Gravitation problems from prior exams:
1)
Ekapluto is an unknown planet that has two moons in circular orbit. Moon A has a mass of
4 x 1020 kg, a mean orbital radius of 3.0 x 108 m and an orbital period of 4 x 106 s. Moon B
has a mass of 1.5 x 1020 kg and a mean orbital radius of 3.9 x 108 m. The orbital period of
Moon B is closest to
5.6 x 106 s
a)
6
b) 5.9 x 10 s
6.6 x 106 s
c)
6
d) 6.9 x 10 s
7.3 x 106 s
e)
2)
A moon, Oyo, travels at a speed vo around its planet. If the mean orbital radius of another of
the planet’s moons, Froyo, is twice as big, Froyo’s orbital speed, vf , is
a)
v f = 2v o
b)
v f = 2v o
!
c)
not changed.
!
d)
v f = vo / 2
e)
v f = v o /2
!
3) A drome weighs 50 stobes on its home planet of Nedrom. It travels to a new planet,
!
Xarxes, that has 3 times the mass and 5 times the radius of Nedrom. How much does
the drome weigh on Xarxes? Explain your reasoning below (A stobe is a unit of
weight; no conversions to familiar units are necessary for this problem.)
a)
30 stobes
b)
18 stobes
c)
6 stobes
d)
150 stobes
e)
83 stobes
4) Two planets move around their Sun. The first one is twice as massive and three times farther
from their Sun than the second one. Compare their periods.
5)
a)
T1=3T2
b)
T1=√3T2
c)
T1=3√3T2
d)
T1=27T2
e)
T1=9√3T2
A geosynchronous orbit (period = 1 day) has a radius of 4.22 x 107 m. Suppose we want a
satellite to revolve around the earth 4 times a day. What should the radius of its orbit be?
(Neglect the presence of the moon.)
a.
1.67 x 107 m
b.
1.01 x 107 m
c.
2.11 x 107 m
d.
1.41 x 107 m
e.
2.03 x 107 m