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Q1 Mars is our outer neighbor in the solar system (the 4th planet from the Sun.

ID: 1782019 • Letter: Q

Question

Q1 Mars is our outer neighbor in the solar system (the 4th planet from the Sun. Its average distance from the sun is 52.4% larger than that of Earth, its mass is 10.7% of the mass of Earth, and its radius is 53.2% of that of Earth (it has a lower density). (a) [8 pts] How large is the force the force from the Sun on Mars compared to that of the force from the Sun of Earth? How large is the force from Mars on the Sun? (b) [8 pts] How long is the Mars year? Assume that the Earth year is 365 days. (c) [8 pts] How large is the acceleration due to gravity on the Mars surface? Assume that g = 9.8 m/s2 on Earth.

Explanation / Answer

a)

rm = distance of mars from sun

re = distance of earth from sun

rm = 1.524 re

Mm = mass of mars

Me = mass of earth

Mm = 0.107 Me

Rm = radius of mars = 0.532 Re

Fsm = force by sun on mars = G Mm m/rm2

Fse = force by sun on earth = G Me m/re2

Fsm /Fse = (G Mm m/rm2 )/(G Me m/re2 ) = (Mm /Me ) (re2/rm2) = (0.107) (1/1.524)2 = 0.046

so 0.046 times the force on earth by the sun

Fsm = (0.046) (GMe m/re2) = (0.046) (6.67 x 10-11) (5.98 x 1024) (2 x 1030)/(1.5 x 1011)2 = 1.63 x 1021 N

b)

T2m/T2e = (rm/re)3

T2m/(365)2 = (1.524)3

Tm = 686.7 days

c)

gm/ge = (Mm/Me) (Re/Rm)2 = (0.107) (1/0.532)2 = 0.378

gm = 0.378 x 9.8 = 3.7