• Earth orbits the sun in the counterclockwise direction as seen from the north.
• Mars orbits the sun in the counterclockwise direction as seen from the north.
• Both orbits are approximately circles.
• Both orbits are approximately in the same plane.
• The radius of the earth's orbit is 1.0 AU.
• The radius of Mars' orbit is approximately 1.5 AU.
• The period of the earth's orbit is 1 year.
• The period of Mars' orbit is approximately 2 years.

It is useful to plot the path of Mars taking the earth as fixed. To do this, first draw two arrows, the first is just the same as an arrow from the sun to Mars, but beginning at Earth, the second is just the same as an arrow from Earth to the sun, but beginning at the end of the first arrow.

• The first arrow starts at the earth, has a fixed length of 1.5 AU, and rotates counterclockwise once per 2 years.
• The second arrow starts at the end of the first arrow, has a fixed length of 1.0 AU, and rotates counterclockwise once every year.

The result.

Here is drawn by computer, with the point representing Mars moving around a little circle of radius 1.0 AU once per year while the center of the little circle moves around a big circle of radius 1.524 AU once every 1.881 years.

Prediction for what we see.

Mostly Mars should move from west to east across the celestial sphere. (Ie. counter clockwise as seen from the north.)

But when it is closest to us, it should move in the opposite direction. ("retrograde")