Question

Astronomers discover an exoplanet (a planet of a star other than the Sun) that has an orbital period of 3.97 Earth years in its circular orbit around its sun, which is a star with a measured mass of 3.41 times 10^30 kg. Find the radius of the exoplanet's orbit. _____ m

Answer 1

Given,

orbital period of exoplanet = 3.97 Earth years

mass, m = 3.41 × 10³⁰ kg

The orbital period of the planet = 3.97 earth years = 3.97 x 365 x 24 x 3600 seconds = 125197920 seconds

G = 6.6726 x 10^-11N-m²/kg²

From kepler's third law equation

The orbital radius, r = (T² GM/4π²)^(1/3) = [(125197920² x 6.67 x 10^-11 x 3.41 x 10³⁰ )/(4π²)]^1/3 = 4.486 x 10¹¹ m

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