A vector is a mathematical construct that has magnitude and direction. The cross product of two vectors is a binary operation in three-dimensional space that results in a third vector that is ...
In the present situation, both Earth and Mars are moving in the same direction around the Sun, but the slower one, Mars, appears to move backwards compared to the faster one, Earth. Just an illusion. The retrograde motion of Mars â like the apparent motion of the slower car on the highway â is nothing more than an illusion.
The explanation for retrograde motion in a heliocentric model is that retrograde occurs roughly when a faster moving planet catches up to and passes a slower moving planet. How the planet Mars would appear to have both prograde then retrograde then prograde motion is shown in the diagram below. Notice that it is all due to the fact that the Earth moves faster in its orbit than does Mars.