Answer:
686 days for sideral period of Mars.
615 days for synodic period of Venus.
Explanation:
The equations we need to use is:
[tex]\frac{1}{P}=\frac{1}{E}\pm\frac{1}{S}[/tex]
Where P is the sidereal period, S the synodic period and E the Earth's period (365 days) and where the + is used for inferior planes (Venus) and the - for superior ones (Mars).
For the sidereal period of Mars we then have:
[tex]P_M=\frac{1}{\frac{1}{E}-\frac{1}{S_M}}=\frac{1}{\frac{1}{365days}-\frac{1}{780days}}=686days[/tex]
And for the synodic period of Venus we then have:
[tex]S_V=\frac{1}{\frac{1}{P_V}-\frac{1}{E}}=\frac{1}{\frac{1}{229days}-\frac{1}{365days}}=615days[/tex]
(Commonly for Venus a sidereal period of 225 days is given, which changes this result to 587 days).
