Q1 Mars is our outer neighbor in the solar system (the 4th planet from the Sun.
ID: 1782019 • Letter: Q
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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
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