Two planets P 1 and P 2 orbit around a star S in circular orbits with speeds v 1

Question

Two planets P1 and P2 orbit around a star S in circular orbits with speeds v1 = 44.6 km/s, and v2 = 60.0 km/s respectively.

(a) If the period of the first planet P1 is 7.50 years, what is the mass of the star it orbits around?

HINT!!!!The gravitational force of the star on the planet supplies the centripetal force needed to keep the planet in its circular orbit.

(b) Determine the orbital period of P2.

HINT!! Consider the relationship between the orbital speed and the orbital period in terms of the known variables.

Explanation / Answer

a) v1 = 44.6 km/s, P1 = 7.50 yr

R1 = P1 v1 / 2 pi

G M / R12 = v12 / R1

M = v12 * R1 / G = p1 v13 / 2 pi G

= (7.5 * 365 * 24 * 3600 * 446003) / (2 pi * 6.67 * 10-11)

M = 5 * 1031 kg

b) orbital period P2 = 2 pi R2 / v2 = 2 pi * GM / v23

= (2 pi * 6.67 * 10-11 * 5 * 1031) /(600003 * 365 * 24 * 3600)

= 3.08 yr

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