Physics 20 - STA
Note Booklet
Unit 2 – Dynamics
Chapter 4 – Gravitational Force
Name: ______________________________________________________________________________
1|Page
Table of Contents
4.1 Gravitational Forces due to Earth
4.2 Newton’s Law of Universal Gravitation
4.3 Gravitational Field strength
2|Page
4.1 Gravitational Forces due to Earth
In the previous chapter, we studied the effect of various forces on an object. One force that is always
present, is the force of gravity. Gravity is one of the four fundamental forces of nature. These
fundamental forces of nature are responsible for all interactions in nature.
The four fundamental forces of nature (in descending order of strength):
1. Strong Nuclear
2. Electromagnetic
3. Weak Nuclear
4. Gravity
The gravitational force (Fg) attracts any two objects together. This attraction is a direct consequence of
Newton’s third law.
Example 1: Homer has a mass of 120 kg, the Earth has a mass of 5.98 x 1024 kg. The gravitational field
strength on the earth surface is g = 9.81 m/s2.
a.
What is the gravitational force on Homer?
b.
What is the gravitational force on the Earth?
c.
What is the resultant acceleration of the Earth?
Recall from last chapter the concept of weight and the difference between weight and mass. Mass
(inertial mass) is a measurement of the amount of atoms present in an object. Weight is dependant on
location and is equivalent to the force of gravity acting on an object due to another object, usually a
celestial body.
Weight = Fg = mg
Example 2: I have a 5.00kg rock.
a) Determine how much it weighs on the Earth and on the Moon. The acceleration due to gravity on the
Moon is 1.67m/s²
b) Determine its mass on the Earth and on the Moon.
Example 3: An object is accelerated at 3.24m/s² by a 6.72 x 104 N force. Determine its inertial mass.
3|Page
Fields are regions of influence around an object. If these fields exert a force, they are called vector
fields. Fields that do not exert a force are called scalar fields. Michael Faraday is credited for inventing
the idea of a field in the 19th century. Field lines are vector arrows around an object indicating the
magnitude and direction of the field. The closer the lines are together, the stronger the field.
A gravitational field is a region around any object of mass such that if another object enters that region,
it will experience this force. For this reason, an object may experience a force without coming into
contact with the other object causing the force. For the diagram above, notice how the field lines are
pointing toward the centre of the Earth. The gravitational force is always directed toward the center of
mass that is creating the force.
The gravitational field strength is simply the amount of gravitational force per unit of mass. We often
refer to gravitational field strength as the acceleration due to gravity
g

F
m
g
*Note: Mtest is the mass of the object placed in the gravitational field, not
test
the mass of the object creating the gravitational field.

It is important to note that gravitational field strength has an inverse square relationship with the
distance from the centre of the mass creating the field.
4|Page
4.2 Newton’s Law of Universal Gravitation
Forces exist between two objects. If object A exerts a force on object B, then object B will apply a force
on object A. Newton concluded that:
F
 ma mb
Recall from 4.1, that force has an inverse square relationship with the distance from the object creating
the force:

F

1
r
2
Newton determined that if you combine these formulas you get the following:

F

mm
r
a
b
2
This mathematical relationship is true but is missing a constant value (G) that when multiplied by the
two masses and divided by the square of the distance (r) will give you the gravitational force between
two objects. The Cavendish
experiment used a torsion balance to determine the constant G.
Newton’s law of Universal Gravitation was now complete:
F

Gmm
r
a
2
b
where F is the gravitational force (N) between two objects, ma and mb are the masses (kg) of both of the
objects involved, r is the distance (m) separating the centres of the objects, and G is a constant called the
gravitational constant (6.67 
x 10-11 Nm2/kg2).
Examples
1. Two pumpkins have masses of 2.0 kg and 3.0 kg and there are placed 40 cm apart. What is the force
due to gravity between them?
5|Page
2.The Earth has a mass of 5.97 x 1024 kg, and the moon has a mass of 7.35 x 1022 kg, the Earth’s moon
is a distance of 3.84 x 108 m. What is the force due to gravity between the Earth and the moon?
3. Dexter has a mass of 45 kg and stands on the surface of the Earth, the Earth has a mass of 5.97 x 1024
kg and a radius of 6.37 x 106 m. The altitude of the International Space Station ISS varies from 320 km
to 347 km.
a. What is the force due to gravity on Dexter on the Earth’s surface?
b. What is the force due to gravity on Dexter if he is on board the ISS (320 km)?
4. Two dogs are sitting on the front porch. The force due to gravity between them is 4.00 x 10-8 N. What
is the new force due to gravity if:
a. One of the masses is doubled?
b. The distance between them is doubled?
c. Both masses are tripled?
d. Both masses are doubled and the distance between them is halved?
5.
6|Page
4.3 Gravitational Field strength
We already know that the acceleration due to gravity on the surface of the Earth is approximately 9.81
m/s2 (depending on the location). This acceleration due to gravity is caused by the Earth itself. It
influences any object that is present on or near the surface of the Earth.
The strength of the gravitational field can be found in one of two ways. If you have information about
the object that is causing the field (the source), use the following equation:
where g is the gravitational field strength (m/s2 or N/kg), G is the gravitational constant (6.67 x 10-11
Nm2/kg2), m is the mass of the producer that is causing the gravitational field (kg), and r is the distance
from the centre of the producer where you are trying to find the gravitational field strength (m).
If you have information about the object that is experiencing the field (the test mass if there is even one
present), use the following equation:
g

F
m
g
test
where g is the gravitational field strength (m/s2 or N/kg), F is the force of gravity (weight) felt by the

source (N), and m is the test mass (kg).
Examples
1. The Earth has a mass of 5.97 x 1024 kg and a radius of 6.37 x 106 m. What is the gravitational field
strength at the Earth’s surface? Why is this number different then 9.81m/s2?
7|Page
2.Using the data from the chart, what is the gravitational field strength on:
a.
Mars?
b.
the Sun?
3.How much more do you weigh on Jupiter than you do on Earth?
4. The ISS is at an altitude of 320 km above the Earth’s surface, what is the gravitational field strength
of the Earth on the ISS?
8|Page