# Static model of the Earth motion

Believe it or not, an old man I know in 2015 still negates the Earth orbital motion around the Sun.

He believes the earth is rotating on itself and acknowledges this gives day and night on every place on earth.

But as for seasons, he reckons the earth axis is slowly tilting through the year and the earth is not going around the sun, but standing still in place, always in the same position relative to the sun.

If you were to convince him this cannot be true, what would the arguments against be and what simple experiments (with ordinary means) could he perform to reveal the earth revolution motion and the fact the rotation axis is fixed in space (at least within a matter of a human life)?

I can think of some of the theoretical and practical reasons, but wanted to hear all about this from those better than me and will refer to the man.

• So he accepts the rotation of the Earth, but not revolution around the Sun? Wow! How about changes of positions of stars from week to week with the regular repetition of those patterns every year. He would have a touch time explaining that. Commented Nov 5, 2015 at 22:30
• He believes the earth rotation axis wobbles from season to season and pretends to explain the seasons as long as the star shifts with that. Commented Nov 7, 2015 at 21:25

Quite simply, the Sun moves relative to the stars. If you could see stars during the daytime then this would be somewhat easier to measure, but as it is you need some to look at night. Choose a time (say, 9pm) after dark, and go outside and look at the stars everyday for about one or two months. Observing at the same time will keep the Sun in the same direction relatively to the Earth, but over multiple weeks you can observe changes. More specifically, over time each star will rise earlier and earlier.

On the other hand, with the exception of planets, all the constellations keep their shape and relationships to each other. The implication is that the stars are rotating relative to the Earth-Sun axis, or vice versa.

After that it gets tricky, because there isn't all that much to stop you from concluding that the Sun is fixed in space and the stars rotate about the solar system once a year. Indeed, the frame equivalence of classical mechanics treks you that this is a perfectly valid viewpoint, at the minor price that the Earth-Sun frame is no longer quite an inertial frame. Detecting this is in principle doable, but definitely not as a home experiment. A sufficiently dedicated craftsman can build, given enough time and money, a working Foucault pendulum which will demonstrate the Earth's rotation, but extending this to its motion around the Sun is definitely a huge challenge.

That said, the model doesn't make much sense in and of itself. Heliocentric models are a lot cleaner than geocentric ones in good measure because they don't require the stars to rotate around the Earth every day. A model that includes the rosin of the Earth but also has the stars rotating around the solar system is a working proposition but it's definitely a strange hybrid of a proposal, with all the philosophical disadvantages of both parents.

Also, there is parallax for the closer stars so that over the course of a year, the nearby stars will move back and forth with respect to more distant stars. The measurements are good to about 100 parsecs which equates to the limit of measurement of 0.01 arcsecond. The only way to explain the back and forth motion of the parallax is that the earth is moving in an orbit.

The historical "proof" was about the motion of planets along the year, but it needs some patience and observation. Earth-centric model yields pretty complicated cycloidal motion for planets, while Sun-centric yields simple ellipses (with moderate excentricity). Also the seasonal tilting of the axis is alot simpler in the second case, since the axis keeps a constant tilt angle during its rotation around the Sun.

Also, I guess he either does not believe on Newtonian gravity or in the size and distance of Sun ? (or did not notice the contradiction). Since to be in orbital equilibrium, both objects turn around their common center of mass... which is quite inside the Sun itself !

Another proof: relative to stars, the day is 23h56, while relative to Sun, the day is 24h. https://en.wikipedia.org/wiki/Earth%27s_rotation

So Earth rotation couldn't expain both stars and Sun rotation, there must be a differential rotation between these two.

I'm trying to answer my own question. Please feel free to comment and complement me! The earth goes around the sun and it is fixed with respect to it because: ... I have three reasons to give to the man and all things he can check in first person:

• Mercury and Venus, the other inner planets have phases if you look at them through a telescope. If they were fixed just like the Earth, they would not have changing phases. In order to show phases they have to move relative to the Earth or the sun. Since my friend does not believe in geocentrical mode, he will be willing to accept the Earth companion planets move around the sun, and so does the Earth, which is no different from them to this respect.
• If you look at Jupiter, he has no phases. We know this is because it is very far away from the sun and very little light gets there. Anyway it looks like a bright star when it's high on the sky at night and a light disc with a telescope. It has its own light source. But the feature that matters here is it has satellites. Jupiter and its four largest satellites are visible through a cheap telescope and the scene resembles a small solar system. So my friend could look at this solar system from the outside and realize Jupiter satellites go around it, and so must the Earth with respect to the Sun.
• If you drop a stone, the stone falls on the Earth and not vice versa. This is because the Earth is much more massive than the stone. If I could convince my friend the Sun is much bigger than the Earth, he will probably admit it would be much heavier, despite not being made of rocks. Therefore like the lighter stone falls towards the much bigger one, the Earth falls towards the Sun. But instead of falling it goes around a circle, so that every second it has fallen by the same vertical quantity. but the circle curvature reports it to the same distance and so it keeps falling and keeping the same distance and a perfect circle it's the only way to do both. Although the orbit is actually elliptic, the eccentricity is so low, so very little changes if we assume it circular for this argument. So we just have to show the Sun is more massive. Since the Sun and the Moon have almost the same angular distance (they look the same size from the Earth, as seen in solar eclipses), but the Sun is much more lighter that you can't even look at it, it could be much bigger and much farther. This is not a demonstration, but one could determine the Earth-Sun distance using the same naked-eye method Aristarchus found and even if the distance is underestimated as it was historically, it is still enough to conclude.