Newton’s Law of Universal Gravitation
Name ____________________
The following equation is Newton’s Law of Universal Gravitation:
f G
m1m2
d2
Where G = 6.67  10 –11 N (m/kg)2
Remember:
The force of gravity between two objects is directly proportional to the product of the two
masses. If you double the mass of either object, you double the force of gravity between them. If
you triple the mass of either object, you triple the force.
The force of gravity is inversely proportional to the square of the distance between the centers of
the two masses. If you double the distance, the force is four (22) times smaller. If your triple the
distance, the force of gravity is nine (32) times weaker.
1.
If you weigh 945 N on the surface of the earth, how much would you weigh on the top of
a building that was 25,500 km high -- so high that you were four times further away from
the earth’s center than you were at the surface?
2.
Suppose you weighed 945 N when you went to bed, and for some strange reason the
Earth shrank so small during the night that when you woke up its radius was only 1/10th
its normal size, yet its mass remained constant. How much would you weigh in the
morning?
3.
If you weigh 654 N on Earth, how much would you weigh on a planet that had the same
radius as the earth, but only half the mass?
4.
If you weigh 746 N on earth, how much would you weigh on a planet with the same mass
as earth, but with a radius that was three times bigger than earth?
5.
A climber weighs 128 lbs standing at the bottom of Mt. Everest (6,378,000meters above
the center of the earth). How much would she weigh at the summit (6,386,850 meters
above the center of the earth)? (hint: how many times further away from the center is
she?)
6.
If you have a mass of 55 kg and you are standing 3 meters away from your car, which has
a mass of 1234 kg, how strong is the force of gravity between you and the car?
7.
The moon has a mass of 7.34  10 22 kg and a radius of 1.74  106 meters. If you have a
mass of 66 kg, how much would you weigh if you stood on the moon?
8.
The moon has a mass of 7.34  10 22 kg and its center is 3.86  10 8 meters above you. If
you have a mass of 58 kg, how much upward force does the moon exert on you when it is
directly overhead?
9.
The sun has a mass of 1.99  10 30 kg and its center is 1.50  10 11 meters above you. If
you have a mass of 58 kg, how much upward force does the sun exert on you when it is
directly overhead?
10.
Newton knew exactly how to find the mass of the Earth, but he was unable to make the
calculation because he didn’t know the value of G. As soon as G was found to be
6.67  10 –11 m2/kg2 scientists quickly computed the earth’s mass. If 1 kg of mass has a
weight of 9.8 N at a distance of 6.38  106 meters above the earth’s center, what is the
mass of the Earth?
11 -13. Romeo is a 68 kg astronaut. Juliet is a beautiful cosmonaut who is standing on the
balcony of a 4.58  105 kg space station that is at rest and out of gas. Romeo is floating
25 meters away from the space station’s center of mass, and is 10 meters away Juliet. If
Romeo’s only form of locomotion is Universal Gravitation, how long will it take him to
reach her loving embrace?
11.
Step 1: Use the Law of Universal Gravitation to find the force acting on Romeo.
12.
Step 2: Calculate his rate of acceleration using Newton’s Second Law of Motion.
13.
Step 3: Determine the time it will take Romeo to travel 10 meters at this rate
of acceleration using d = ½ at2 (Assume that acceleration stays constant, and
that the space station does not move.)
moon
radius = 1737 km
mass 7.34  1022 kg
1/6th surface gravity of earth
distance 384,400 km
orbital velocity = 1000 m/s
sun
700 million meters = radius
distance 149,600 million meters
mass 330,000 x Earth
Earth
12,753 km = diameter
radius = 6376500 meters
mass = 5.98e24 kg