What is the minimum mass of the exoplanet orbiting 70 Virginis if it has an orbital period of 116.69 days (p = 1.0082 x 10⁷ s) and an average orbital distance a = 7.18 x 10¹⁰ m. The star's orbital velocity is measured to be 291 m/s and its mass is 2.19 x 10³⁰ kg.

Question

Quizplus · Accepted Answer

The minimum mass of an exoplanet can be calculated using the formula: 
M = (P^2 / 4π^2) x (a^3 / G x M*)
where P is the orbital period, a is the average orbital distance, G is the gravitational constant, and M* is the mass of the star.

Substituting the given values, we get:
M = (1.0082 x 10^17 s)^2 / (4 x π^2) x (7.18 x 10^10 m)^3 / (6.674 x 10^-11 m^3 kg^-1 s^-2 x 2.19 x 10^30 kg)
M = 1.42 x 10^28 kg

Therefore, the minimum mass of the exoplanet is 1.42 x 10^28 kg or approximately 14 Jupiter masses. The correct answer is B.

What Is the Minimum Mass of the Exoplanet Orbiting 70