If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## High school physics - NGSS

### Course: High school physics - NGSS>Unit 2

Lesson 1: Newton's law of universal gravitation

# Newton’s law of universal gravitation

Review your understanding of Newton's law of universal gravitation in this free article aligned to NGSS standards.

## Key terms

TermMeaning
Gravitational force (F, start subscript, start text, g, end text, end subscript)Attractive force between two objects with mass.
Gravitational field (g)A model explaining the influence an object extends to produce a force on other objects.
Gravitational mass (m)The property of matter that causes it to experience a force in a gravitational field. Two objects that balance each other on a scale have the same gravitational mass. Gravitational mass is experimentally equivalent to inertial mass, and has SI units of start text, k, g, end text.

## Equations

EquationSymbol breakdownMeaning
F, start subscript, g, end subscript, equals, G, start fraction, m, start subscript, 1, end subscript, m, start subscript, 2, end subscript, divided by, r, squared, end fractionF, start subscript, g, end subscript is gravitational force, G is the gravitational constant, m, start subscript, 1, end subscript and m, start subscript, 2, end subscript are point-like masses, and r is the distance between the masses.The gravitational force between point-like mass m, start subscript, 1, end subscript and m, start subscript, 2, end subscript is directly proportional to their masses and inversely proportional to the square of the distance between them.
g, equals, start fraction, F, start subscript, g, end subscript, divided by, m, start subscript, 2, end subscript, end fraction, equals, G, start fraction, m, start subscript, 1, end subscript, divided by, r, squared, end fraction g is the gravitational field strength.The gravitational field strength is directly proportional to mass creating the field and inversely proportional to the square of the distance.

## Newton’s law of universal gravitation

Gravitational force F, start subscript, g, end subscript is always attractive, and it depends only on the masses involved and the distance between them. Every object in the universe attracts every other object with a force along an imaginary line between them.
The equation for Newton’s law of gravitation is:
F, start subscript, g, end subscript, equals, G, start fraction, m, start subscript, 1, end subscript, m, start subscript, 2, end subscript, divided by, r, squared, end fraction
where:
F, start subscript, g, end subscript is the gravitational force between m, start subscript, 1, end subscript and m, start subscript, 2, end subscript,
G is the gravitational constant equal to 6, point, 67, times, 10, start superscript, minus, 11, end superscript, start fraction, start text, m, end text, cubed, divided by, start text, k, g, end text, dot, start text, s, end text, squared, end fraction, and
m, start subscript, 1, end subscript and m, start subscript, 2, end subscript are masses.
The force is directly proportional to the product of the masses. It is also inversely proportional to the square of the distance between the centers of mass. This is sometimes called an inverse-square law.
For example, if we double the distance between Earth and the Moon, the attractive force between them would decrease (because it has an inverse relationship to distance), and it would go down by a factor of 4 instead of 2 (because r is squared).
Newton’s law of universal gravitation describes objects falling down as well as objects in a circular orbit, such as a satellite orbiting Earth.

## How to find gravitational field strength

All objects attract other objects by producing a gravitational field g, which is defined as gravitational force per unit mass. We can find the strength of the gravitational field of mass m, start subscript, 1, end subscript on any object with mass m, start subscript, 2, end subscript by dividing the above equation by m, start subscript, 2, end subscript, and simplifying.
\begin{aligned} g &=\dfrac{F_g}{m_2} \\\\ &=G\dfrac{m_1m_2}{r^2m_2}\\\\ &=G\dfrac{m_1}{r^2} \end{aligned}

## What else should I know about Newton’s law of universal gravitation?

• Gravity causes attraction between all objects. Every mass attracts every other mass. That means you are gravitationally attracted to your friend, your pet, and even your pizza.
• The variable r is the distance between the centers of mass. We measure the distance between the objects from their centers, not their surfaces.