Gravitational Field Strength Equation (College Board AP® Physics 1: Algebra-Based): Study Guide
Gravitational field strength equation
The magnitude of the gravitational field,
, created by a system of mass,
, at a point in space is equal to the ratio of the gravitational force,
, exerted by the system on a test object of mass,
, to the mass of the test object,
Consider the Moon in orbit around the Earth:
The Earth is the system of mass
that creates the gravitational field of magnitude
The Moon is the test object of mass
within the Earth's gravitational field
Hence,
is equal to the ratio of
and
Gravitational field strength of Earth on Moon

This defines the gravitational field strength formula:
Where:
magnitude of the gravitational field or gravitational field strength, measured in
gravitational force, measured in
mass of test object, measured in
This is also equal to:
Where:
universal gravitational constant
the mass of the system creating the gravitational field, measured in
the radius of the system creating the gravitational field, measured in
Derived equation
The magnitude of the gravitational field,
, created by a system of mass,
, at a point in space is equal to the ratio of the gravitational force,
, exerted by the system on a test object of mass,
, to the mass of the test object,
Derivation:
Step 1: Identify the fundamental principles
Step 2: Apply the specific conditions
Newton's second law
When the gravitational force is the only force exerted on an object the acceleration,
, is equal to the magnitude of the gravitational field,
Hence,
Newton's law of gravitation
The mass of the system creating the gravitational field is
which represents
The mass of the test mass in the gravitational field is
which represents
Step 3: Combine and simplify the two conditions
The gravitational force from Newton's second law equals the gravitational force from Newton's law of gravitation
Divide by the test mass
Simplify
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