Gravitation Quiz
Name: _________________________
I. MULTIPLE CHOICE QUESTIONS
1
3
A spacecraft orbits Earth in a circular orbit of
radius 𝑅, as shown above. When the
spacecraft is at position 𝑃 shown, a short burst
of the ship’s engines results in a small increase
in its speed. The new orbit is best shown by
the solid curve in which of the following
diagrams?
A small satellite is in elliptical orbit around
Earth as shown. If 𝐿 denotes the magnitude of
its angular momentum and 𝐾 denotes kinetic
energy:
(A) 𝐿2 > 𝐿1 and 𝐾2 > 𝐾1
(B) 𝐿2 > 𝐿1 and 𝐾2 = 𝐾1
(C) 𝐿2 = 𝐿1 and 𝐾2 = 𝐾1
(D) 𝐿2 < 𝐿1 and 𝐾2 = 𝐾1
(E) 𝐿2 = 𝐿1 and 𝐾2 > 𝐾1
4
2
Satellite 𝑋 moves around Earth in a circular
orbit of radius 𝑅. Satellite 𝑌 is also in a circular
orbit around Earth, and it completes one orbit
for every eight orbits by satellite 𝑋. What is
the orbital radius of satellite 𝑌?
(A) (1/4)𝑅
(D)
4𝑅
(B) (1/2)𝑅
(E)
8𝑅
(C) 2𝑅
The graph above shows the force of gravity on
a small mass as a function of distance 𝑅 from
the center of the Earth of radius 𝑅𝑒 , if the
Earth is assumed to have a uniform density.
The work done by the force of gravity when
the small mass approaches Earth from far
away and is placed into a circular orbit of
radius 𝑅2 is best represented by the area
under the curve between
(A) 𝑅 = 0 and 𝑅 = 𝑅𝑒
(B) 𝑅 = 0 and 𝑅 = 𝑅2
(C) 𝑅 = 𝑅𝑒 and 𝑅 = 𝑅2
(D) 𝑅 = 𝑅𝑒 and 𝑅 = ∞
(E) 𝑅 = 𝑅2 and 𝑅 = ∞
5
8
A newly discovered planet is found to have
twice the radius and five times the mass of
Earth. If the acceleration of gravity at the
surface of Earth is 𝑔, the acceleration of
gravity at the surface of the new planet is
(A) 6.0 kgm2 /s
(D)
72 kgm2 /s
(B) 12 kgm2 /s
(E)
576 kgm2 /s
(C) 48 kgm2 /s
A comet moves in the Sun’s gravitational field,
following the path shown above. What
happens to its angular momentum as it moves
from point 𝑋 to point 𝑌?
9
(A) It increases steadily.
(B) It remains constant.
𝐺𝑀
(A) 𝑣 = √
𝑅
(C) It decreases steadily.
(D) It increases as it approaches the Sun
and decreases as it moves away from
the Sun.
(B) 𝑣 =
(E) It decreases at it approaches the Sun
and increases as it moves away from
the Sun.
6
(D)
270 N
(B) 30 N
(E)
810 N
𝐺𝑀
2𝑅
𝐺𝑀
(C) 𝑣 = √
2𝑅
An object at the surface of Earth (at a distance
𝑅 from the center of Earth) weighs 90 N. What
is its weight at a distance 3𝑅 from the center
of Earth?
(A) 10 N
A satellite of mass 𝑚 is in a circular orbit about
the Earth (mass = 𝑀) at a height ℎ above the
surface, where ℎ = 𝑅, the radius of the Earth.
What velocity should this satellite have in
order to maintain its orbit?
𝐺𝑀𝑚
(D) 𝑣 = √
2𝑅
(E) 𝑣 = √𝐺𝑀
2R
(C) 90 N
7
The escape speed for a rocket at Earth’s
surface is 𝑣𝑒 . What would be the rocket’s
escape speed from the surface of a planet with
twice Earth’s mass and the same radius as
Earth?
(A) 2 𝑣𝑒
(B) 𝑣𝑒
(C)
1
𝑣
2 𝑒
1
√2
What event will produce the greatest increase
in the gravitational force between the two
masses shown above?
(A) doubling the large mass
(D) √2 𝑣𝑒
(E)
10
𝑣𝑒
(B) doubling the distance
(C) reducing the small mass by half
(D) reducing the distance between the
masses by half
(E) The gravitational force is constant
II. FREE RESPONSE QUESTION
Mech. 2. A student is given the set of orbital data for some of the moons of Saturn shown below and is asked to
use the data to determine the mass 𝑀𝑆 of Saturn. Assume the orbits are circular.
Orbital Period, 𝑇
(seconds)
Orbital Radius, 𝑅
(meters)
8.14 × 104
1.85 × 108
1.18 × 105
2.38 × 108
1.63 × 105
2.95 × 108
2.37 × 105
3.77 × 108
(a) Write an algebraic expression for the gravitational force between Saturn and one of its moons.
(b) Use your expression from part (a) and the assumption of circular orbits to derive an equation for the orbital
period 𝑇 of a moon as a function of its orbital radius 𝑅.
(c) Which quantities should be graphed to yield a straight line whose slope could be used to determine Saturn’s
mass?
(d) Complete the data table on the previous page, by calculating the two quantities to be graphed. Label the top
of each column, including units.
(e) Plot the data on the graph on the previous page. Label the Axes with the variables and appropriate numbers
to indicate the scale.
(f) Using the graph, calculate a value for the mass of Saturn. Show your work in the space below.