Why do planets occasionally move backward in the night sky? This video explains the phenomena known as 'apparent retrograde motion'. (Spoiler Alert): The backward or 'retrograde' motion of the planets is caused by nothing more than the optical illusion known as 'parallax'. Simply put, parallax is the apparent change of position of an object when viewed from different positions and distances. Imagine you are in a car traveling on the highway and looking out the side window - the street lamps close to you appear as if they are moving backyard extremely fast, whereas the trees 50 meters away will appear to be moving a bit slower, and the hills in the far distance will appear to be hardly moving at all. Of course, the street lamps, trees and hills aren't actually moving backward, it is YOU that is moving forward. Although obvious in this example, from the point of view of the observer, determinding whether it is the OBJECTS that are moving (proper motion) or YOU that is moving (apparent motion) is harder to determine than you might think. The dead give away is 'paralax'... the illusion that objects CLOSER to our viewpoint appearing to move faster and further than objects FURTHER AWAY.
As a real world example, scientist have used this method to determine the distance to far away stars. As the earth moves from one side of the sun to the other (a straight line distance of approximately 300,000,000 km) stars display 'stellar parallax' - closer stars display more parallax (apparent movement) than stars further away.
You might think to yourself that it should be easy to determine if an object has apparent motion or proper motion.... If you have ever been sitting on a stationary train, with another train sitting on the tracks right next to you, then you would have experienced that sensation when one of the trains begins moving, and you can't tell if you are moving forward or the train next to you is moving backward!
In regards to Earth and Mars, both planets are in motion and moving in the same direction, however earth is moving FASTER than mars, and therefore and one point during Earth orbit, it OVERTAKES Mars. If we go back to the car analogy, imagine you are traveling on the highway at 100km/h and you're overtaking a car that is only traveling at 80km/h. Although the other car is traveling at 80km/h, from your perspective the car can appear to be moving backwards as you pass it!
Motion and speed are all relative - something that appears to be moving backward to one person, can appear to be moving forwards to another person who is viewing it from a different reference frame.
Okay, still havn't got it? Don't worry, you are not alone! Try this simple experiment: place an object (like a bottle of water) on a table, and then place a second object about half a meter behind it. Move your face very close to the first object. Now, looking straight ahead, move your body from one side of the bottle to the other. Both bottle will appear to be moving agaist the still background, but the bottle closest to you will appear to be moving a greater distance than the object further away from you.
Music: Made of Words, The Talos Principle OST