Gravitational Force (College Board AP® Physics 1: Algebra-Based): Study Guide

Ann Howell

Written by: Ann Howell

Reviewed by: Caroline Carroll

Updated on

Gravitational force

  • The gravitational force between two objects or systems is attractive

    • An attractive force is a force that pulls objects together

  • There is a universal force of attraction between all matter with mass

    • The gravitational force is always exerted along the line connecting the centers of mass of the two interacting systems

    • The gravitational force on a system can be considered to be exerted on the system’s center of mass

Gravitational force between two masses

A person dancing in the air above Earth's surface, with arrows showing gravitational force between the dancer's center of mass and Earth's center of mass.
The gravitational force between two masses is attractive and acts from their centres of mass
  • Gravitational force has an infinite range, meaning it affects all objects in the universe

    • There is a greater gravitational force around objects with a large mass (such as planets)

    • There is a smaller gravitational force around objects with a small mass (almost negligible for atoms)

  • The Earth's gravitational force is the centripetal force that keeps the Moon in a circular orbit around the Earth

Gravitational force as centripetal force

Satellite motion around Earth, showing centripetal force, gravitational force towards center of Earth, radius of orbit, linear speed, and orbital path.
A satellite in orbit around the Earth travels in circular motion due to the gravitational force from the Earth

Gravitational force between two systems

  • The relative position between the centers of mass of two systems can change due to:

    • one or both objects rotating around the other

    • one or both objects moving away from each other

  • When the relative position of the centers of mass changes but the change in the gravitational force is negligible, then the gravitational force is considered constant

    • The gravitational force is considered constant at all points between the initial and final positions of the systems

Earth rotating around the Sun

Earth's orbit around the Sun with vectors indicating gravitational force pulling towards the Sun and instantaneous velocity at perpendicular tangents.
Gravitational force is constant for the Earth rotating around the Sun
  • The separation distance between the initial and final positions of the systems has to be very small to create a negligible change in the gravitational force between them

Satellite moving away from the Earth

A satellite in orbit around Earth with labeled vectors (r1, r2) and equations indicating orbital changes (Δr, r2-r1). The satellite is in Orbit 1 and then Orbit 2.
A small change in orbital radius from orbit 1 to orbit 2 will create a negligible change in the gravitational force between the two systems

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Ann Howell

Author: Ann Howell

Expertise: Physics Content Creator

Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students, no matter their schooling or background.

Caroline Carroll

Reviewer: Caroline Carroll

Expertise: Physics & Chemistry Subject Lead

Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.