Astronomers have observed a planet orbiting a near-by star. Through close observ

Question

Astronomers have observed a planet orbiting a near-by star. Through close observation, they learn the following information about the orbit of the planet:

i. The planet is in an elliptical orbit.

ii. The perigee distance from the center of the star is 1.03 x 10^11 m.

iii. The apogee distance from the center of the star is 1.13 x 10^11 m.

iv. The velocity at perigee is 35.9 km/s.

v. The period of the orbit is 225 days.

(a) What is the velocity at apogee, in km/s, for the planet?

(b) What is the mass of the star?

Explanation / Answer

D1= 1.03 * 10^11 m , D2 = 1.13* 10^11 m . V1 = 35.9 km/s,

a) So D2*V2 = D1*V1 => V2 =V1 *D1/D2 = 32.723 km/s.

b) P = 2 * pi * SQRT(r3 / G * M) where r = (D1 +D2)/2 = 1.08 * 10^11 m,

so (9.5727 * 10^12 )* G*M = r^3 => M = r^3/638.867 = 169049270 kgs = 1.69 * 10^8 Kgs

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