It’s commonly taught in school that the Earth orbits the Sun. So what? The unique strength of science is that it’s more than mere received wisdom from the past, taught to us by our elders. If some “fact” in science is really true, we can check it ourselves. Recently I’ve shown you how to verify, in just over a dozen steps, the basics of planetary astronomy; you can
- 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,
- and infer from these laws that the same gravity that makes ordinary objects fall creates an inward acceleration, one that follows an inverse square law, holding certain objects in orbit around the Earth and others in orbit around the Sun.
But important unanswered questions remain. Perhaps the most glaring is this: Does the Earth orbit the Sun, or is it the other way around? Or do they orbit each other around a central point? The Sun’s motion in the sky relative to the stars, which exhibits a yearly cycle, indicates (when combined with evidence that the stars are, on yearly time scales, fixed) that one of these three must be true, at least roughly. But which one is it?
We saw that the Earth satisfies Kepler’s law for objects orbiting the Sun; meanwhile the Sun does not satisfy the similar law for objects orbiting the Earth. This argues that Earth orbits the Sun due to the latter’s gravity, but the logic is circumstantial. Isn’t there something more direct, more obvious or intuitive, that we can appeal to?
I won’t count high-precision telescopic observations that can reveal tiny effects, such as stellar aberration, stellar parallax, and Doppler shifts in light from other stars. They’re great, but very tough for non-experts to verify. Isn’t there a simpler source of evidence for this very basic claim about nature — something we can personally check?
Your thoughts? Comments are open. [Be careful, when making suggestions, that you are not assuming that gravity is the dominant force between the Earth and the Sun. That’s something you have to prove. Are you sure there are no additional forces pinning the Earth in place, and/or keeping the Sun in motion around the Earth? What’s your evidence that they’re absent?]
58 Responses
How about choosing a coordinate system that minimizes the angular momentum? That of course is completely arbitrary choice.
But equally “of course” you still have to assume equality of inertial and gravitational mass, and know the masses.
You could also consider minimizing radiation of gravity waves.
Yes, it makes sense. Its exactly what I was saying.
As to “assume otherwise than a two body system” it assumes the inertial and gravitational mass of Earth are the same. My “initial supposition” was that and that the earth was fixed. If so, you need to have another
body or two to clamp the earth to keep it fixed. I suggested a couple of extremely heavy masses — to provide an inertial frame — coupled to Earth using tongue in cheek things called “turtles” and “strings”. In an earlier post
you did suggest clamping with “dark forces”. I could have said “fake extremely large inertial mass for Earth” instead and my math remains identical. I could have said the turtle strings were tethered to a near-infinite distance near infinite mass “spherical celestial sphere” instead. There’s no gravitational force anywhere inside a hollow shell. Turtles and inequivalent gravitational/inertial masses are equally unlikely. I believe Galileo and Cavendish. I held in my hand my frosh teacher’s gravity measurer that actually had, that very gizmo, replicated Cavendish “well enough” in a public demo (tungsten carbide bricks . I was trying to be funny with the turtles.
I’ll trust Galileo about inertial/gravitational mass equivalence … It need not be very accurate.
My math using the real sun mass simply makes it slow down at the measured distance … which does not fit the data.
I’ll just have read your official method to see how, if any, we disagree.
I’ve been thinking. The usual laws of planetary motion only are exact for
a two body system. Matt, you are asking us to assume otherwise, even for just Earth and Sun.
You want a clamped Earth. For example, we postulate the notion of an invisible, massless, Fermion known as a “turtle”. These attract each other as well as the core of the earth (and only that!) with very stiff harmonic potentials. A “string” of turtles extends out from Earth in both directions for a few light years, where it is tethered to fixed bodies.
This creates an inertial frame in which the Earth is essentially at rest (the string tension is enough that the lateral motion of the Earth is negligible).
But its mass remains the same! The usual formula for two-body motion (m is earth, M sun, mass) and gravity (sun assumed fixed) is (r is vector distance)
m d^2r/dt^2 = -GMm * r / |r|^3
The “m” s cancel. But with the turtles holding the Earth still …. the assumption in the equation becomes that the Earth is still! The Sun is
accellerated around it. The equation becomes
M d^2r/dt^2 = -GMm * r / |r|^3
and the “M”s cancel! The enormous force on the Earth by the Sun
is mostly absorbed by the turtles.
The period is still controlled, for constant distance, by the mass that is still.
So my original supposition otherwise is wrong! An unless I have screwed up,
the whole affair is trivial once the Sun-Earth distance is measured (which you explained) and the mass of Earth is known (which Cavendish did) and G are known. The mass of the orbiting body is unneeded.
If I did screw up … explain? I did calculations assuming that angular momentum is essentially negligible (set to zero), actually just enough to avoid collision, thus avoiding vectors,
Here’s a simpler way to say it: a clamped Earth behaves the same as an Earth of infinite inertial mass but finite gravitational mass. The force between the Sun and Earth remains the same. But the effect of the Sun’s gravity on the Earth now becomes zero (because of the infinite inertial mass). Meanwhile, acceleration of the Sun due to Earth’s gravity is too small (at the Sun’s distance) to keep the Sun orbiting once a year… you can see this from the Kepler-like law for the Earth-Moon system. So to get the correct period, clamping the Earth is not enough; you would also have to boost the pull of the Earth on the Sun, and this could not merely be gravitational without messing up gravity on the Earth and in the Earth-Moon system.
Does that make sense? Also, I’m not sure what you meant by “my original supposition.”
We know that the sun emits photons, a fact that cannot be refuted.
We can simply watch the photons from sunup to sundown as they interact with the atmosphere and calculate their trajectory (as a function of redshift/blueshift) over the course of a month and it will show that the photons trajectory changes, but their origin matches the location of the sun. Only one one explanation for change in trajectory with same origin point, and that’s we’re moving and the sun isn’t, relative to us.
Track that movement for a year and you’ll see the ellipse the sun makes in the sky as out orbit changes. Basic geometry tells you that we’re moving around the sun.. that is if you believe geometry.
The red/blueshift measurement can be done with consumer available equipment/software : https://astronomy.stackexchange.com/a/1399
An interesting suggestion, but it doesn’t work. You can’t tell the difference this way between the Sun orbiting the Earth and the Earth orbiting the Sun. Geometry does not tell you the answer, and the photon trajectories do not distinguish the two options.
Specifically, you wrote: “Only one one explanation for change in trajectory with same origin point, and that’s we’re moving and the sun isn’t, relative to us.” The problem is that you have not established that the photons have the same origin point. You have only established that their origin matches the location of the Sun, but not that the origin is fixed in space.
To say this more clearly: if the Sun orbited the Earth, what *exactly* would be different in the measurements that you have suggested, from the case where the Earth orbits the Sun?
I may have misremembered this, but I always thought this question is unanswerable if you consider the earth alone, but if you include other planets, you quickly find that simple Newtonian mechanics describes the motion of all the planets around one body (the sun) very nicely
This isn’t really true, nor is it really false. We can try to say *whether* the Earth goes round the Sun, and in principle that has nothing to do with Newtonian mechanics, which tells us *why* it does so. As for whether you need multiple planets, that’s also an aesthetic question rather than a simple “whether or not” question. The point of the discussion here is in part to highlight how difficult it is to answer this “whether or not” question without making assumptions.
Matt: what’s YOUR answer to the question of which orbits which, Sun or Earth? (I. e. the proof)
That will be coming soon…
I need to withdraw my comments, since I overlooked the need to have access to the actual surface area (or its radius) before the total power output of the sun can be determined from its spectrum.
Sorry
I’m afraid so; that was what I was alluding to. It’s a good idea to use radiated power, but it just doesn’t work. We only know the power per unit area from the spectrum. As a result, the actual distances scale out of the problem.
You might think, for instance, that measuring the orbital times of Jupiter’s moons would give you an estimate of Jupiter’s mass and radius, and then from its apparent size in the sky you could estimate its distance. But again, everything scales out.
Or how about the fact that the Sun’s tide is about the same size as the Moon’s? Nope. You can estimate the Sun’s density, but not its size or distance; they scale out. (Even the estimate of the density requires discussion, however.)
There is something rather deep in the fact that, for so many questions, the overall distance scales out.
So we really need to find an independent measurement of the size or distance of a planet or the Sun, in order to fix our standard candle or standard ruler. Lots of good ideas involving gravity and light can’t do it. Parallax, where we use the Earth’s size as a standard ruler to fix the length of a triangle, provides a path to success. There aren’t so many others.
Would you prefer I delete your last two messages? I think the idea itself is worth leaving up here, because it’s clever, even though it fails.
I am in two frames of mind about deleting as you suggested. On the one hand, my comments show that I did not think through what I wrote, and that isn’t good for my reputation. On the other hand, I did admit it, without being forced to do so, and making a mistake is only a step towards success, since it shows that the direction taken was not the right one, and that I need to change my approach to the subject. In that sense, from having made the mistake I should get a better grasp on what direction will lead to success – see your comments about parallax.
What I would like to ask you, however, is access to your e-mail address, and this request should be deleted from public view as soon as possible. Why I want it? I have an idea on why quantum physics and general relativity cannot be reconciled into a single theory, and, if that idea holds up, what needs to be done to make them merge into a single one. Unfortunately, I do not have anywhere near the training in physics and mathematics that I need to be sure, thus I need to bounce this idea off a theoretical physicist, since I suspect I might make the same type of mistake as I did here. Would you be willing to critique that idea?
You can find my email address at the Harvard physics department; however I must tell you that I receive about four or five similar ideas each week, and I can’t guarantee I’ll have the time to really look at it. The challenges of the quantum physics and relativity problem tend to be much, much greater than non-experts suppose. String theory does provide a solution, however, so we know *that* it can be solved; and it would be wise to try to understand why string theory succeeds — but the math behind this turns out to be excruciatingly confusing, and so even though we have a solution, understanding it proves extremely challenging. You should probably first make sure your idea addresses this problem: https://profmattstrassler.com/articles-and-posts/relativity-space-astronomy-and-cosmology/black-holes/black-hole-information-paradox-an-introduction/
What do you mean by “Earth goes around the Sun”? In the coordinate system that makes calculations the simplest, then this is true. However, I can construct a coordinate system in a non-inertial frame where the Earth is stationary and the sun is in motion. Maybe we should rephrase the question as “how do we show that the frame of reference where the Earth is in motion around the Sun is the most reasonable choice?”. But I’d then argue that what you label as circumstantial evidence – Kepler’s laws applying for the Earth orbiting the Sun, but not the Sun orbiting the Earth – shows precisely that the heliocentric coordinate system is indeed the most reasonable choice. But I can still ultimately always choose to have a non-inertial frame where the Sun does go around the Earth – it will just have a bunch of epicycles, and so on.
I was quite surprised that it took so long for someone to raise this issue — it is, of course, a central one. “What do we mean by `Earth goes round the Sun?’ ” is a question which we do indeed need to address. The idea that it’s a matter of simplicity, however, isn’t entirely the right answer. Also we have to be careful about notions of inertial frames and coordinate systems when it comes to general relativity… the choice of coordinates is truly arbitrary, and nothing meaningful lies in those coordinates. So our discussion should really transcend the choice of coordinates. What we should ask is this: “What is the *coordinate-independent meaning* of the phrase `Earth goes round the Sun’?”
Any thoughts, folks?
Has anyone considered to treat the sun, and the planets, as black bodies emitting / reflecting black-body radiation? By measuring the spectrum, i.e. the intensity of the light emitted as a function of its wavelength, the surface temperature of the body can be determined, and, once this temperature is known, the energy radiated to earth is determined by the Stefan-Boltzmann law. Knowing the total energy output of the sun, measuring the portion arriving on earth, and some reasonable assumptions about absorption in interplanetary space and earth’s atmosphere, the distance between sun and earth is known, and not just a distance/radius ratio.
When applied to the planets, their spectra obviously do not match the expected black-body radiation, and thus they have to be illuminated by reflected light originating from the sun. Taken that into consideration, the light intensities, together with the angular positions, allow to construct actual positions in space, preferably in a spherical coordinate system. And with actual positions known, it may be shown that the Kopernican reference frame, in which earth and planets rotate around the sun, is much simpler than the Ptolemaian frame in which the earth is the center of rotation. Quod Erat Demonstrandum.
What I have not demonstrated is that a citizen scientist can build, for a reasonable cost, a device that does indeed measure the spectrum of a astronomical body with adequate precision, and thus obtain the surface temperatures of sun and planets using black-body radiation laws, as I had never reason to investigate that. On the other hand, building a photometer to measure the intensities of light reflected by the planets is fairly simple and well within the means of a citizen scientist, if he/she is so inclined.
This is an interesting idea, but I don’t think it is right. First, I think the overall scale of the solar system cannot be determined this way, because when you scale both the distances between objects *and* the size of the sun (and after all we don’t immediately know the sun’s size, just its angular size), the scale of the solar system cancels out. So you still only know ratios of distances using this method. Second, and more serious, the simplicity of the Kopernican reference frame compared to the Ptolmaeic doesn’t imply its accuracy. The question I’ve been raising is not whether a heliocentric solar system looks simpler than a geocentric one; I agree it’s simpler, though the motion of our Moon in a helioentric system is pretty complicated, and one should be humble about that. The issue I’m raising is whether we can directly check that the Earth goes round the Sun, and how. Simply measuring distances precisely doesn’t tell us the answer.
Are we agreed that, starting from the assumption the sun is a black-body radiator and thus that we can deduce, from its spectrum, the power that the sun radiates? Once we are agreed on that, we can treat the sun as what astronomers call a standard candle. We can also measure the power irradiated by the sun onto, say, one square meter of earth’s surface. Then, the sun’s power divided by the power received by one square meter on earth gives us the surface area, in square meters, of a sphere whose radius is the distance between sun and earth. In the same way, after establishing that the planets are illuminated by the sun, and the sun only, we can obtain the sum of the distances (Sun to Planet) + (Planet to Earth) from the power radiated onto the planets and reflected from there toward the earth.
We can also measure the angular positions of sun and planets in the sky, and taken together, we have full coordinates for sun, earth and planets in any coordinate system we may choose. Now, we need to choose which coordinate system we prefer. And here the answer is: we opt for simplicity, and that means we choose spherical coordinates, and we place the origin inside the sun, and let the planets rotate around the sun. End of argument. Rien ne va plus!
Simply measuring distances precisely doesn’t tell us the answer.
Agreed.
But measuring full coordinates, i.e. angles, distances, and time, does change the picture, and that is what I suggest here. But even having full coordinates does not tell us: who circles around whom? To answer that question, we need to assign coordinates to the origin of our preferred coordinate system / reference frame, and that is an arbitrary assignment. To make it non-arbitrary, within the science I have learned this has always meant: Choose the most simple reference frame!
And the most simple system is: Moon circles around earth, earth around the sun, the sun around the center of the milky way, and the milky way around . . .
This last question on center of rotation I need to be left unanswered, because the available data are not accurate enough to decide.
A gyroscope maintains its orientation with respect to any inertial reference frame. An inertial reference frame is one in which objects with no force on them remain at rest or in uniform motion (i.e., moving in a straight line with constant velocity). Here it is Earth’s motion (geodesic is ~ straight line here?) not ‘pinned down’!
Gravitational time dilation not depends on Gravitational potential as believed, but like the difference between orbit of earth around the Sun (year) and the orbit of Moon around the earth (Moonth), in small scale?
The difference in Time shows ‘earth orbit around the Sun”?
/Earth’s daily spin causes the moon – like the sun – to rise in the east and set in the west each day./
Rest-mass (momentum) is conserved with respect to Time dilation (spacetime coordinates?), otherwise we could not talk about BigBang and CMB?
I looked around on the net. I almost have the equipment to detect the 1420 MHz hydrogen line. See
https://www.rtl-sdr.com/cheap-and-easy-hydrogen-line-radio-astronomy-with-a-rtl-sdr-wifi-parabolic-grid-dish-lna-and-sdrsharp/
I’ve got a suitable receiver. I’d just need to get a suitable antenna and the good preamp. With my current antenna and preamp I just checked and
the local noise is a killer where I live, and it looks like a big enough antenna
is infeasible.
It looks like some sources could have their frequency measured to about 50 kHz or a little better. See
https://www.uah.edu/images/administrative/Honors/Papers/v02n1-Friederich.pdf
The Doppler shift difference looks like it would be
about one part in 5000. 1420000kHz/50kHz is 1 part in
28,000 so it looks doable.
I do suspect you’d need a motorized mount to keep the antenna
pointed at the same spot in the galaxy, as different sources have different
Doppler shifts. A bigger dish would of course
increase the S/N and possibly narrow the line by seeing a smaller patch of sky.
There are oodles of people out there who have a suitable motorized
dish. They probably also have the same receiver I do (they are cheap!).
They’d need the preamp and a proper horn for that frequency.
So, the Doppler shift method is for sure doable.
Wow, that’s cool. It shows my biases and blind spots that I hadn’t even thought about doing radio astronomy for this purpose.
Imagine a website with data from someone who tracks a couple of dozen radio sources, measuring them once a month. The correlation between the Doppler shift and the relevant angles on the sky would be pretty convincing; each source would peak and trough at its own time, excepting those to the north and south. That would be a great resource for science teachers. And it sounds as though some of them could actually build their own, if they have access to a radio-quiet valley.
I am surprised that no one mentioned the intuitive fact. Once you know that sun is more than million times as big as earth, it will be indeed astonishing if sun would go around earth. Is this acceptable argument? This also raises a question. Has Kepler telescope observed any large body revolving around a small body?
I’m surprised no one mentioned it either, but there are two issues to address. First, you are assuming conservation of momentum, which is true as long as there is nothing somehow pinning the Earth in space, which is still to be demonstrated. Second, you are assuming size correlates to mass, which is not true. For example, a neutron star with the Sun’s mass would be much smaller than Earth, but the Earth would still orbit it if gravity were the only force holding them together. In fact there are known examples: https://www.science.org/doi/10.1126/science.264.5158.538 . So you first have to prove that the Sun’s mass is larger as well as its size (and do we know how to do that yet?) It’s a remarkable accident that the Sun’s average density is just a bit smaller than Earth’s; its density varies enormously across its interior.
OK! How about this argument?. Once you know sun’s volume is 10^6 times that of earth, you can show that sun has to be much more massive than earth. Suppose sun is entirely made out of hydrogen gas (density 70 kg/m^3) then the ratio of sun’s mass to earth’s mass (taking earth’s density 5500 kg/m^3) comes out to about 12700 in round numbers. So there is no way sun can have smaller mass than earth!
Clever! It has some merit, I agree.
But the sun’s density varies by many orders of magnitude from its center to its atmosphere: https://solarscience.msfc.nasa.gov/images/Dalsgaard1_density_vs_r.jpg …. (and remember there’s an r^2 factor in the differential volume, so much of the Sun has density below what you’re assuming) and thus you are assuming things about the Sun which aren’t true… and that puts you in a dangerous spot.
Moreover, you’re assuming you know the Sun is made largely from hydrogen, which isn’t something you can easily verify. For all you can tell from the outside, until you know a lot of detailed physics and have lots of understanding of fusion, the Sun’s just a hollow shell. So I don’t think you’ll convince someone who’s not already an expert with an argument like this.
On top of that, you’re assuming you know the distance to the Sun and thus its size. How did you measure that? In this sequence of posts that I’ve been putting together, we can so far only put a lower bound on the Sun’s size, at a few times larger than Earth. So unless you have a plan to measure that distance yourself, your conclusion won’t easily follow.
The goal here is to avoid assuming things that we can’t check, and when we have to assume things to make progress, to have a plan to check them later.
Oh, one more comment. About measuring the mass of the sun. I explicitly described how in my first comment. You fit all the bodies in the Solar System
to Newton’s law. This gives all the masses relative to each other. You already explained a good enough distance scale. But Cavendish measured the constant using bodies of known “human sized” mass (presumably in pounds mass). This gave the mass of the earth in pounds mass. Its easy to convert to kilograms. Given the mass of Earth in kilograms gives all the others.
My freshman physics teacher invented and sold (made him rich!) a “breadbox sized” gizmo sensitive enough to measure the gravity of
a ton of tungsten. He demoed in class the difference in gravitational potential between the top and bottom row of seats!
And if you believe in forces that effect only Earth, you must believe in
either magic or religion or (ahemmmmm) supersymmetric dark matter.
As to comets, there’s currently one from outside the solar system still here.
The known ones are not enough for statistics.
🙂 You know, you have to prove the Earth isn’t special. It’s not right to assume it. After all, the Earth is the only object in the solar system from which the two objects that are largest in the sky appear to be the same angular size… that would seem quite special indeed. (What, you believe that’s just an accident? 🙂 ) The whole point of this exercise is to avoid taking things on faith … to avoid basing them on principles (such as a dislike of epicycles) that you cannot check. If a reasonable person can question your assumptions, it is neither fair nor convincing to berate them for their skepticism. If they’re not reasonable, that’s their problem, but one should not lightly accuse people of believing in magic or religion when all they’re doing is forcing you to justify your reasoning. If indeed there are no other forces affecting Earth than gravity, than this should be demonstrable. The fact that Earth satisfies the same Kepler’s law as the other planets is a strong argument, but to close the case, you must show that the Earth actually does orbit the Sun!
For the spectroscopic thing I did (in 1961 for a science fair project) I used a 6 inch reflector with a spectrograph I made myself using a replica transmission grating with 15,000 lines per inch, about 3/4 inch diameter.
It used two “achromatic” lenses with a one foot focal length, onto 2-1/4 x 3-1/4 inch Panatomic X (very fine resolution) film. The film was curved to fit the secondary chromatic aberration. Astigmatism was, of course, immaterial,
and spherical and coma negligible. It used a slit and was guided by hand.
The resolution was good enough that the yellow Na doublet was about
6 or 8 resolution elements apart. That was not quite good enough. Sirius needed a 6 minute exposure. (As an aside: my project won 2nd place …
the prize was a two day visit to Bell Labs at their peak …. we got what was touted as the first “for the regular public” demo of digital audio … little
did we know that that had been used in WWII for audio communications by
FDR using digital one-time pad encryptation encoded on phonograph records!)
For the test of parallax, I used a standard 8″ Schmidt cassegrain with an autoguider. The guiding was inadequate to get small enough images
to get enough precision on faint comparison stars. The images were
plenty sharp enough to measure with the needed precision IF the guiding were good enough AND the seeing good enough … which it never is
anyplace I have lived. And remember that you need years of measurements to get the proper motion measured accurately enough!
But in fact I just realized you’d actually do the needed spectral measurement using a Fabry-Perot inteferometer. Much of my research was done using such things. They are easy to make, just buy the necessary mirrors and any machine shop can make the holders. You just need to choose materials and thicknesses carefully to get zero thermal expansion problems. You could buy a fixed one with an internal fused silica
spacer, just for the line you wanted, but it would cost thousands. I had those too. The yellow one easily had enough resolution for the Na lines, by a factor of maybe 100 or more. Perhaps the commercial filters for the Sun’s Balmer-alpha line would be good enough … I don’t know.
Its a terrible pity, but I was forced by state law to throw all that away when I retired. If you could not promptly give it away to another state school it had to be destroyed. I could only keep what I could put in a display case in my office. The key was “promptly”.
What a shame you had to discard that stuff! I wonder if what’s commercially available nowadays might make the measurement possible for only moderate cost. With all the star-tracking, webcams and computer interfaces that were not available to you when you tried this last, maybe it’s no longer so difficult! If you or any other reader wants to explore this, it would be great to hear if you can see a method by which this could be done.
Dear Prof. Strassler
Thank you for your “from the first principles” astronomy introduction, and the very important and deep question concerning Sun and Earth relative motion.
To resolve the problem we start with the following observation. Any celestial body in orbital motion has its heading and trailing hemispheres. If the body’s own rotation is synchronized with its orbital period (like Moon’s) these hemispheres are fixed, but generally they sweep around the body’s surface. They have two important properties. First, for a test particle approaching the body’s heading hemisphere, their relative velocity is on average greater than for a particle approaching from the trailing hemisphere. This is very much like driving through heavy rain when drops are splashing vigorously against the windshield but not so much against the rear glass. Then, for a celestial body in a ~circular orbit and having its rotation axis ~perpendicular to the orbital plane (like Earth’s), the hemispheres are fixed against the body’s central vector. In case of a luminous central body (like Sun) that implies the hemispheres are fixed against local time. Knowing that observing from the celestial North Pole the Earth rotates and orbits the Sun counter-clockwise we conclude that on the Earth surface points reside in the trailing hemisphere at dusk, and go to the heading one at dawn.
Having established the hemispheres’ properties we may proceed to the main problem. Earlier we found that Solar System’s celestial bodies are overwhelmingly governed by the Sun’s gravity. Those include dust left from comets disintegration which fills the Solar System plane where the Earth rotates. During orbital motion the Earth encounters these grains, and when burning in the atmosphere they shine as meteors, beautiful falling stars. Meteors’ brightness depends on their kinetic energy, which in turn depends on the approaching velocity. Therefore, at dawn meteors are brighter on average than at dusk, and by carefully observing lots of meteors, any person may conclude that the Earth’s orbital velocity is about 30 km/s, consistent with the Earth orbiting the Sun.
Thanks — this is the method that I, too, prefer, though I have some important questions about it. (And I appreciate your thoughtfully reasoned argument.) Even without careful measurements, a person can observe that almost any meteor shower tends to have longer and slower meteors before midnight and faster, shorter meteors after midnight. This is indeed consistent with the argument that the Earth orbits the Sun in the direction of the morning hemisphere. I suppose you are right that one could measure the 30 km/s velocity this way, though that would take some effort. But in any case, I agree that this essential asymmetry — that meteors are typically faster in the morning than in the evening — may naturally be interpreted as due to Earth’s motion around the Sun.
But here’s my question. How do we know this asymmetry doesn’t come from the meteor orbits themselves? If you simply changed coordinates to an Earth-centered system, that’s what would appear to be the cause. Moreover, the orbits *do* have an asymmetry, since their parent comets *do* tend to orbit (on average) in a preferred direction around the Sun.
In short, this argument would be airtight if the origins of comets were from outside the solar system, because then their directions and speeds would not be correlated with the Earth’s motion or the Sun’s motion. But this is not the case, and so there’s a loophole. I’m not sure if it can be convincingly closed. Your thoughts?
Definitely, the dust distribution within the orbital plane is not uniform. Its main source are “dead” comets which almost or completely disintegrated but whose orbits are still being followed by the dust they expel. The dust gradually spreads along the orbit, and when the Earth crosses one of those orbits the meteor “stream” activity happens. As the dust grains share the same orbit and travel on roughly parallel paths, the meteors they produce appear to emerge from a fixed point on the celestial sphere. But also there exist “sporadic” meteors which seemingly comes from random orbits. So to compensate for the non-uniform dust distribution one may take just sporadic meteors into analysis.
The idea of using sporadics is interesting, though it makes the observations a lot harder. During a meteor shower, an ordinary observer can watch the meteor tracks change in just a few hours. Sporadics are sufficiently rare that one might have to put out a camera and try to capture their track lengths and brightness over many days, in order to get enough statistics.
There may also be some meteor showers whose orbits have especially high ellipticity and are sufficiently far from the ecliptic that any influence from the Sun’s possible motion within the ecliptic is mitigated. For them the argument may be more convincing.
Matt: I’ve actually personally tried both parallax and spectroscopic
measurements with 6 and 8 inch telescopes. They were not good enough.
The parallax might be using Alpha Centauri … but would be slow since you also have to measure proper motion.
As to my suggestion: if you calculate in an Earth-centered coordinate system you will get the center of mass of the whole solar system
rotating around in a complicated path … with no force on it. This is equivalent to epicycyles. The only coordinate system without epicycles is the center of mass.
I’m not surprised that parallax was tough. How did you attempt the spectroscopic measurement, and what was the main problem?
I don’t really quite agree about the epicycles. I think that if you assume (a) one gravity force pulls things toward the Sun, and the Earth and Moon carry no charge under that force, and (b) another separate gravity force pulls the Moon and ordinary materials toward the Earth, under which the Sun and other planets are immune, and finally (c) some other more complex force pulls the Sun and the other planets around the Earth, you can kind of cobble together an argument for a universe that’s complicated but not necessarily wrong.
And I believe your argument about the center of mass doesn’t hold, for two reasons. First, how did you measure the mass of the Sun? It’s big, yes, but maybe its density (and that of the planets) is very low. Second, how do you know the Earth isn’t pinned in space by other forces (such as would be exerted, literally, by a pin), so that momentum is not conserved within the solar system’s objects? The point is that if you look closely, there are a lot of assumptions going into your argument, and some of them have not yet been tested in this discussion.
There are always going to be some assumptions in any argument, but we ought to be very careful to lay them out and test the ones that we can’t avoid.
Concerning Earth-pinning modified gravity your suggested. I believe the assumptions can be made more specific as follows. (a) One (ordinary, Keplerian) gravity pulls all Solar System bodies into each other. (b) In the Solar System there exists a pervasive, uniform, non-stationary gravity-like field having such a property that at any moment the acceleration it induces is equal and opposite to the Earth barycenter acceleration relative to the Solar System barycenter’s. The Earth barycenter is postulated stationary, but its acceleration is computed assuming the Solar System barycenter is stationary with no additional fields (“shut up and calculate” approach). The question is how we may disprove existence of such a field. Apparently it may produce Doppler shift mimicking the orbital one through gravitational redshift when photons from distant stars enter the Solar System.
🙂 This is one of the reasons that it’s good to have multiple arguments for anything this important. Any mechanism which can imitate a Doppler shift will have trouble also getting parallax right *and* stellar aberration too, not to mention the meteors… and the relative motion between certain spacecraft and the Earth.
Some additional considerations.
– A field which is pervasive and uniform and non-stationary seemingly violates locality.
– A distant spacecraft going out of the Solar System would be a good probe, but anything within the Solar System would behave identically with or without the field, according to the equivalence principle.
>> – A field which is pervasive and uniform and non-stationary seemingly violates locality.
Anyway, the Keplerian gravity is also non-local, with instant action at a distance.
Are changes in redshifts detectable when measured 6 months apart?
Yes. That’s because atomic emission lines in an earth-based lab stay at a fixed frequency, so you can compare their frequencies in starlight to those in the lab on some chosen day, and then repeat that comparison at any later time that you choose. In fact this method is used, at much higher precision than needed for our current discussion, to detect planets around other stars: e.g. https://www.planetary.org/articles/color-shifting-stars-the-radial-velocity-method
Then I think that could be used to provide good evidence that the earth is moving around the sunor some point inbetween. You’d be able to note that the changes in redshift are strongest when looking perpendicular to the line between the sun and earth and in the plane of the sun’s and/or earth’s motion around the other. It wouldn’t tell you if the sun is also changing its motion as well. So you won’t know if both were going around some point inbetween or if just the earth was moving.
I largely agree. There are some issues, though.
The first is that the shift, in the part per thousand range, is too small for you and I to measure with easily available equipment (though perhaps I’m wrong about this? perhaps modern equipment that can be put on an ordinary layperson’s telescope can address this nowadays? I’d be very interested if someone knows how to do that… and it would be fun to try it out.) That’s why I discounted this option in the post above.
Meanwhile, no websites that I’m aware of provide data to the public that could be used to make this measurement. It’s even hard to find websites that explain how to do this measurement even in principle… which is an egregious omission, I think. There’s more out there about how to discover other planets than there is about how to just check the basics of the Earth’s orbit!
Your point about not being able to check the Sun’s motion is interesting. (Incidentally this issue affects the parallax and stellar aberration methods too.) The Doppler redshift (and a measurement of the speed of light) would tell you the Earth’s speed, and thus the circumference of its yearly orbit, and hence the radius of its orbit. If you knew the Earth-Sun distance, you could compare that to this radius, and if these two distances were essentially the same, you’d know the Sun moves relatively little. So this is doable… but measuring the Earth-Sun distance to better than a factor of 2 with simple methods isn’t easy, and in fact in my do-it-yourself series we haven’t even tried to do it yet.
I don’t think there can possibly be an intuitive answer. If you’re not allowing Newtonian gravity as an assumption, and you’re not allowing precision measurements either, then your hypothetical layman is in the exact same position as a Greek astronomer. They were as smart as us, and they had no obvious reason to prefer heliocentrism over geocentrism. If you look at it historically, heliocentrism did start to gain favor over geocentrism before Newton’s laws came around, but only because their models of the solar system were simpler in aggregate. Knowing that required fitting both models to a huge amount of precise data painstakingly collected over generations.
Thanks for this reply; there’s considerable wisdom in it, and I agree with a lot of it. The one thing you’re potentially leaving out, though, is modern science and technology.
The fact that the Earth spins was also unclear to the Greeks, but (as I discussed in my blog posts on the spinning Earth, linked above) today we can confirm it using the 19th century’s Foucault pendulum (a somewhat confusing demonstration but easily observed) and the 21st century’s gyroscopes (whose workings may be a bit obscure but whose measurements are very clear.) We also have circumstantial evidence from human-launched satellites, which orbit west to east but never east to west.
From this point of view, the question is whether there exists any modern invention or insight, unavailable to the Greeks, which could provide more direct evidence of the Earth’s path around the Sun. I agree that in the absence of some recent (post-1600) addition to human knowledge, we’re no better off than the Greeks, and there’s no way to confirm either that the Earth spins or that it orbits the Sun.
If you allow modern technology, then I think there are lots of ways to do it, but it quickly gets beyond what a layperson can reasonably do themselves. For example, the Earth’s motion leads to annual “wind” effects as we move into and away from various backgrounds (neutrinos, cosmic rays, and the CMB). The latter two are the easiest to observe, but you still need a dedicated apparatus to do it, either a fairly large cosmic ray counter to see the rate fluctuation, or a really good microwave receiver to see the CMB temperature fluctuation. Another option is to use a sensitive gyroscope in space to pick up the precession from the Earth’s orbit around the Sun, but that’s definitely beyond the layperson’s budget.
Right — so this focuses our attention on two possibilities: (1) we find a modern way of observing these “winds” that’s not so hard for a non-expert to verify, or (2) we scientists make it easier for non-experts to access the relevant data, so they can easily follow these “wind” effects. I like these approaches because the concept of a wind is relatively intuitive.
At least cosmic ray muons are easy to observe in a science museum. How large a cosmic ray counter would you actually need, and is there an existing one whose data can be tapped for this purpose? I don’t have intuition for this. [Note added: so far, all of the annual modulation I can find in cosmic rays seems to be dominated by yearly atmospheric effects, not cosmic ray velocities…] Neutrinos will be tough. If we want to use photons, then are CMB photons easier than Doppler measurements of atomic lines from stars…?
The gyroscopic precession effect is probably quite hard to explain.Actually, I’m not sure I understood what you meant here. Did you just mean: point a gyroscope at a star and see that the Earth-Sun line rotates relative to the gyroscope?I don’t think we need to (or can) put everything within a non-expert’s budget. But I think it would be useful to make the information that supports our conclusions more accessible.
if one can measure it, parallax shift of some fixed star indicates the Earth has moved, and since this is repeatable at yearly intervals this shows that Earth is following some sort of closed path. I’m not sure though how to tie this in to orbiting the Sun.
This is certainly correct. Parallax can be observed for a small number of stars, and the pattern of angles and timings in the parallax for these stars can be used, in combination, to confirm the earth goes around the sun. But it requires extremely careful measurements with excellent telescopes, which is why it wasn’t even observed until the 19th century. It’s not the kind of thing that an ordinary person can check. In fact, I’ve never checked it either. Nor, as far as I know, is there any website that provides real-time data or visuals on parallax measurements. It’s all hearsay — plausible to you and to me, but presumably not to everyone. So this is not a very satisfactory situation.
You said we could not assume the law of gravity. But what about actually prove it? You could buy a nice 8″ Schmidt-Cassegrain telescope with
computerized auto-locate. Mount on a fixed pedestal. With that, verify over a couple of years that
it, which uses Newton’s laws, works correctly. This is just a complete version of your previous reasonings. Allow you to assume that the publicly available source code for similar programs uses the same laws and data. Look at it.
I actually have. Write a computer program that integrates Newton’s laws
for the available data on masses and distances. It will fit the source code that fits reality. This verifies all of Newton’s laws except the numerical value of the constant, in kilograms (it would still be relative to the mass of the
Sun or Earth … you’d need a Cavendish experiment too.)
That done, the whole solar system would obviously rotate about its global center of mass, which would be proven to be inside the Sun.
The big great advantage to doing this is that you’d also get, as a side effect, georgous views of celestial objects.
I’m not opposed to this approach, as long as the logic is laid out really carefully, so that a beginner could follow all the steps. I’d be glad to assemble such a step-by-step procedure on this blog at some point. The problem I see with your current proposal is the assertion that gravity controls the motion of the Earth relative to the Sun. Even if gravity controls the other planets around the Sun, and also the Moon and artificial satellites around the Earth, at what step in your procedure do you show that the Earth-Sun system is subject to no forces other than gravity? And if you simply appeal to the orbit that gravity and Newton’s laws of motion predict, the problem is to prove that the Earth actually travels on that orbit, rather than merely appealing to plausibility or simplicity. The argument can’t just be something that you could easily deny by changing coordinates to an Earth-centered coordinate system.
How about using the moons of Jupiter as a clock, and showing from the light-travel-time delays that Earth moves around on a yearly cycle?
That’s clever… but all it shows, I think, is that the Earth-Jupiter-Sun system has a cycle that combines Sun-Jupiter motion with Earth-Sun motion, from which we can extract Jupiter’s year and Earth’s year. We do know already that the Earth and Sun have a yearly cycle (by watching the Sun move across the stars, for one thing), and that Jupiter goes around the Sun. But I don’t think your method can be used to distinguish Sun-around-Earth from Earth-around-Sun… (Just choose coordinates with the Earth at the center and compare that with coordinates that put the Sun at the center; would the calculations of the timing delays be any different? The distances would all be unchanged.)
OK, so pick a clock outside the solar system. I suggest eclipsing binary stars where one component is a white dwarf (to produce a sharp ingress/egress that can be timed accurately). There are dozens of these with periods of order a day (so lots of eclipses to observe), and which have visual magnitudes of V = 10 to 12 (e.g. https://arxiv.org/abs/1310.4863, fig A1). Off-the-shelf amateur equipment (Meade LX200 and a CCD camera) could readily time these accurately enough to discover the Earth’s yearly cycle with 8-minute amplitude. Observing several would show that it must be Earth, not the binary doing that. That would prove that Earth is moving on a yearly cycle, and show a finite light speed, as the only reasonable explanation. (It wouldn’t show what the sun is doing.)
PS I guess one could try arguing that the entire galaxy is anchored to the Sun as it goes round the Earth, producing the same effect . . .
This is on the right track, definitely. There are multiple types of clocks out there in the galaxy and even across the universe; eclipsing binaries, millisecond pulsars, and atomic/molecular emission/absorption lines (which, having frequencies, are clocks too) These provide evidence for changes in Earth’s relative motion on a yearly basis, and are relatively easy to explain.
As you say, amateur astronomers can try to measure some of these things. It’s often difficult, though. The radio astronomy idea that Doug McDonald has suggested here seems feasible. Yours might work too, yes.
Meanwhile, I’d be happy if professional astronomers, who face this effect in all sorts of contexts, would make their data more transparent for this educational use. Usually the professionals subtract the effect of Earth’s motion without ever thinking about it, and so non-experts never get to see it.