# Prove that the earth goes around the sun

## Main Question or Discussion Point

I find it obvious, as did many previous people, that the sun goes aroudn the earth. I of course know htis to be untrue as it has been drummed into me again and again for the past 16 years.

Can someone please prove to me (so that i can prove to others as well) that the earth goes around the sun. Do not be afraid to explain using mathematics, as i see that as the only way of undeniable proof.

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The parallax proof - empirical

The first person who had experimental evidence for this was the astronomer F.W. Bessel who in 1838 was able to measure the parallax of a nearby star. This showed that the earth was at a different place, relative to the star, in June than it was in January. And geometry showed that the two places were on opposite sides of the sun. More parallax measurements since his time have confirmed that the earth follows a closed path around the sun.

Phobos
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Welcome to Physics Forums, rattis.

It certainly looks like it, doesn't it? But looks can be deceiving.

The "aberration of starlight" was the definitive proof of the heliocentric solar system.
http://www.encyclopedia.com/html/a1/aberstrlt.asp [Broken]

And then there's all the spacecraft we send around the solar system which (1) successfully reach their destinations based on a heliocentric model of the solar system and (2) take photographs showing the sun at the center.

If you accept the values for the mass of the Earth and Sun, then the laws of gravity & planetary motion show you that the orbit around the common center of mass is near the center of the sun, not the Earth.

There are other evidences too...

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Zero
You can start with basic gravitational theory, throw in a little bit of ballistics and orbital mechanics, and of course our successful navigation of craft through the solar system, all of which show conclusively that the earth orbits the sun.

I thought the doctrine of Galilean relativity asserted that we couldn't know which orbited which. The maths is a lot easier in a heliocentric solar system, but that doesn't in itself entail that it is one. Surely all we know is that a heliocentric solar system is a very useful assumption? Or is this nonsense?

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Zero
Originally posted by Canute
I thought the doctrine of Galilean relativity asserted that we couldn't know which orbited which. The maths is a lot easier in a heliocentric solar system, but that doesn't in itself entail that it is one. Surely all we know is that a heliocentric solar system is a very useful assumption? Or is this nonsense?
Just because it is a useful assumption, that does not mean it is nonsense. If both views are assumptions, but one is more useful and practical, guess which one we should go with?

Plus, of course, I'm not sure if Galilean relativity even applies?

And then there's all the spacecraft we send around the solar system which (1) successfully reach their destinations based on a heliocentric model of the solar system and (2) take photographs showing the sun at the center.
well yes, but i dont know if the spacecarft have every acctually gone into space or if it is just a con by government (worse case sinario).

Can i see some mathematical proof that the earth does infact go around the sun?. Like i say the only proof i have at the moment is that i can see the sun move around the earth everyday, but this is not the case as everyone says.

I am not an astronomer but mathematician, so im not sure if this whould be in the maths section

just edited to fix quote tag - Phobos

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Zero
Originally posted by rattis
And then there's all the spacecraft we send around the solar system which (1) successfully reach their destinations based on a heliocentric model of the solar system and (2) take photographs showing the sun at the center.
well yes, but i dont know if the spacecarft have every acctually gone into space or if it is just a con by government (worse case sinario).

Can i see some mathematical proof that the earth does infact go around the sun?. Like i say the only proof i have at the moment is that i can see the sun move around the earth everyday, but this is not the case as everyone says.

I am not an astronomer but mathematician, so im not sure if this whould be in the maths section
You may as well give up, if you have to try to account for people who think the entire space program is a lie...

Originally posted by Zero
Just because it is a useful assumption, that does not mean it is nonsense.
I didn't suggest that the assumption was nonsense. I was wondering if what I said was nonsense.

but one is more useful and practical, guess which one we should go with?
No argument - but it's not really relevant.

Plus, of course, I'm not sure if Galilean relativity even applies? [/B]
No I'm not either, that's what I'm checking. But I can't immediately see why not, it's relative motion after all.

Phobos
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Originally posted by Canute
I thought the doctrine of Galilean relativity asserted that we couldn't know which orbited which. The maths is a lot easier in a heliocentric solar system, but that doesn't in itself entail that it is one. Surely all we know is that a heliocentric solar system is a very useful assumption? Or is this nonsense?
At the time of/preceding Galileo, you could model it (the motion of the planets, etc.) very well either way. But the aberration of starlight nailed the sun down in the center with the Earth going around it. (that required very precise telescope measurements...something not available at the time of Galileo)

Phobos
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Originally posted by rattis
well yes, but i dont know if the spacecarft have every acctually gone into space or if it is just a con by government (worse case sinario).

Can i see some mathematical proof that the earth does infact go around the sun?. Like i say the only proof i have at the moment is that i can see the sun move around the earth everyday, but this is not the case as everyone says.

I am not an astronomer but mathematician, so im not sure if this whould be in the maths section
Diehard skeptic, eh? Check the math on parallax & aberration of starlight. (Google search or wait for some helpful PF member to present it here.)

Originally posted by Phobos
At the time of/preceding Galileo, you could model it (the motion of the planets, etc.) very well either way. But the aberration of starlight nailed the sun down in the center with the Earth going around it. (that required very precise telescope measurements...something not available at the time of Galileo)
Thanks. Can you explain that aberration a bit?

Nereid
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rattis,

If you want a mathematical proof, completely disconnected from any observation or experiment, then you'll be disappointed - without any observations at all, you can't even know of the existance of the Sun, Moon, or even the Earth!

If you distrust everything that you read, and need proof of your own, you can do the stellar aberration experiment yourself. You could buy the equipment, probably for less than the cost of an average US house, or make it all yourself, from scratch. You may find an interested physics teacher at a nearby high school, who would welcome the chance to have her class take part in some real, 'hands-on' physics, so you could have the benefit of a critical audience.

Canute (and rattis) -> A one page, mathematical introduction to stellar aberration.

Thanks, I'll try to understand it. However I'm not sure it proves anything other than that if one assumes that the sun is going around the earth then one must also assume that the stars are as well.

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How do you feel about the earth's rotation on its axis? Skeptical there too? Look up Foucalt's pendulum and coriolis force. If you can accept the earth's rotation then it affects you candidate idea that the stars go around the earth.

The point is that it's your responsibility, denying the common wisdom, to come up with a self consistent alternative. If you can't find one, that in itself is an argument for the orbiting earth.

Incidentally, parallax shows that the stars move relative to the earth in an annual cycle, and abberation shows that light moves relative to the earth in an annual cycle (90o out of phase with the first one). If you assume the earth stationary, then these are two curious unexplained facts, but if you assume it orbits, then it is explained, the earth is moving relative to the stars and as it moves its speed causes the abberation of light. Even the phases are in sync.

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How do you feel about the earth's rotation on its axis? Skeptical there too?
Not at all. Spin is a different case. (BTW I'm not skeptical about
the fact the the earth goes around the sun, just wondering about whether it is the only way of interpreting the facts. I understood that with enough Ptolemaic circles you could model a stationary earth).

The point is that it's your responsibility, denying the common wisdom, to come up with a self consistent alternative. If you can't find one, that in itself is an argument for the orbiting earth.
That's the possibility I'm exploring.

Incidentally, parallax shows that the stars move relative to the earth in an annual cycle, and abberation shows that light moves relative to the earth in an annual cycle (90o out of phase with the first one). If you assume the earth stationary, then these are two curious unexplained facts, but if you assume it orbits, then it is explained, the earth is moving relative to the stars and as it moves its speed causes the abberation of light. Even the phases are in sync. [/B]
Surely some fancy maths could sort that out, based on a stationary earth and an orbiting universe? I agree that it would a peverse way of looking at it, but it seems possible.

Originally posted by rattis
I find it obvious, as did many previous people, that the sun goes aroudn the earth. I of course know htis to be untrue as it has been drummed into me again and again for the past 16 years.

Can someone please prove to me (so that i can prove to others as well) that the earth goes around the sun. Do not be afraid to explain using mathematics, as i see that as the only way of undeniable proof.

Rattis, the Earth and Sun both spin around the common centre of mass, called the barycentre, or baricentre. Exactly the same as if you hold hands with someone and both spin around each other, leaning out.

Off topic but re. your signature - have Americans really all volunteered to be fingerprinted by their government? I find that impossible to believe. Weren't there any riots?

Phobos
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Originally posted by Phobos
At the time of/preceding Galileo, you could model it (the motion of the planets, etc.) very well either way. But the aberration of starlight nailed the sun down in the center with the Earth going around it. (that required very precise telescope measurements...something not available at the time of Galileo)
Oops...aberration of light was the first major evidence and then stellar parallax nailed it down.

Phobos
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Originally posted by Canute
Off topic but re. your signature - have Americans really all volunteered to be fingerprinted by their government? I find that impossible to believe. Weren't there any riots?
No. "The Onion" (source of that quote) is a website that makes up fictional/funny news stories.

http://www.theonion.com/index.php?i=1 [Broken]

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LURCH
Originally posted by Canute
Surely some fancy maths could sort that out, based on a stationary earth and an orbiting universe? I agree that it would a peverse way of looking at it, but it seems possible.
According to relativity, there is no difference between an orbitting Earth in a stationary universe and a stationary Earth with the universe rotating around it; they are the exact same situation viewed from two different frames of refference.

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Originally posted by LURCH
According to relativity, there is no difference between an orbitting Earth in a stationary universe and a stationary Earth with the universe rotating around it; they are the exact same situation viewed from two different frames of refference.
Um, I don't think these accelerated (rotating) frames can be equated so simply via special relativity. And if you're thinking of the equivalence principle, remember that's only true in the limit; in extended frames tidal effects will easily detect which frame is moving. Note that Mercury, for example, revolves in the Schwartzschild geometry near the Sun, not the other way around.

Nereid
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"The dipole signal seen by an observer moving with speed $$v$$ relative to the rest frame of the CMB is $$T_0 v/c$$, where $$T_0$$ is the absolute temperature of the CMB, and $$c$$ is the speed of light. Thus, additional sources of error that could affect the absolute calibration of the WMAP data include errors in the determination of WMAP’s velocity with respect to the solar system barycenter (the point of reference for the COBE dipole) and errors in the absolute temperature of the CMB. The velocity of WMAP is routinely measured with respect to geocentric inertial coordinates (GCI) with an accuracy of < 1 cm s-1. The velocity of the Earth is determined from the JPL ephemeris with similar accuracy."
http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/syserr/wmap_syserr.pdf

Pity rattis, (s)he will have to build and launch a space probe like WMAP to convince him/herself that the Earth moves around the barycentre (so Jupiter's, Saturn's etc motion is included), as measured against the CMB.

Canute's model of the universe will have not only horribly complex orbits of the solar system planets (and asteroids, comets etc), but a very odd semi-annual ~2.73 K blackbody that goes round the Earth is just the same plane as the Sun does, but is clearly not connected to the Sun!

In principle, you could make observations of the CMB from the surface of the Earth, but ...

So, other indicators of semi-annual motion?

- pulsars (you have to know where you are wrt the barycentre to get the timing right - in fact, rattis could build a telescope, fit a webcam and good clock, and measure the Earth's motion quite accurately, all by looking at M1, the Crab pulsar!)
- (BTW, really good, coordinated observations by LBI radio telescopes will also show the ~200 million year motion of the solar system around Sag A*)
- doppler signals etc from the Voyagers and Pioneers (I think there's only one still broadcasting)
- fast binary timing (this is a variation on pulsars, but with quite different objects, and different physics)
- interstellar meteor streams (yes, we do have samples of particles from other stellar systems, burning up in the atmosphere every few seconds)
- doppler shifts in stars all around the celestial sphere, with a 6 months' period, and a magnitude which exactly matches a model of the Earth in orbit around the barycentre, in a plane pole at coordinates ($$\alpha, \delta$$), ellipticity e, nodes at ...

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Does this mean that orbital motion is not relative?

Ok. Is there any proof of this topic from a few hundred years ago? using just observations from earth and mathematics?

I am sorry to be a sceptic, but generally until i have proof i do not believe.