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## 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

NGSS.HS:

HS‑PS2‑4

, HS‑PS2‑5

, HS‑PS2.B.1

, HS‑PS2.B

, HS‑PS2

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

## Key terms

Term | Meaning |
---|---|

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

Equation | Symbol breakdown | Meaning |
---|---|---|

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 | F, 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:

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.

## 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.

## Want to join the conversation?

- Why does gravitational potential energy increase as the masses get farther apart?(19 votes)
- I'm confused about calculating all numbers like this "6.67 x 10^-11 m^3/kg*s^2". I know that is gravitational constant but how to solve that kind of number?(8 votes)
- Remember that 10² is 100. 10³ is 1,000. So 10^10 is a one followed by ten zeros, or ten billion. 10^-10 is going backwards: a decimal point followed by nine zeros and then a one. Whatever this is then multiplies the number in front, and at the end are just a bunch of units. For example, 2.345*10^-6 m²/kgs is the same thing as 0.000001*2.345 meters squared / kilogram seconds, which is 0.000002345 of the same thing.(4 votes)

- How do I calculate after I input the numbers in the formula? What does N stand for?(3 votes)
- N stands for Newtons, which is a unit of force. Could you clarify what you mean about inputting the numbers in the formula?(1 vote)

- How would you calculate the distance between an object and an object with a gravitational pull?(3 votes)
- Is the "little g" just a gravitational field? And is it specifically Earth's gravitational field?(2 votes)
- Little g is the numerical value of Earth's gravitational field's pull at the Earth's surface.

Another planet would have a different value for its own gravitational pull.(3 votes)

- Will
`G`

always be 6.67 x 10^-11 m^3/kg*s^2?(2 votes)- Yes. By definition, G is a constant.(3 votes)

- as a freshman student i want to know why there are so many videos(2 votes)
- Would you rather none?(2 votes)

- I just did the Law of Universal Gravitation for the earth and me. I used 6.67430 (N*m^2)/(kg^2) for the constant, my mass is 56.699 kg, the earth's mass as (5.972*10^24)kg, and 1,700,000 m as r(distance from the surface of the earth to its center of mass). I got F = (7.81579625 * 10^14) (Newtons/meters^2). Could someone fact check this?(2 votes)
**G**which of these is 6.67 x 10^-11 N*m^2 / kg^2 or 6.67 x 10^-11 m^3/kg*s^2.(2 votes)- What is gravitational mass and inertial mass? How are they different? Is gravitational mass the same as weight?(2 votes)