Question

Problem 3) The Gravitational Force:

The average distance between the center of the Earth and the center of the Moon is 384,000 km. A 3.00 x 10^4 kg spaceship is located halfway between the center of the Earth and the center of the Moon. Let the Earth be to the right of the spaceship and the Moon be to the left.

a) Draw a force diagram of the spaceship.

b) Solve for the net force (magnitude and direction) acting on the spaceship at this location. (Earth's mass= 5.98x10^24 kg, Moon's mass= 7.36x10^22 kg)

c) Why does the net force point towards the Earth in this case?

d) Solve for the acceleration of the spaceship at this location.

Answer #1

The average distance separating Earth and the Moon is
384000 km. Mass of the earth is 5. 98 x 1024 kg and mass of the
moon is 7. 36 x 10 kg. Find the gravitational forces exerted by
Earth and the Moon on a 3. 00 x 10 kg spaceship located halfway
between them, (G - 6. 67x10 - "Nr / kg)

Calculate, using Newton's law of gravity, the size of the force
of attraction between the earth and a mass of 2.0 kg on the earth.
Data: Distance to the center of earth from the surface = 6370 km.
Mass of earth = 5.98·1024kg. Gravitational constant G = 6.67·10-11
Nm2/kg2.
Calculate, using Newton's law of gravity, the size of the force
of attraction between the moon and a mass of 2.0 kg on the earth's
surface nearest the moon. Data: Distance...

(a) Find the magnitude of the gravitational force (in N) between
a planet with mass 8.25 ✕ 1024 kg and its moon, with mass 2.50 ✕
1022 kg, if the average distance between their centers is 2.60 ✕
108 m.
_________________ N
(B) What is the moon's acceleration (in m/s2) toward
the planet? (Enter the magnitude.)
_________________ m/s2
(c) What is the planet's acceleration (in m/s2)
toward the moon? (Enter the magnitude.)
__________________ m/s2

(a) Find the magnitude of the gravitational force (in N) between
a planet with mass 8.00 ✕ 1024 kg and its moon, with mass 2.65 ✕
1022 kg, if the average distance between their centers is 2.90 ✕
108 m.
N
(b) What is the moon's acceleration (in m/s2) toward the planet?
(Enter the magnitude.)
m/s2
(c) What is the planet's acceleration (in m/s2) toward the moon?
(Enter the magnitude.)
m/s2

(a)
Find the magnitude of the gravitational force (in N) between a
planet with mass 8.50 ✕ 1024 kg and its moon, with mass
2.40 ✕ 1022 kg, if the average distance between their
centers is 2.70 ✕ 108 m.
N
(b)
What is the moon's acceleration (in m/s2) toward the
planet? (Enter the magnitude.)
m/s2
(c)
What is the planet's acceleration (in m/s2) toward
the moon? (Enter the magnitude.)
m/s2

Find the magnitude of the gravitational force (in N) between a
planet with mass 8.75 ✕ 1024 kg and its moon, with mass
2.45 ✕ 1022 kg, if the average distance between their
centers is 2.90 ✕ 108 m.
N
(b)
What is the moon's acceleration (in m/s2) toward the
planet? (Enter the magnitude.)
m/s2
(c)
What is the planet's acceleration (in m/s2) toward
the moon? (Enter the magnitude.)
m/s2

(a) Find the magnitude of the gravitational force (in N) between
a planet with mass 6.75 ✕ 1024 kg and its moon, with mass 2.60 ✕
1022 kg, if the average distance between their centers is 2.10 ✕
108 m. Incorrect: Your answer is incorrect. N (b) What is the
moon's acceleration (in m/s2) toward the planet? (Enter the
magnitude.) m/s2 (c) What is the planet's acceleration (in m/s2)
toward the moon? (Enter the magnitude.) m/s2

uring a solar eclipse, the Moon is positioned directly between
Earth and the Sun.
The masses of the Sun, Earth, and the Moon are 1.99×1030
kg,1.99×1030 kg, 5.98×1024 kg,5.98×1024 kg, and 7.36×1022
kg,7.36×1022 kg, respectively. The Moon's mean distance from Earth
is 3.84×108 m,3.84×108 m, and Earth's mean distance from the Sun is
1.50×1011 m.1.50×1011 m. The gravitational constant is G=6.67×10−11
N⋅m2/kg2.G=6.67×10−11 N·m2/kg2.
Find the magnitude FF of the net gravitational force acting on
the Moon during the solar eclipse...

(a) Calculate the magnitude of the
gravitational force exerted on a 407-kg satellite that is a
distance of 2.45 earth radii from the center of the earth.
(b) What is the magnitude of the gravitational
force exerted on the earth by the satellite? (c)
Determine the magnitude of the satellite's acceleration.
(d) What is the magnitude of the earth's
acceleration?

Let
F equal the gravitational force between the Earth and Moon. If the
distance between (centers of) Earth and Moon is halved, what would
the gravitational force between them equal ?

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