Notice that the Earth is moving faster than Mars. Think through what it looks like from Earth when it passes Mars each time. Mars will appear to move in the same direction as the Earth but at a slower speed as the Earth approaches, then will appear to move in the opposite direction just after the Earth passes it.
Now that you have a mental picture, you can understand what's happening in the gif below. This is identical to the previous gif except that it is centered on the Earth.
The apparent backwards movement is really apparent here.
Finally, here is the same thing from Jupiter's POV:
Nothing really new here...it just seemed right to include it.
One thing worth noting...this phenomenon is called 'apparent retrograde motion'.
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