Question 8.1: Calculate the synodic period of Mars relative to that of the...

In Table A.1 we find the orbital periods of earth and Mars:

T_{\text {eath }} = 365.26 days (1 year)

T_{\text {mars }} = 1 year plus 321.73 days = 687.99 days

Hence,

T_{\text {syn }}=\frac{T_{\text {earth }} T_{\text {Mars }}}{\left|T_{\text {earth }}-T_{\text {Mars }}\right|}=\frac{365.26 \times 687.99}{|365.26-687.99|}=777.9 \text { days }

These are earth days (1 day = 24 h). Therefore, it takes 2.13 years for a given configuration of Mars relative to the earth tonoccur again.

Table A.1 Astronomical data for the sun, the planets, and the moon