You are the science officer on a visit to a distant solar system. Prior to landi

Question

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8×107m and its rotation period to be 22.3 hours . You have previously determined that the planet orbits 2.2×1011m from its star with a period of 432 earth days. Once on the surface you find that the free-fall acceleration is 12.2m/s2.

Part A

What is the mass of the planet?

Express your answer with the appropriate units.

mp =?

Part B

What is the mass of the star?

Express your answer with the appropriate units.

Explanation / Answer

A) radius of the star, R = 1.8*10^7/2 = 9*10^6 m

g = 12.2 m/s^2

g = G*Mp/R^2

==> Mp = g*R^2/G

= 12.2*(9*10^6)^2/(6.67*10^-11)

= 1.48*10^25 kg

B) given, Time pesriod, T = 432 years = 432*365*24*60*60 = 1.362*10^10 s

r = 2.2*10^11 m

we know, T = 2*pi*r^(3/2)/sqrt(G*Ms)

T^2 = 4*pi^2*r^3/(G*Ms)

Ms = 4*pi^2*r^3/(G*T^2)

= 4*pi^2*(2.2*10^11)^3/(6.67*10^-11*(1.362*10^10)^2)

= 3.4*10^25 kg

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.