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The opportunities for a launch to Mars

Earth and Mars move at different angular rates around the Sun: the Earth takes 1 Earth-year to complete 1 revolution while Mars takes 1.88 Earth years to complete 1 revolution. Consequently the planets are sometimes close together (on the same side of the Sun) and sometimes far apart (on opposite sides of the sun). The two images below show examples of relative positions for the planets.

diagram

Initially, the planets are close together, but one Earth year later the Earth is back in its initial position but Mars has completed little more than half a revolution.

diagram

We can calculate the time it takes for Earth and Mars to reach similar relative positions. It is the time at which the Earth has traveled one complete revolution further than Mars:

Now the angle traveled by either planet is its angular rate multiplied by elapsed time:

We can substitute in the first equation and rearrange terms:

Earth's angular rate is 360 degrees per year, and Mars angular rate is 360 degrees per 1.88 years.

formula

The time between launch opportunities is a little greater than 2 years (about 25 to 26 months). That's why NASA sends missions to Mars at about 2 year intervals.