A very nice response, thank you. Sorry if I'm not very sensitive, yours is a culture unfamiliar to me. My points will be taken
from this web page. It is the official web site of the Ahmadiyya Muslim Community. Red quotes are from the Qur'an (translated in to English), blue quotes are from the website.
One argument I've heard from many Christians is that Christianity uniquely has some principles, therefore it's more correct. The same can be said of Islam, however, as words in the Qur'an have correctly stated some of the natures of our universe. The fact that it's alluded to in the Qur'an means that it's true, at least in the Muslim faith, and therefore acceptable.
And the heaven We built with Our own powers (aydin) and indeed We go on expanding it (musi'un).1
Do not the unbelievers see that the heavens and the earth were a closed-up mass (ratqan), then We clove them asunder (fataqna)? And We made from water every living thing. Will they not then believe?2
The first refers to the fact that the universe is ever expanding, and the second both talks about the big bang and black holes. Therefore, you should accept these as truths if it must be stated in the Qur'an to happen.
Now to the good part: Earth's movement.
The mountains that you see, you think they are stationary while they are constantly floating like the floating of clouds. Such is the work of Allah Who made everything firm and strong...8
If the mountains are declared to be in constant motion, then the only logical inference to be drawn from this would be that the earth is also rotating along with them.
What this means is that they're rotating. Things above appear to move, things below don't. Everything is in a constant state of some sort of motion. Not to mention the phrase "orbit":
... everything is gliding along smoothly in its orbit.12
This all-embracing statement covers the entire universe, our solar system being no exception. In addition to this, there are many other verses which mention the elliptical movement of all the heavenly bodies.
One bit that you mentioned is that the Sun moves. This verse, right?
And the sun is constantly moving in the direction of its ultimate abode of rest. This is the decree of the Almighty, the All-Knowing.
But the moon, too, must move.
If it were only the sun which was moving in a fixed direction, the verse which follows this statement would not have proclaimed that the sun and the moon strictly maintain their mutual distance; they will never be able to gain or move away from each other, an unchangeable destiny till their appointed time
And since the moon isn't moving away from the Earth (or at least, not too far away
yet), the Earth has to move as well. I haven't shown that the Earth revolves around the Sun yet, but can you see that it states the the Earth moves, and even rotates?