**Planetary
Opposition**

Consider two planets whose orbits about the sun are circular and in the same plane called the “ecliptic”. These planets are said to be in opposition when they are the closest together. From the perspective of the inner planet, this will happen when the outer planet is exactly opposite the sun. This is illustrated below for the Earth and Mars.

At opposition the outer planet will appear to slow down and briefly stop in the sky. Immediately afterwards the outer planet will apparently reverse direction before again resuming its normal path. This is the phenomenon of “retrograde motion” and happens once at each opposition.

**TIME BETWEEN OPPOSITIONS**

The angle “ of any planet relative to the sun changes a rate determined by its period, T, which is the time required to make one revolution.

We will denote the time in days it takes for the Earth and
Mars to revolve once around the Sun as T_{Earth} and T_{Mars}
respectively.

Opposition will occur
at intervals of t = T_{Opposition} when their relative angular rates
are equal to multiples of 360°
or 2π radians. The is
expressed as

We can then use this relation to calculate either the length
of the Martian year in the heliocentric model, T_{mars}, or the observed
time between oppositions, T_{Opposition}, as

or

From long multi-generational study and by as early as 3000
B.C., the length of the Earth year or T_{Earth }, (about 365.25 days or
more precisely 365.2422 days) was known from measurement of the equinoxes. We
also knew the time between oppositions or T_{Mars} (about 780 days or
more precisely 779.94 days). Assuming a heliocentric model, this allows us to
calculate the length of the Martian year T_{Mars} (about 687 days or
more precisely 686.98 days). As for instance