Question

Calculat the sideral period of Mars given its synodic period is 780 days. 7. Calculate the synodic period of Venus given its sidereal period is 229 days.

Answer 1

Answer:

686 days for sideral period of Mars.

615 days for synodic period of Venus.

Explanation:

The equations we need to use is:

$\frac{1}{P}=\frac{1}{E}\pm\frac{1}{S}$

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:

$P_M=\frac{1}{\frac{1}{E}-\frac{1}{S_M}}=\frac{1}{\frac{1}{365days}-\frac{1}{780days}}=686days$

And for the synodic period of Venus we then have:

$S_V=\frac{1}{\frac{1}{P_V}-\frac{1}{E}}=\frac{1}{\frac{1}{229days}-\frac{1}{365days}}=615days$

(Commonly for Venus a sidereal period of 225 days is given, which changes this result to 587 days).