Lesson 9
LAW OF UNIVERSAL
GRAVITATION
AP Physics B Standards
LESSON 9:
Law of Universal Gravitation

I.F.4. Newton’s Law of Gravity
Students should know Newton’s Law of Universal Gravitation, so they
can:
a) Determine the force that one spherically symmetrical mass exerts
on another.
b) Determine the strength of the gravitational field at a specified point
outside a spherically symmetrical mass.
Lesson Objectives


Calculate the force of gravitational attraction between any
two massive bodies.
Calculate the acceleration of a massive object toward a
more massive object.
Isaac Newton

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Arguably the greatest scientific genius ever.
Came up with 3 Laws of Motion to explain the
observations and analyses of Galileo and Johannes Kepler.
Discovered that white light was composed of many colors
all mixed together.
Invented new mathematical techniques such as calculus
and binomial expansion theorem in his study of physics.
Published his Laws of Motion in 1687 in the book
Mathematical Principles of Natural Philosophy.
The Universal Law of Gravitation


Newton’s famous apple fell
on Newton’s famous head,
and led to this law.
It tells us that the force of
gravity objects exert on each
other depends on their
masses and the distance they
are separated from each
other.
Newton’s Law of Gravity
Gm1m2
F
2
r
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The force of attraction between two masses is directly
proportional to the product of the masses and inversely
proportional to the squared distance between the
centers of the masses.
G = 6.67 x 10-11 N m2/kg2
The Universal Law of Gravity ALWAYS works, whereas
FG = mg only works when you’re standing on the surface
of the earth.
Sample Problem 9.1:
a) How much force does the earth exert on the moon? b) How much force does the moon exert on the earth?
me= 5.97 x 1024 kg, mm = 7.36 x 1022 kg,
rem=3.84 x 108 m
Sample Problem 9.2:
Using centripetal force and Newton’s Law of Universal Gravitation, derive the mass of the sun using the orbit of the earth. Sample Problem 9.3:
What would be your weight if you were orbiting the earth in a satellite at an altitude of 3,000,000 km above the earth’s surface? (Note that even though you are apparently weightless, gravity is still exerting a force on your body, and this is your actual weight.)
Acceleration due to gravity
Remember g = 9.8 m/s2?
 This works find when we are near the
surface of the earth.
 For space travel, we need a better formula!

Acceleration due to gravity
g
2
= GM/r
This formula lets you calculate g anywhere
if you know the distance a body is from the
center of mass of a planet.
 We can calculate the acceleration due to
gravity anywhere!
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Sample Problem 9.4:
Derive the numeric value of the acceleration due to gravity on the surface of the earth. Start with Newton’s 2nd Law.
Acceleration due to gravity
g
2
= GM/r
This formula lets you calculate g anywhere
if you know the distance a body is from the
center of mass of a planet.
 We can calculate the acceleration due to
gravity anywhere!

Acceleration and distance
Surface gravitational acceleration depends on
mass and radius.
Planet Radius
Mass
g
Mercury
2.43 x 106
3.2 x 1023
3.61
Venus
6.073 x 106
4.88 x1024
8.83
Mars
3.38 x 106
6.42 x 1023
3.75
Jupiter
6.98 x 107
1.901 x 1027
26.0
Saturn
5.82 x 107
5.68 x 1026
11.2
Uranus
2.35 x 107
8.68 x 1025
10.5
Neptune
2.27 x 107
1.03 x 1026
13.3
Pluto
1.15 x 106
1.2 x 1022
0.61
(m)
(kg)
(m/s2)
Sample Problem 9.5:
What is the acceleration due to gravity at an altitude equal to twice
the earth’s radius?
Sample Problem 9.6:
What is the acceleration due to gravity at the surface of the moon?