Is there any clear and concrete proof that says the Earth is rotating and orbiting? As the title states, I am wondering if there exists a clear and concrete proof that proves that the earth is revolving around the sun on an orbit, and proves that the sun is not revolving around the earth.
I've heard of the Foucault pendulum, but that doesn't prove that the sun isn't revolving around the earth. And stellar parallax, I was able to find a lot of material explaining about what it is and why it works, and all the theory behind it is explained in detail on several articles and videos, but I couldn't find any solid experiments or evidences to prove it in any of them.
 A: Kepler's laws of planetary motion are observational laws that are most simply explained by a heliocentric model of the solar system in which the orbits of the planets are governed by Newton's law of universal gravitation (with some tweaks from general relativity to account for the exact precession of Mercury's orbit).
It is possible that this is all an illusion created by a malicious deity, that the sun and the rest of the universe actually revolves around the Earth once a year, that our understanding of gravity is incorrect, and that Kepler's laws only hold by coincidence. It is also possible that none of this really exists at all, it is all just coloured lights in the sky, the moon landings were a hoax etc. etc. But Occam's razor tells us that such complex and baroque explanations are very unlikely.
A: See this question on quora.com

How do I prove that the Earth rotates once on its axis in 24 hours?

and the answer given there

Err...
Well if you look up, then those fixed things in the sky are are going round us.
Which is like a pretty huge clue.
So either
a) the Earth is spinning once every 24hrs, or
b) EVERYTHING IN THE UNIVERSE is glued to a big ball and is rotating around the Earth.
The first theory works. You can check it with pendulums etc.
The second is nuts.

So, theory (a) seems to be simpler than (b).
And furthermore, (a) makes some testable predictions:

*

*Due to the Coriolis force by the rotation a Foucault
pendulum will slowly rotate with $360° \sin\phi/$day
(with $\phi$ being the geographical latitude).

*Due to the centrifugal force by the rotation the body
of the earth will be slightly oblate (i.e. the radius
larger at the equator, and smaller at the poles).
Due to the same effect the gravity of the earth will
increase slightly with geographical latitude (i.e. smaller
at the equator, and larger at the poles).

All these effects have indeed been experimentally confirmed.
Theory (b) has no explanation for these effects.

And now for your second question:
How to prove that the sun isn't revolving around the earth.
Let's consider the observed movement of the planets relative
to the background of the stars.
In the course of the year the planets move in a somewhat
erratic way.
As an example, here are the trajectories of Mars (the bright orange
dots) and Uranus (the faints dots above Mars) in 2003.

(image from Online Astronomy eText: The Sky / Orbital Motions / Retrograde Motion)
Most of the time the outer planets (Mars, Jupiter, Saturn, ...)
move from west to east.
But for a few months they move "backwards" (from east to west).
In principle there are different models to explain this:

*

*Geocentric model of Ptolemy:
The earth stands still.
The sun moves around the earth in a nearly circular orbit.
The planets move around the earth in a complicated way.

*Heliocentric model of Copernicus:
The sun stands still.
The earth and the planets move around the sun in nearly circular orbits

The model (2) is much simpler than model (1), because it explains
the motion of the planets with less complicated assumptions.
Therefore model (2) is preferred.
Furthermore, both models make some more predictions which
can be tested with experiments.
The heliocentric model predicts:

*

*Due to the position of the earth varying in the course of the year
the positions of nearby foreground stars will vary slightly relative
to the background stars further away. See stellar parallax.
This indeed had been measured experimentally.

(image from Humble 1st attempt for stellar parallax)

*Due to the velocity vector of the earth varying in the course of
the year the spectra of stars will be slightly
Doppler-shifted in a yearly rhythm.
This also had been measured expeimentally.

On the other hand, the geocentric model predicts the  parallaxes
and Doppler-shifts of the stars not to vary in a yearly rhythm,
because of the earth standing still.
This contradict with the experimental facts, and hence this model
is disproved.
