Question

An exoplanetary system has two known planets. Planet X orbits in 290 days and Planet Y orbits in 145 days. Which planet is closest to its host star? If the star has the same mass as the Sun, what is the semi-major axis of the orbits for Planets X and Y?

Answer 1

Answer:

Planet Y

Rx = 1.587 Ry

Explanation:

Tx = 290 days

Ty = 145 days

Let the semi major axis of planet X is Rx and of plant Y is Ry.

According to the Kepler's third law of planetary motion

$\frac{T_{x}^{2}}{T_{y}^{2}}=\frac{R_{x}^{3}}{R_{y}^{3}}$

$\frac{290^{2}}{145^{2}}=\frac{R_{x}^{3}}{R_{y}^{3}}$

$4=\frac{R_{x}^{3}}{R_{y}^{3}}$

$1.587=\frac{R_{x}}{R_{y}}$

Rx = 1.587 Ry

So, planet Y is closest to star.