I didn't say other planets orbit the sun > I said all orbit earth; as the old belief says!
So, would we still observe the movement of the sun and the moon on this model, as we do naturally?
The problem with that model of the solar system is the matter of the "retrograde motion", where planets appear to move for a time in the "wrong direction". All the planets, except Mercury demonstrate this at some time.
If all the planets orbited the earth this could not happen. This is part of what the
Flat Earth Society Wiki has to say on "Retrograde Motion":
Retrograde Motion
Q. Why do the planets retrograde in the sky?
Apparent retrograde motion of Mars in 2003 as seen from Earth
<< note that I have replaced the Wiki still with a similar motion .gif >> A. Retrograde motion occurs from the fact that the planets are revolving around the sun while the sun itself moves around the hub of the earth. This particular path the planets take makes it appear as if several of them make a loop along their journeys across the night sky.
Please note that the planets are moving very slowly around the sun and would not retrograde several times a day as might be implied by the above diagram. The diagram is for illustration purposes only. Several retrogrades a year would be more appropriate, depending on the planet.
The retrograde happens very slowly in the night sky, over a long period of time.
The theory that the sun, moon, planets and stars orbited the earth simply could not be fitted to observations.
Ptolemy had a complicated model with
deferents, epicycles and eccentrics and still, it wouldn't fit.
The theory Copernicus proposed had
perfectly circular orbits (they thought
perfect circles were
so cool in those days
).
This Copernican model was better that Ptolemy's but still far from accurate, so Tycho Brahe, certainly the
best pre-telescope astronomer, was commissioned to make more precise measurements.
He made a very careful study of the planets, studying the retrograde motion in orbit of Mars in particular.
Tycho Brahe came then up with his own
hybrid geocentric globe model, in which the moon and sun orbited the earth, but the planets (only Mercury, Venus, Mars, Jupiter, and Saturn) orbited the sun.
This model fitted his data better than the Copernican model, but was still far from perfect.
And it wasn't till Kepler found that all the planets orbiting the sun with
elliptical orbits fitted much better that a solar system close to the presently accepted one was accepted.
It should be noted that Kepler's laws strictly only apply to one planet and a massive sun.
The planets do interact but the sun so dominates the solar system that the Kepler model is close till we get to Neptune and Pluto.
But please note
all of these people from Aristotle, Ptolemy, Copernicus, Brahe and Kepler accepted that the earth was a sphere.
Sorry for the length, again, but it is really a huge topic.