Answer to Question #138115 in Astronomy | Astrophysics for hala

Question

A large planet orbiting a distant star is discovered. The planet's orbit is nearly circular and close to the star, the orbital distance is 7.5 cross times 1010 m , and its period is 105.5 days. calculate the mass of the star

Answer 1

According to the third Kepler law, the radius r of the orbit, the orbital period P and the mass of the star are related by

$\dfrac{P^2} {r^3} = \dfrac{4\pi^2} {GM}.$

Therefore, the mass can be calculated as

$M=\dfrac{4\pi r^3} {GP^2} = \dfrac{4\cdot3.14^2\cdot(7.5\cdot10^{10})^3}{6.67\cdot10^{-11}\cdot(105.5\cdot86400)^2} = 3\cdot10^{30}\,\text{kg}.$

It is approximately 1.5 solar masses.