Download Newton`s Law of Universal

Newton’s Law of Universal Gravitation
Name_____________________________________
https://www.explorelearning.com/ simulation: Gravitational Force
Newton’s law of universal gravitation states that any two bodies in the universe attract each other with a force that is
directly proportional to the product of their masses and inversely proportional to the square of the distance between
them.
Newton’s law of gravitation resembles Coulomb’s law.
Both are inverse square laws.
Use the simulation to help you answer the following:
1. Gravitational force is always attractive/repulsive. (circle)
2. If a gravitational force exists between two objects, one very massive and one less massive, then the force on the
less massive object will be greater than/equal to/ less than the force on the more massive object.
3. As the distance between masses decreases, force increases/decreases.
4. Doubling the mass of both objects would result in the change in force of 4x/2x/no change/ 12x/ 14x
5. Doubling the distance between two objects will change the force of 4x/2x/no change/ 12x/ 14x
Fill out the chart below with data from the simulation. Calculate the average G value and compare to the
published value. Change the mass by clicking in the mass box and typing in your own value. Change the distance
by grabbing a mass and dragging it.
Mass Object 1
Mass Object 2
Distance
Force
Average value of G ________________ Published Value of G ________________
How do the values compare?
Gravitation Constant,
G
Gravitational Force and Centripetal Motion
The gravitational force is the force that makes a satellite (manmade or a moon or a planet) move in a circle around
another larger mass. The gravitational force is the centripetal force.
FG =
𝑚𝑣 2
𝑟
m = the mass of the rotating object
r = the distance between the centers of the two objects
V = the speed of the rotating object –can be found with v=
2𝜋𝑟
𝑇
if you know the period and radius
1. Calculate the orbital speed for a satellite 1000 km above the Earth’s surface. Mass of the Earth = 5.97 X 1024 kg. Radius
of the Earth 6378 km. Ans: 7346.5 m/s
2. A satellite is in a circular orbit around the Earth. The period of the satellite is 22.0 hr. Calculate the radius of the orbit
of the satellite. Mass of the Earth = 5.97 X 1024 kg Ans: 3.98 X 107 m
Gravity on the surface of Planets
The acceleration due to gravity on Earth is accepted at 9.8 m/s2 toward the center of the Earth. This can be derived using
Newton’s Law of Gravitation.
Apply Newton’s 2nd Law
We can use this to find the acceleration due to gravity at any point in space or on any
planet as long as we know the radius of the planet and the distance an object is from the
surface. Notice that the mass the object cancels out and does not factor into the
acceleration due to gravity.
1. Calculate the acceleration due to gravity on the Moon. The Moon’s radius is 1.74 X 10 6 m and its mass is 7.35 X 1022 kg. Ans: 1.62
m/s2.
2. Suppose you are on a distant planet and you are trying to determine the acceleration due to gravity there. You drop a rock from
40 meters and it hits the ground in 2.4 seconds. How many times greater is the acceleration due to gravity on this planet than it is on
Earth? Ans: 1.4gearth
3. An artificial satellite circles the Earth in a circular orbit at a location where the acceleration due to gravity is 4.26 m/s 2. Determine
how far above the Earth’s surface the satellite is orbiting. Mass of the Earth = 5.97 X 1024 kg. Radius of the Earth 6378 km. Ans: 3.3 X
106 m
4. An astronaut’s pack weighs 15.5 N when she is on Earth but only 3.97 N when she is at the surface of an asteroid. (a) What is the
acceleration due to gravity on this asteroid? (b) What is the mass of the pack on the asteroid? Ans: 2.51 m/s2, 1.58 kg