A couple of years ago I wrote a series of posts (see below) showing how anyone, with a little work, can verify the main facts about the Earth, Moon, Sun and planets. This kind of “Check-It-Yourself” astronomy isn’t necessary, of course, if you trust the scientists who write science textbooks. But it’s good to know you don’t have to trust them, because you can check it on your own, without special equipment.
The ability to “do it yourself” is what makes science, as a belief system, most robust than most other belief systems, past and present. It also explains why there aren’t widely used but competing scientific doctrines that fundamentally disagree about the basics of, say, the Sun and its planets. Although science, like religion, is captured in texts and teachings that have been around for generations, one doesn’t need to have faith in those books, at least when it comes to facts about how the world works nowadays. The books may be from the past, but most of what they describe can be independently verified now. In many cases, this can be done by ordinary people without special training, as long as they have some guidance as to how to do it. The purpose of the “Check-It-Yourself-Astronomy” series is to provide that guidance.
As I showed, nothing more than pre-university geometry, trigonometry, and algebra, along with some star-gazing and a distant friend or two, is required to
- confirm that the Earth’s a spinning (almost-)sphere,
- estimate the size of the Earth and Moon and the distance between them,
- show the Sun’s larger than the Earth and much further than the Moon, and that the stars are further still,
- verify the other planets orbit the Sun and estimate their relative distances from the Sun and their orbital times,
- infer a relation between these distances and times known as Kepler’s law, and show that a similar Kepler-type law works for objects orbiting the Earth,
- infer from these laws that the same gravity that makes ordinary objects fall does so by creating an inward acceleration, one that follows Newton’s inverse square law, holding certain objects in orbit around the Earth and others in orbit around the Sun
- confirm that the Earth orbits the Sun, by invoking Kepler’s law.
- (Incidentally, this last statement is unambiguous, despite some claims to the contrary, even in Einstein’s theory of gravity.)
However this list is missing something important. From these methods, one can only obtain the ratios of planetary sizes to each other and to the Sun’s size, and the ratios of distances between planets and the Sun. Yet I did not explain how to measure the distance from the Earth to the Sun, or the distance from the Sun to any of the other planets, or the sizes of the other planets. It’s difficult to learn these things without sophisticated equipment and extremely precise measurements; the easiest things to measure about the planets and the Sun — their locations, motions and sizes — aren’t sufficient. (I’ll explain why they’re not sufficient in my next post.)
But shouldn’t there be a way around this problem?
Just One Good Measurement
It shouldn’t be that hard, should it? If we knew any one of these distances or sizes, we could figure out all the others.
For example, in earlier posts we saw how easily one can determine that the ratio of Jupiter’s distance from the Sun to Earth’s distance from the Sun is about 5. [In this paragraph, to keep the argument simple, I use very rough numbers.] Once we learn Earth is about 100 million miles [about 150 million km] from the Sun (which also allows us to compute the Sun’s size), we just multiply this number by 5 to get Jupiter’s distance, about 500 million miles [750 million km] from Earth. That means that Jupiter is about 400 million miles [600 million km] from Earth when the two planets are closest. Then, knowing from a simple backyard telescope that when Jupiter is closest to Earth, and thus 4 times the distance to the Sun, its apparent diameter on the sky is about 1/40 of the Sun’s diameter, we learn that Jupiter’s true diameter is about 4*(1/40) = 1/10 that of the Sun. The same methods can be applied to all the other planets as well as their moons.
However, finding any one of these distances or sizes is challenging for you and me. A simple geometric method used by Aristarchus in classical Greek times can be used by anyone to prove that that the Sun is at least a few million miles away and thus larger than the Earth. (This in turn tells us that Jupiter is far away and that its size is comparable to or larger than Earth.) But this method does not provide a crisp measurement. It can’t distinguish between the true answer of 100 million miles and a distance of several billion or even several trillion miles.
(Note: Later pre-telescope astronomers claimed a measurement that is only a factor of 2 below the true answer. However, it is not clear to me, from what I’ve read of the historical record, if they truly measured the distance or simply bounded it from below using Artistarchus’ approach, and got lucky that their bound is not far from the real answer. Part of the problem is that estimates of uncertainties are a modern invention; the Greek authors just state a value without any recognition that this value might be wildly off [especially on the high end] simply because of the method used. If any readers have additional insight into this, please let me know. In any case, I am currently unaware of any easy and accurate check-it-yourself method that ancient astronomers could have employed.)
In the 1600s and 1700s, the distances to other nearby planets were determined using difficult parallax measurements, in which a planet was observed carefully at two distant locations (or two different times) on Earth. Modern methods often involve firing a strong radar pulse at another planet, Mars or Venus typically; the pulse reflects off that distant planet, and the arrival time of the faint echo, times the known speed of light (also known as the cosmic speed limit, 186000 miles [300000 km] per second), equals twice Earth’s distance to the planet. As I emphasized above, it only takes one such measurement to fix the distances and sizes of all the distant, large objects in the solar system. Unfortunately, none of these techniques is easily reproduced without highly precise measurements and/or fancy equipment.
Nevertheless, it turns out that there are less well-known methods that, via an indirect route, can get us a good estimate of the distance to the Sun, in ways that don’t suffer from the problems of Artistarchus’ approach. This is what I will explain over the next few posts…
14 Responses
A check-it-yourself approach to science might be also the following, notwithstanding its rather “empirical” nature.
It if true that our Earth revolves around the Sun in the slightly elliptical orbit calculated by Astronomers (e=0.017), the image of the Sun as seen from this orbit, should never be the same in size, no matter how tiny its everyday visual variation, impossible to measure unless the Earth is at perihelion and aphelion.
At perihelion, 147 milliion km from the Sun, 1-5 January, the Sun, as seen from the Earth, must appear slightly bigger than when the Earth is at aphelion, 152 million km from the Sun, 2-5 July, its farthest point from the Sun.
Comparing the two images we can check ourselves the apparent difference in size of the Sun, as seen from the Earth, a fact that confirms the (not perfectly circular) revolving motion of the Earth around the Sun.
Visual evidence. The difference is clearly shown by the accurate comparison of two photos of the Sun, respectively at perihelion and at aphelion, taken by dr. Peter Lowenstein, retired geochemist and skillful photographer. Dr. Lowenstein has taken the two photos, because of weather conditions just a few days from a perihelion, in Jan 2016, and from an aphelion , in July 2017. Then he has created a “composite image”superimposing one photo to the other. The “composite image” shows “unmistakably” the size difference of the Sun as viewed from the Earth, across our yearly orbit. You notice a “grey rim around the sun”, actually the perihelion photo on which the aphelion one has been superimposed. The presence of the rim shows that, as seen in our sky, “the sun is about 3.6 per cent bigger at perihelion than aphelion, a difference impossible to be dectected with the eye” (Here’s how much smaller the sun looks at aphelion/Today’s image, published by earthsky.org/todays-image/composite-image-size-of-sun-aphelion-perihelion, 2 pages, published on 9 July 2018).
Paolo Pasqualucci
Thanks! This is is a very nice way, and probably the only relatively simple way, to prove that the Earth’s orbital distance isn’t constant. It’s still quite tricky to do, though, because the ellipticity is small.
There might be another way to do it using the flux of solar energy hitting the Earth, but that has a lot of tricky issues that dramatically complicate the measurement.
Kepler’s original method is a tour-de-force of scientific creativity. Even Einstein called it a work of “genius.” https://galileoandeinstein.phys.virginia.edu/1995/lectures/morekepl.html
Tycho Brahe used naked-eye observations to estimate the solar eccentricity – he observed the midday altitude of the Sun over the year “using his large mural quadrant firmly affixed to an inside wall of his castle.” He actually derived an atmospheric refraction table to improve his residuals. However, he always used a much too small historical estimate for the astronomical unit – about 1/20th of the correct value – and his naked eye data weren’t good enough to determine the diurnal parallax and correct that.
Thank you Prof. Strassler for your appreciation and for suggesting the text on Kepler, which I have read with great interest and profit.
Paolo Pasqualucci
Speaking of “check-it-yourself science”, what is the best way to use AI in science and “of particular significance”, particle physics?
PS: Will you be updating us on the Fermilab g-2 muon experiment? What’s the chance they find a “fifth force”? Assuming they do, could that indicate that a theory can be produced that uses forces as the depended variables to construct a unfied theory?
Happy New Year.
I don’t have anything to say about AI because there’s too much to say and it is a moving target. At some level, particle physicists have been using low-level AI for a decade. It is used more and more all the time. But it’s not a game-changer yet.
At some point I’ll probably give an update on the g-2 muon experiment. But I doubt it represents a discovery of something beyond the Standard Model, because there are disputes about what the Standard Model actually predicts. When those disputes settle, we’ll see.
Even if there’s something there, the chance they will find a fifth force is nil. The experiment is not designed to do that. All they can do is measure g and show that its difference from 2 is not what was expected. They might, if we are very lucky, be giving a hint of something that later, after other experiments in the coming decades, we will recognize as a new force. [Note this would really be the sixth force, since the Higgs force, not yet measured but known to exist, is already number 5 — something journalists and many physicists forget.]
> Nevertheless, it turns out that there are less well-known methods that, via an indirect route, can get us a good estimate of the distance to the Sun..
Speed of light plus the time skew of the observed orbits of the Jovian moons?
Yes, that will work. Historically, the distance to Mars (and thus the distance scale) was measured first by Cassini with the assistance of Richter in 1672, and then Romer, noticing unexpected time delays for Jupiter’s moons, and now knowing (thanks to Cassini) the distance to Jupiter, derived the speed of light in 1676 from those time delays.
Today, knowing the speed of light from laboratory measurements, one could now turn it around, and the time delays of Jupiter’s moons can now be used to measure the distance to Jupiter. But this takes a lot of work to map out the expected timings of the moons, to recognize the presence of delays, and measure those delays.
Great Insights..Thanks