What causes the apparent movement of mars against the fixed background of stars in the night sky?
Mars orbits the Sun as well as the Earth Since it is farther out from Earth's Orbit it travels slower Earth Over takes it almost twice on the inside Per Mars Orbit That is what makes it the easiest Planet to get to Half the work is already done for it Coming back actually takes more power because you are continually playing catch up
The apparent movement is caused by the change in the positions of Earth and Mars, causing the line of sight from Earth to Mars to change against the fixed background of stars in the night sky. It's called "parallax".
The movement of Mars.
Mars and Earth are orbiting the Sun at different speeds., and Mars orbit is more elliptical than Earth's orbit. That's why planets do retrograde loops when Earth catches up to and passes them.
Mars orbiting the Sun and the changing POV of it from Earth
It IS moving. Nothing "apparent" about that. If you mean the times when Mars appears to go backwards (it is in retrograde), that's because Earth, moving faster, overtakes Mars every time the two planets are closest to each other. Let's imagine they're cars on a racetrack, you're in the Earth car and I'm in the Mars car. You'll see me ahead, soon you will be beside me, and then I'll fall behind so to see me, you have to look behind you. Relative to you, I'm moving backwards, aren't I? I'm still moving forwards, but not as fast as you so from where you're sitting, I'm going in reverse. Simple as that! And it will happen every time you come round again and pass me. It's just harder to see what's happening with real planets. The only reference point you have is the fixed background of stars. But it's still the same in our car race - as you pass me, I will appear, for a while, to be going backwards relative to whatever is beside the track. Let's say you pass me exactly as we go past the winning post. As you approach, you'll see me apparently in front of it. As you pass me, I'll be beside it. Then as you pull ahead, I'll appear to be behind it.
The apparent movement is caused by the motion of the Earth.