Question

Astronomers discover an exoplanet, a planet obriting a star other than the Sun, that has an orbital period of 3.75 Earth years in a circular orbit around its star, which has a measured mass of 3.21×1030 kg . Find the radius ? of the exoplanet's orbit.

Answer 1

Using Kepler's 3rd law:

T^2 = 4*pi^2*a^3/(G*M)

a = orbital radius of exoplanet's orbit = ?

G = Gravitational constant = 6.674*10^-11

M = Mass of star around which exoplanet is orbiting = 3.21*10^30 kg

T = time period of exoplanet = 3.75 Earth years = 3.75*3.154*10^7 sec = 1.182*10^8 sec

So,

a^3 = G*M*T^2/(4*pi^2)

a = [G*M*T^2/(4*pi^2)]^(1/3)

Using given values:

a = [6.674*10^-11*3.21*10^30*(1.182*10^8)^2/(4*pi^2)]^(1/3)

a = radius of orbit = 4.23*10^11 m

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