Is there an experimental proof that an Earth/Moon barycenter exists?

[Ron Hargrove]

TL;DR Summary

Is there historic observable or experimental proof of the existence of an Earth/Moon barycenter or is its existence just assumed?

I am having difficulty located experimental or observational proof that a barycenter exists between the Earth and Moon. All I can find seems to just assume that a barycenter exists because the Moon revolves around the Earth based on the assumption that the Earth and Moon are tied as a unit with gravity between the two as a constraining force. There must be some observed prograde and retrograde movements of planets or other bodies that prove a barycenter exists. But all I am seeing is that the parallax would be too small to measure, which I find hard to believe with the scientific instruments that we have available. Does anyone know of historical experimental or observable PROOF that a barycenter exists?

 

[PeroK]

The barycentre is the centre of mass. How can there not be one?

 

[phinds]

"barycenter" is DEFINED as a mathematical point, so the concept of "proving" that one exists between two objects that orbit each other seems ridiculous. You don't "prove" a definition. Finding exactly where it IS, to a great degree of precision, might be interesting but I'm sure it's already been done (and it will vary over time since the orbits are not circles)

 

[Bandersnatch]

Let's rephrase the question to: what observations require the motion of the Earth around the E-M barycentre to be taken into account.
The gist is the same, but it sounds less like the OP disbelieves that things have centre of mass, and it might garner some more concrete answers.

I kinda wonder if this shows up in ephemerides, or if the effect is too small to measure.

 

[sophiecentaur]

if the effect is too small to measure.

I think that's very likely. An almost circular motion of the Earth around the barycentre at such a low frequency. What would you actually measure? Doppler shift relative to light from a star? Gravity waves?
I hope the OP has no real doubts about the CM of two bodies and the consequent motion. That would change how we could look at his(?) question.

 

[Bandersnatch]

What would you actually measure?

I did refer to ephemerides, so additional parallax of solar system objects over half a month of orbit.

 

[OmCheeto]

Interesting question.
Someone answering questions at NASA, when asked this said; "I don't know." [ref]
The answerer also states; "Of course, the motion of the Moon and the Earth and is really a three-body problem, also involving the Sun. It is extremely complicated: low-precision equations for describing the motion have about 30 coefficients" {bolding theirs}

Off the top of my head, I would have guessed it wouldn't be that complicated. But that's probably because I have no idea what is involved in solving a three-body problem.

Anyways, I think it would be an interesting maths problem.

Numbers I've collected so far:

The Earth-Moon barycenter is (supposedly) 4.671 million meters from earth’s center​

Earth's radius is 6.378 million meters​

Initial doodle:

And can I measure that with my 76mm reflecting telescope?

 

[sophiecentaur]

I did refer to ephemerides, so additional parallax of solar system objects over half a month of orbit.

Would that be measurable? Actually, the shift in Earth's position is not that much less than its diameter so maybe not so daft after all. A few thousand km relative to a distance of a few hundred million km. That's around 10^-5 radians which is no problem for astronomers. Edit: well, errr measuring stellar distances in parsecs relies on the full AU.
But I see @OmCheeto has beaten me to it and Mars would be the obvious choice.

 

[Vanadium 50]

Once again, we're down the PF rabbit hole of "guess what the OP must have meant", which is often followed by "argue about what the OP must have meant". Maybe we should wait for him to clarify?

 

[phinds]

Maybe we should wait for him to clarify?

Nah ... we NEVER do that

 

[Ron Hargrove]

Sorry that I was not clearer.

I am looking for proof that gravity is an internal pulling force between the Earth and the Moon that is locking them together and causing them to rotate as a unit around the barycenter of the two masses. I cannot find a single example of someone proving that the barycenter exists, only the assumption that the barycenter exists based on the fact that the moon orbits the Earth and the assumption that a gravitational pulling force exists between the two masses without proving same. If a barycenter can be proven to exist that would clinch the notion that the orbit of the Moon is inextricably tied to the Earth through the force of gravity which must be an internal pulling force between the two bodies. If it does not exist, there must be some other force involved.

Doing a quick Google search, it would appear that if there is an actual barycenter of rotation it would be calculated to be 4,761 kilometers from the center of the Earth or roughly 3/4 the distance to the surface. It just seems to me that if the Earth was wobbling about a secondary axis far out of line with the spin axis that is that close to the surface the secondary rotation should be felt more significantly, the planets' paths should show some kind of measurable prograde and retrograde, or the Earth's axis should not remain constantly pointed at Polaris as a result. My concern is that the Earth and Moon are assumed to be locked together through an internal pull force and traveling though space rotating around a common barycenter without anyone proving this is to be true.

 

[DaveC426913]

Sorry that I was not clearer.

I am looking for proof that gravity is an internal pulling force between the Earth and the Moon that is locking them together and causing them to rotate as a unit around the barycenter of the two masses. I cannot find a single example of someone proving that the barycenter exists, only the assumption that the barycenter exists

See phinds post 3. The Earth rotates around a point (at least, ideally) . We know this.

The question you seem to want to ask is "is the point about which the Earth rotates somewhere other than its centre of mass?"

If a barycenter can be proven to exist that would clinch the notion that the orbit of the Moon is inextricably tied to the Earth through the force of gravity which must be an internal pulling force between the two bodies.

The notion is clinched.

Newtonian gravity requires that two bodies revolving around each other have a common centre of mass.

If it does not exist, there must be some other force involved.

You are proposing an alternate force? Is there any evidence to suggest it is needed?

Note that, if you go down this road, this thread will surely be moved out of the A&A forum (and possibly locked).

It just seems to me that if the Earth was wobbling about a secondary axis far out of line with the spin axis that is that close to the surface the secondary rotation should be felt more significantly...

Earth - and every particle on it - including you and me - are also moving about that centre. So nothing to feel.

 

[Ron Hargrove]

My question is merely has it been PROVED or is it just a universal assumption?

"Newtonian gravity requires that two bodies revolving around each other have a common centre of mass." -only if gravity is proven to be a pulling force between the two bodies that forms the bond.

 

[phinds]

My question is merely has it been PROVED or is it just a universal assumption?

AGAIN, re-read post #3.

Also, you are stuck in Newtonian gravity, which, while quite accurate on a slow-moving, low-gravity system such as the Earth/moon, is NOT an actual description of reality. General Relativity is the actual description of reality (*), although on a slow-moving, low-gravity system such as the Earth/moon, you'd likely have to do computations out to 10 decimal places (maybe less) before you saw any difference. Anyway, in GR, gravity is NOT a force it is the geometry of space-time and yes, the Earth and the moon are tied together. The moon travels on a geodesic that keeps it in orbit around the Earth (or, to be completely accurate, keeps the Earth/moon system rotating about the barycenter).

I just don't get why you have so much trouble with the concept that the Earth and moon are tied together.

* Newtonian Gravity is GR out to a good many decimal places for slow-moving, low-gravity systems.

 

[russ_watters]

Sorry that I was not clearer.

I am looking for proof that gravity is an internal pulling force between the Earth and the Moon that is locking them together and causing them to rotate as a unit around the barycenter of the two masses. I cannot find a single example of someone proving that the barycenter exists, only the assumption that the barycenter exists based on the fact that the moon orbits the Earth and the assumption that a gravitational pulling force exists between the two masses without proving same. If a barycenter can be proven to exist that would clinch the notion that the orbit of the Moon is inextricably tied to the Earth through the force of gravity which must be an internal pulling force between the two bodies. If it does not exist, there must be some other force involved.

Doing a quick Google search, it would appear that if there is an actual barycenter of rotation it would be calculated to be 4,761 kilometers from the center of the Earth or roughly 3/4 the distance to the surface. It just seems to me that if the Earth was wobbling about a secondary axis far out of line with the spin axis that is that close to the surface the secondary rotation should be felt more significantly, the planets' paths should show some kind of measurable prograde and retrograde, or the Earth's axis should not remain constantly pointed at Polaris as a result. My concern is that the Earth and Moon are assumed to be locked together through an internal pull force and traveling though space rotating around a common barycenter without anyone proving this is to be true.

Well this is much weirder than I guessed after reading the OP. You don't need to measure (not prove) the location of the barycenter to prove the gravitational link. The observed motion of the moon over the course of a month proves the gravitational link.

Note that for objects that are closer together in mass, it is easier to measure the location of the barycenter because the larger object moves more.

 

[Ron Hargrove]

My problem with our current understanding of gravity started with that blasted simulation of the mass of the Earth warping space/time to create gravity. You know the one. It looks like a bowling ball on a sheet of rubber with a satellite falling into the well that creates an orbit around the bowling ball. I have at least two problems with this:

The first is how this scenario would allow satellites to orbit in something other than an equilateral plane around the mass depending upon their weight when they fell into the well. The heavier the satellite the lower in the well they would orbit. Which does not relate to the real world since all orbits around the Earth can only occur when the orbit is centered over the mass of the planet. You cannot have a satellite orbiting above the tropic of Capricorn, for example. Which could happen with the simulation mentioned previously.

The second is the fact that the planet is shown with its weight applying force downward to create the well and downward only. How can you explain the downward pull of gravity toward the center of a planet-sized object by starting off with an unexplained downward force? Sure, this scenario MIGHT explain an equilateral orbit of a satellite of the exact weight and speed required for the weight of the mass on the rubber space/time rubber sheet, but it cannot explain how a 90 degree opposed polar orbit of another satellite can be occurring at the same time. The only way that this could work is if the mass of the Earth was applying a force equal to its mass warping space/time in all directions simultaneously with none of the forces of one direction interfering with any of the forces in any other direction. Which would mean that the Earth would have to have infinite weight being applied in infinite directions to explain how any satellite can orbit the Earth on any given plane as a result which simply is not correct. I have no idea how the mass of the Earth on this space/time-warped plane would adjust itself to accommodate thousands of satellites of any weight from a piece of debris to the Moon in order to have a perfect equilateral orbit around the earth.

In any case, my question is simple: does anyone know of any experiments or observations that PROVE the Earth and Moon rotate around a barycenter? Yes or no?

 

[russ_watters]

You are proposing an alternate force? Is there any evidence to suggest it is needed?

Let me expand: if the current math/explanation works, then there is no need for an alternate one, and nothing for it to "do". It would have to match the success of the current one.

 

[phinds]

My problem with our current understanding of gravity started with that blasted simulation of the mass of the Earth warping space/time to create gravity. You know the one. It looks like a bowling ball on a sheet of rubber with a satellite falling into the well that creates an orbit around the bowling ball. I have at least two problems with this:

The first is how this scenario would allow satellites to orbit in something other than an equilateral plane around the mass depending upon their weight when they fell into the well. The heavier the satellite the lower in the well they would orbit. Which does not relate to the real world since all orbits around the Earth can only occur when the orbit is centered over the mass of the planet. You cannot have a satellite orbiting above the tropic of Capricorn, for example. Which could happen with the simulation mentioned previously.

The second is the fact that the planet is shown with its weight applying force downward to create the well and downward only. How can you explain the downward pull of gravity toward the center of a planet-sized object by starting off with an unexplained downward force? Sure, this scenario MIGHT explain an equilateral orbit of a satellite of the exact weight and speed required for the weight of the mass on the rubber space/time rubber sheet, but it cannot explain how a 90 degree opposed polar orbit of another satellite can be occurring at the same time. The only way that this could work is if the mass of the Earth was applying a force equal to its mass warping space/time in all directions simultaneously with none of the forces of one direction interfering with any of the forces in any other direction. Which would mean that the Earth would have to have infinite weight being applied in infinite directions to explain how any satellite can orbit the Earth on any given plane as a result which simply is not correct. I have no idea how the mass of the Earth on this space/time-warped plane would adjust itself to accommodate thousands of satellites of any weight from a piece of debris to the Moon in order to have a perfect equilateral orbit around the earth.

In any case, my question is simple: does anyone know of any experiments or observations that PROVE the Earth and Moon rotate around a barycenter? Yes or no?

Apparently you are not interested in listening to what you are being told. That raises the question of why you have brought the question to a forum where people are giving you an explanation of your issue since you are indifferent to our answers.

 

[russ_watters]

My problem with our current understanding of gravity started with that blasted simulation of the mass of the Earth warping space/time to create gravity. You know the one. It looks like a bowling ball on a sheet of rubber with a satellite falling into the well that creates an orbit around the bowling ball. I have at least two problems with this:

The first is how this scenario would allow satellites to orbit in something other than an equilateral plane around the mass depending upon their weight when they fell into the well.

It's an analogy and you are over-applying it. It isn't 2-dimensional it is 3-dimensional, but personally I can't envision a 3-D rubber sheet.

In any case, my question is simple: does anyone know of any experiments or observations that PROVE the Earth and Moon rotate around a barycenter? Yes or no?

The answer is "no", but mostly because you are misusing the word "prove", so I don't see this as a useful question/answer.

 

[Ron Hargrove]

Apparently you are not interested in listening to what you are being told. That raises the question of why you have brought the question to a forum where people are giving you an explanation of your issue since you are indifferent to our answers.

You are giving explanations for a question that was not asked. I did not ask how gravity works, general relativity, Newtonian gravity, or theorem. I am merely asking for my own research purposes if anyone is aware of any experiments that prove the existence of what is a universally accepted barycenter of an EM rotation which I have been unable to locate on my own. No more, no less.

 

[Klystron]

If you accept Kepler's laws of planetary motion , for example for the Earth revolving around the Sun; the Sun is at a focal point of the ellipse, not at the center of the ellipse.

If you work through Kepler's equations updated by Newton and still require more "proof" of orbital mechanics, consider Earth-Moon tides or the lunar tidal bulge to enhance understanding. This encyclopedia entry demonstrates the Earth-Moon center of mass using tidal data.

In the case of an infinitesimally small elastic sphere, the effect of a tidal force is to distort the shape of the body without any change in volume. The sphere becomes an ellipsoid with two bulges, pointing towards and away from the other body. Larger objects distort into an ovoid, and are slightly compressed, which is what happens to the Earth's oceans under the action of the Moon. The Earth and Moon rotate about their common center of mass or barycenter, and their gravitational attraction provides the centripetal force necessary to maintain this motion. To an observer on the Earth, very close to this barycenter, the situation is one of the Earth as body 1 acted upon by the gravity of the Moon as body 2. All parts of the Earth are subject to the Moon's gravitational forces, causing the water in the oceans to redistribute, forming bulges on the sides near the Moon and far from the Moon.[8]

 

[hutchphd]

Does @Ron Hargrove believe that one could launch a spacecraft from Earth orbit to within 100 km of the limb of the moon without understanding where the "barycenter" is ??

 

[phinds]

Does @Ron Hargrove believe that one could launch a spacecraft from Earth orbit to within 100 km of the limb of the moon without understanding where the "barycenter" is ??

Yes, but he is on some weird quixotic quest to get someone to PROVE that the barycenter exists.

 

[Ron Hargrove]

I see that the answer is no. Sorry to have bothered you all.

 

[russ_watters]

I see that the answer is no. Sorry to have bothered you all.

I hope we helped, but I'm not sure we did. Good luck to you.

 

[Ron Hargrove]

The root of the matter is in the universal acceptance of Newton's law of universal gravitation which, to simplify, pulls objects toward the center of the Earth and that all objects with mass attract each other. This argument may be fundamentally flawed. I and at least one other Mensan in my local group (yes, I am a member) have been pondering whether or not gravitation is actually a 'push' force and not a 'pull' force. Hence my need to find out whether or not it has been proved that an EM barycenter exists in order to prove myself wrong.

The only thing I am seeing that we don't have the technology to detect it and that I should just accept that it is there without proof just like everyone else. Which is bogus.

 

[romsofia]

https://en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment

 

[hutchphd]

In your mensa group has anyone defined what is required to "prove" the existence of a barycenter? Operationally it is not clear to me how such a proof would be undertaken to your satisfaction.

 

[russ_watters]

The root of the matter is in the universal acceptance of Newton's law of universal gravitation which, to simplify, pulls objects toward the center of the Earth and that all objects with mass attract each other. This argument may be fundamentally flawed. I and at least one other Mensan in my local group (yes, I am a member) have been pondering whether or not gravitation is actually a 'push' force and not a 'pull' force.

Frankly, I would have expected a Mensa group to include people who understood basic physics and the well known dead-end that is push-gravity.

The only thing I am seeing that we don't have the technology to detect it and that I should just accept that it is there without proof just like everyone else. Which is bogus.

Frankly, I would have expected a Mensa group to understand how limited and pointless of a request the measurement of the Earth-Moon barycenter is...and of course someone in the group to understand the scientific method itself, and teach it to the rest of you.

If this is representative of Mesa, I'm not impressed.

 

[Tom.G]

-only if gravity is proven to be a pulling force between the two bodies that forms the bond.

The Ocean tides are a pretty good detector of that.

And Henry Cavendish measured it over 220 years ago (https://en.wikipedia.org/wiki/Cavendish_experiment)

Cheers,
Tom

 

[Nugatory]

In any case, my question is simple: does anyone know of any experiments or observations that PROVE the Earth and Moon rotate around a barycenter? Yes or no?

@romsofia has pointed you at the lunar ranging measurements and @hutchphd has pointed out that we have successfully navigated spacecraft from the surface of the Earth to where the surface of the moon will be if the two bodies are orbiting their barycenter.

 

[Bandersnatch]

Yeah, so this does definitely show in ephemerides, since ignoring the barycentric motion when measuring parallax of a hypothetical stationary object at 10 AU over the base of a fortnight's worth of orbit would introduce an error on the order of 1 arcsecond vs ~miliarcsec or better accuracy of modern ephemerides.

So each time anyone uses ephemeris tables (or software, these days) to point their telescope at a solar system object and find it where it's supposed to be, they provide evidence of the kind required by the OP.
Whether this will be accepted as such by the OP is another matter.

 

[Orodruin]

Frankly, I would have expected a Mensa group to include people who understood basic physics and the well known dead-end that is push-gravity.

Frankly, I would have expected a Mensa group to understand how limited and pointless of a request the measurement of the Earth-Moon barycenter is...and of course someone in the group to understand the scientific method itself, and teach it to the rest of you.

If this is representative of Mesa, I'm not impressed.

My personal experience (that admittedly is over 20 years old) is that it is representative. I was a member for a year or so, but most people I interacted with and the local monthly publication gave the impression of people who somehow thought that having a (relatively) high tested IQ (it is not *that* high) made them superior and that any thoghts they had on things they were ignorant about would be pure gold.

 

[Orodruin]

My problem with our current understanding of gravity started with that blasted simulation of the mass of the Earth warping space/time to create gravity. You know the one. It looks like a bowling ball on a sheet of rubber with a satellite falling into the well that creates an orbit around the bowling ball. I have at least two problems with this:

The first is how this scenario would allow satellites to orbit in something other than an equilateral plane around the mass depending upon their weight when they fell into the well. The heavier the satellite the lower in the well they would orbit. Which does not relate to the real world since all orbits around the Earth can only occur when the orbit is centered over the mass of the planet. You cannot have a satellite orbiting above the tropic of Capricorn, for example. Which could happen with the simulation mentioned previously.

Ok, I am going to be pretty blunt, but I think it is necessary here:

So, you have made a number of serious errors here. First of all, the image you are talking about is not a simulation - it is an illustration. Second, it has nothing at all to do with Newtonian gravity - it is an analogue used to popularize general relativity. Third, it is, as most popularizations, an oversimplified image - it has very little to do with the actual description of gravity in GR, it just illustrates curved space. Fourth, you have taken this popularized image way too literally and made your argument based on this.

Each of these errors is a direct killer for any serious argument being made. If you want to have any chance of making a serious argument you need to learn what the theory you are trying to disprove is actually saying, not base your argument on a popularized image from which you have made erroneous extrapolations about what the theory actually says.

 

[PeroK]

The only thing I am seeing that we don't have the technology to detect it and that I should just accept that it is there without proof just like everyone else. Which is bogus.

The barycentre of any system of particles is not a physical thing. You can't detect it. You can measure where each particle in the system is, measure the mass of every particle in the system and then compute where the barycentre is. For example, if you and your friend drive your cars around, then the barycentre of that two-body system will be roughly half-way between your cars (assuming they are of approximately equal mass). But, no one is going to be able to stand by the side of a motorway and "detect" the barycentre of that system! What would they detect that would tell them that a point on the road is half-way between your cars? Every pair of cars (every pair of objects) has a barycentre. How would they distinguish one "detected" barycentre from another?

In short, the barycentre is a geometrically defined point in space, but there is nothing there to identify it as such. It doesn't exist, because it is purely geometrically defined. There is nothing physical at the barycentre.

I was recently looking at a problem involving the orbit of Mercury round the Sun. All the data is there:

https://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury

No one is asking you to believe that Mercury orbits the Sun in an ellipse without proof. The data has been maintained for centuries. But, the ellipse precesses to a degree that the Newtonian model cannot explain. The Newtonian model almost exactly predicts the relative position of the planets of the Solar system over time. But, there was always a doubt over the precession of Mercury. In a way you can't ask for more than that. That is the way science works. That is the way physics is done.

And, of course, General Relativity trumps Newtonian gravity by predicting the additional observed precession of Mercury. That is the way science progresses.