Download Gravitational Calculations

Physics
Name ___________________________
Period ____
Date ___________________
Gravitational Calculations
1.
The Moon remains in its orbit around the Earth rather than falling to the Earth
because of the following reason(s). (Select all that apply.)
The net force on the Moon is zero.
It is outside of the gravitational influence of the Earth.
It is in balance with the gravitational forces from the Sun and other planets.
none of these
2.
A planet has two moons of equal mass. Moon 1 is in a circular orbit of radius r.
Moon 2 is in a circular orbit of radius 5r. Which of the following best describes
the magnitude of the gravitational force exerted by the planet on moon 2?
five times as large as that on moon 1
one twenty-fifth as large as that on moon 1
one fifth as large as that on moon 1
equal to that on moon 1
twenty-five times as large as that on moon 1
3.
Superman stands on top of a very tall mountain and throws a baseball horizontally
with a speed such that the baseball goes into a circular orbit around the Earth.
Which of the following best describes the acceleration of the baseball while it is
in orbit?
depends on how fast the baseball is thrown
zero because the ball does not fall to the ground
equal to 9.80 m/s2
slightly less than 9.80 m/s2
4.
Neptune, the planet farthest from the Sun, has an orbital period that is best
described by which of the following?
less than an Earth year
equal to an Earth year
greater than an Earth year
5.
The weight of an astronaut working in the International Space Station is described
by which of the following?
about the same as the weight of the same astronaut working on the surface of
the Earth
much greater than the weight of the same astronaut working on the surface of
the Earth
much smaller than the weight of the same astronaut working on the surface of
the Earth
zero
6.
If the gravitational force between the electron (9.11 10-31 kg) and the proton
(1.67 10-27 kg) in a hydrogen atom is 1.32 10-47 N, how far apart are the two
particles?
m
7.
8.
What would be the orbital speed and period of a satellite in orbit 1.20 108 m
above the Earth?
orbital speed
m/s
period
s
A satellite with an orbital period of exactly 24.0 h is always positioned over the
same spot on Earth. This is known as a geosynchronous orbit. Television,
communication, and weather satellites use geosynchronous orbits. At what
distance would a satellite have to orbit Earth in order to have a geosynchronous
orbit?
m
9.
During a solar eclipse, the moon, Earth, and sun lie on the same line, with the
moon between Earth and the sun.
(a) What force is exerted on the moon by the sun?
N
(b) What force is exerted on the moon by the Earth?
N
(c) What is the net force exerted on the Moon by the Earth and Sun?
N
Average Earth-moon distance = 3.84 108 m, Average Earth-sun distance = 1.5
1011 m, mass of the moon = 7.35 1022 kg, mass of the Earth = 5.97 1024 kg,
mass of the sun = 1.99 1030 kg
10.
Jupiter's four large moons -- Io, Europa, Ganymede, and Callisto -- were
discovered by Galileo in 1610. Jupiter also has dozens of smaller moons. Europa
has a radius of about 1.57 106 m, and the mean distance between Europa and
Jupiter is 6.71 108 m.
(a) If Europa's orbit were circular, how many days would it take Europa to
complete one full revolution around Jupiter?
days
(b) If Europa's orbit were circular, what would its orbital speed be?
m/s
11.
Find the mass of the Sun using the Earth’s orbital period and mean distance from
the Sun. (T = 3.156 x 107s; r = 1.496 x 1011m)
kg
12.
A satellite is relocated from its original orbit around the Earth to an orbit that is 6
times the radius of the original orbit. As a consequence of this move, the new
period will be ______________the original period.
2.45 times
14.70 times
6 times
the same as
36 times
13.
An engineer is not satisfied with the current state of affairs concerning
geosynchronous satellites. He is annoyed that these satellites orbit at such high
altitudes (36,000 km) precluding their use as spy satellites. To remedy the
situation, he proposes to send a satellite into geosynchronous orbit at a much
lower altitude. He reasons that at a much lower altitude, the circumference of the
orbit will be much smaller and the required speed of the satellite will be
consequently less to cover the shorter distance in 24 hours. If the satellite
company agrees to send a satellite at this lower altitude orbit at a reduced speed,
the result will be which of the following?
a satellite that spirals down to Earth
a satellite that falls straight down to Earth
a satellite that successfully maintains a geosynchronous orbit at this lower
altitude
a satellite that spirals outward away from the Earth eventually escaping the
Earth’s gravity
14.
On the way to the Moon the Apollo astronauts reached a point where the Moon's
gravitational pull became stronger than the Earth's.
(a) Determine the distance of this point from the center of the Earth.
m
(b) What is the acceleration due to the Earth's gravitation at this point?
m/s2
15.
The center-to-center distance between a planet and its moon is 454600 km. The
moon completes an orbit in 26.9 days. Determine the moon's orbital speed.
m/s
16.
Plaskett's binary system consists of two stars that revolve in a circular orbit about
a center of mass midway between them. This means that the masses of the two
stars are equal. Assume the orbital speed of each star is 200 km/s and the orbital
period of each is 11.4 days. Find the mass M of each star. (For comparison, the
mass of our Sun is 1.99 1030 kg.)
solar masses
17.
Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of
4.22 105 km. From these data, determine the mass of Jupiter.
kg
18.
After our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a
white-dwarf state, in which it has approximately the same mass as it has now but
the radius equal to the radius of the Earth.
(a) Calculate the average density of the white dwarf.
kg/m3
(b) Calculate the free-fall acceleration at its surface.
m/s2