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

Planet Y

Rx = 1.587 Ry

Step-by-step 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

`(T_(x)^(2))/(T_(y)^(2))=(R_(x)^(3))/(R_(y)^(3))`

`(290^(2))/(145^(2))=(R_(x)^(3))/(R_(y)^(3))`

`4=(R_(x)^(3))/(R_(y)^(3))`

`1.587=(R_(x))/(R_(y))`

Rx = 1.587 Ry

So, planet Y is closest to star.