavendish took a long piece of very fine wire that was very easy to twist and performed the appropriate measurements on shorter pieces so he could calculate the force necessary to bend it through a relatively large angle like 30 degrees. Then he put a mirror on it near the bottom and bounced a light off of it from a long ways away (say 50 feet). This allowed him to measure very small changes in twist. Then he put two fairly heavy balls on each end of a rod and hooked the rod to the end of the wire. He made the weights as heavy as he could get away with and he made the rod as long as he could get away with. By connecting the center of the rod to the wire he could balance everything so that the wire would hold it all up.
Then he took two really big weights. They could be very large because the thin wire did not need to hold them up. They could sit on heavy carts on the floor of the laboratory. He brought each ball very close to one of the hanging balls. One heavy ball was on the near side of one hanging ball. The other heavy ball was on the far side of the other hanging ball. He brought them very close but did not let them touch. There should be a small gravitational pull between the heavy ball on the floor and its matching ball hanging on the wire. And there should be a similar gravitational pull pulling in the same direction in the case of the other pair of balls and this should cause the wire to twist. It did by a very small amount. But it was enough for Cavendish measure it and to come up with an accurate value for "G".
As another side note: The University of Washington has been on the forefront of doing these kinds of Cavendish experiments for some time now. Things get very complicated when you are trying to measure "G" very accurately. But they have found ways to overcome these complexities. They have succeeded in measured "G" more accurately than anyone else, even themselves in previous experiments, several times now.
So if we know "G" don't we still have a problem? At this point we know neither m-1 nor m-2 so aren't we still in a pickle? Theoretically yes but actually no. What if we put a hundred pound satellite into circular orbit around the earth. A little calculus (which I am going to skip) tells us what "f" must be. And we can measure "d". So that leaves our two "m"s. But not really. We can calculate "m-1 * m-2" because we have all the other values in the formula. But we also know m-1. It's the mass equivalent of a hundred pounds. And that leaves only m-2, the mass of the earth, as an unknown. Plugging all the other numbers in gives us the value of m-2. If we know the mass of the earth we can go through the same process and get the mass of the moon. We can also use the same process to get the mass of the Sun. To get a rough number we just ignore the moon and the other planets. We need to make adjustments for each celestial body's effect to get a more accurate value.
The adjustments can get complicated but astronomers have figured out how to do it so I am going to leave it there. And we can keep going. With the mass of the Sun we can calculate the mass of Jupiter or Saturn or, . . . It's just a matter of using the basic process then applying the necessary adjustments. The math is complex if you want to get an accurate answer but all we need to know is that it can be done. We can use the mass of one celestial body to "bootstrap" us to the mass of other celestial bodies. These techniques certainly work for the planets. With asteroids there are so many bodies close at hand that in most cases only a rough number can be calculated. This is also true in some other "many body" problems. But as computer power increases more and more complex situations can be handled. Back to Asimov.
He gives us the answer for the density of the Earth. It is 5.5 times as dense as water, on average. If we didn't already know, this would allow us to conclude that the Earth is not composed exclusively of pure water. Okay. It it of uniform density? The answer to that question was already known in 1960. The answer is NO. How did we know this back in 1960? From earthquakes. And that's Asimov's segue into the next chapter. And that's my cue to end this post.
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