I read with interest your challenge to "prove that the earth revolves around the Sun". Unfortunately, your challenge was too vague for me to decide whether to agree or disagree. The principle difficulty is with the word "revolve". The dictionary defines it to mean "to orbit around a center". However, "center" can be understood many different ways. I will address 5 of them:
We know by direct observation from the surface of the Moon, that the Sun also revolves around the Moon. From the Moon, the Earth goes through phases, just as the Moon does when observed from the Earth. These are beautiful and spectacular photos from the Apollo Moon mission. From pictures sent back by Mars landers, we know that the Sun also "revolves" around Mars.
Try this experiment. Have a friend stand "still", and walk around him/her while facing one wall. You will see your friend revolve around you. If you ask your friend, they will report seeing you revolve around them. Now, walk around your friend while keeping your face always toward your friend. Now you will see your friend turning slowly around, while the room revolves around you. Your friend will report that you are revolving around them as before, but with your face always toward them.
When we send spacecraft to the distant reaches of the Solar System, their antennae continually move to point directly at Earth in order to stay in communication. The Earth makes epicycles in the sky around these spacecraft (as do the other planets).
A 3D computer graphics system describes objects by means of coordinates in an arbitrary frame of reference. However, the "center" of the scene is the "camera". The camera itself has coordinates in that same frame of reference, but what you see on the screen is determined by the position of the virtual camera. The coordinates of the virtual camera can be changed at will, so that the viewer seems to fly through the scene.
It should be clear by now that revolution in the observational sense is relative, and that the Earth is not unique in having heavenly bodies revolve around it in the observational sense. Does the Earth revolve around the Sun in this sense? We don't yet have direct observations from the Sun, but the upcoming Solar Probe will provide just that. However, straitforward geometry, without regard for any laws of physics, allows us to compute what a hypothetical observer on the Sun would see. They would see the Earth revolving around the Sun.
So, in the observational sense, the Sun revolves around the Earth, but the Earth also revolves around the Sun. The majority of Scripture passages which you cite describe the motion of the Sun in this sense.
You can check this by carefully recording the bearing and azimuth of your favorite inner planet every night along with the exact time over the course of at least a year (outer planets will take much longer). If possible, measure the distance to the planet by measuring the bearing and azimuth from two widely separated locations at the same time. You will also need to measure the distance and direction to the Sun. If you are only interested in the Earths orbit, just the Sun positions will do. Each observation of a Sun or planet is a 3 dimensional vector, with its origin at the Earth. For each observation, subtract the Sun's vector from the Earth or planet vector to get Sun relative position. What are your standards of evidence for observations? Is Kepler's data acceptable? Are my kids data from homeschool astronomy acceptable? How about NASA?
It is much easier to go the other direction. Start with your favorite web site or open source solar system model to predict planet motions. These programs use a numerically approximated gravitation model, however, the resulting orbits can be plotted and observed to be ellipses from the Sun's frame of reference. Many of these program conveniently provide a viewpoint from anywhere, including from Earth or a point "above" the Solar System (so you can see the ellipses). Spot check their predictions of the view from Earth with your actual observed position of the planets.
Is the Sun the geometric center of the Solar System? The answer is yes by direct observation of the position of the planets relative to the Sun. Furthermore, the Sun is the only body in the Solar System which is at the center of simple circles and ellipses formed by the motion of the other bodies. The other bodies (including Earth) lead to more complicated motions when considered as the geometric center. Note that this says nothing about whether the Earth or the Sun is actually moving, only that their positions relative to the Sun form simple geometric shapes.
So in the geometric sense, the Earth revolves around the Sun.
The Sun as geometric center provides a much simpler and easier method of predicting the motions of the planets. Copernicus was humble man, and did not claim that the Sun was the "center" in anything but this obvious geometric sense. As a result, his theory was accepted, with reservations, by the reigning Aristotelians as a mathematical shortcut for the computation of epicycles. The reservation was that some might see this geometric centrality of the Sun as implying something more.
So, in the teleological sense, the Sun revolves around the Earth.
The Earth as the teleological center was in hot dispute after Copernicus. Bruno audaciously proclaimed that not only was the Earth not the "center" of the Solar System, but the Sun itself was only one of multitudes of other suns with planets of their own! He was burned at the stake in 1600 for his blasphemy. Before you judge the actions of the Church in this matter, keep in mind, that Bruno was explicitly using his astronomical theories and geometrical facts as evidence of a religious assertion. His syllogism went something like this:
A little later, Galileo showed Pope Urban the moons of Jupiter through a telescope. The Pope saw and understood that this was contrary to the assertion of the Aristotelians that the heavenly bodies were perfect spheres. He expected trouble, and earnestly counseled Galileo on six occasions to adopt the humble spirit of Copernicus and avoid directly contradicting the reigning Orthodoxy. Galileo did the opposite, and called his opponents "simpletons". The Pope managed to save Galileo from the fate of Bruno (Galileo was willing to "recant"), but he spent the rest of his life under house arrest and his writings no longer had the approval of the Church. (This, of course, made his writings even more popular.)
So, in the gravitational sense, the Earth revolves around the Sun - but this result depends on Newtons laws of motion.
So, in the cosmic sense, there are many competing theories, but in none of them is the Sun at the center of the Cosmos.
In conclusion, your challenge needs to be more specific before anyone can properly decide on its merits. You need to specify what kind of "revolution" is being talked about, and whether its uniqueness is in question.