In this problem, be especially wary of round-off; keep 2-3 (non-zero) digits in

Question

In this problem, be especially wary of round-off; keep 2-3 (non-zero) digits in each answer and throughout your calculations.

Based on the following data about planet X (which orbits around the Sun):

Planet X's distance from Sun = 4.4*10^12 m
Planet X's radius = 1.4*10^6 m
Planet X's mass = 8.2*10^22 kg


d.) At 1 of Planet X's radii above the planet's surface, what is gx? ?m/s2

e.) Find the orbital speed of Planet X around the Sun. ?m/s

f.) How long is a year on Planet X? Express your answers in both seconds and Earth years:
? s
? Earth years

Explanation / Answer

d) g/g'=(r+h)2/r2

where h=r

g/g'=4r2/r2

g'=0.25g

=0.7m/s2

e) GmM/r2=mv2/r   (centripetal force)

=5478.6 m/s (note M is mass of the sun and r is the distance between X and the sun)

f) use v=2r/T

and solve for T.

T=5046x106s

=160 earth years

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