---
title: "Law of Gravitation — AP Physics 1 Definition & Exam Guide"
description: "Newton's law of gravitation says F = Gm₁m₂/r², an attractive force between all masses. Learn how it powers orbit and energy problems on the AP Physics 1 exam."
canonical: "https://fiveable.me/ap-physics-1-revised/key-terms/law-of-gravitation"
type: "key-term"
subject: "AP Physics 1"
---

# Law of Gravitation — AP Physics 1 Definition & Exam Guide

## Definition

The law of gravitation states that every mass attracts every other mass with a force F = Gm₁m₂/r², directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers. It appears in AP Physics 1 Topic 3.3 alongside the electric force.

## What It Is

Newton's law of gravitation says any two objects with [mass](/ap-physics-1-revised/key-terms/mass "fv-autolink") pull on each other. The [force](/ap-physics-1-revised/unit-2/2-forces-and-free-body-diagrams/study-guide/jQ2Obd0dAU4QiTPN "fv-autolink") is F = Gm₁m₂/r², where G is the universal gravitational constant (6.67 × 10⁻¹¹ N·m²/kg²), m₁ and m₂ are the two masses, and r is the distance between their centers. Double either mass and the force doubles. Double the distance and the force drops to one quarter. That last part is the inverse square law, and it shows up constantly in AP problems.

Two features matter most for [AP Physics 1](/ap-physics-1-revised "fv-autolink"). First, gravity is always attractive, unlike the electric force, which can attract or repel. Second, the force comes in a pair. The Earth pulls on you with exactly the same magnitude of force that you pull on the Earth, which is Newton's third law in action. The forces are equal even when the masses are wildly different; the accelerations are what differ. Gravitation is also a conservative force, which is exactly why a system of two masses can store gravitational potential energy.

## Why It Matters

The law of gravitation lives in Topic 3.3 (Gravitational and Electric Forces) in [Unit 3](/ap-physics-1-revised/unit-3 "fv-autolink"): Work, Energy, and Power. That placement is deliberate. The CED's learning objective 3.3.A asks you to describe the potential energy of a system, and the essential knowledge specifies that a system has potential energy when its objects interact only through [conservative forces](/ap-physics-1-revised/key-terms/conservative-forces "fv-autolink"). Gravity is the textbook conservative force, so F = Gm₁m₂/r² is the entry point for understanding gravitational potential energy between two masses. The law also feeds problems far beyond Unit 3, since orbital motion questions combine it with circular motion and Newton's laws. If you can set gravitational force equal to the net centripetal force, you can solve almost any orbit problem the exam throws at you.

## Connections

### Inverse Square Law (Unit 3)

The r² in the denominator is the whole personality of gravitation. The AP exam loves ratio questions built on it, like asking what happens to the force when you triple the separation. The answer is always a clean fraction, in that case 1/9 of the original force.

### [Universal Gravitational Constant (Unit 3)](/ap-physics-1-revised/key-terms/universal-gravitational-constant)

G (6.67 × 10⁻¹¹ N·m²/kg²) is the tiny number that scales the law. Don't confuse it with g, the [gravitational field](/ap-physics-1-revised/key-terms/gravitational-field "fv-autolink") strength near Earth's surface. G is the same everywhere in the universe; g changes from planet to planet.

### Newton's Third Law (Unit 2)

Gravitational forces always come as an equal-and-opposite pair. A moon pulls on its planet with the same [magnitude](/ap-physics-1-revised/key-terms/magnitude "fv-autolink") of force the planet exerts on the moon. This trips up a lot of people, because the smaller object accelerates more, but the forces themselves are identical.

### Electric Force and Coulomb's Law (Unit 3)

[Topic 3.3](/ap-physics-1-revised/unit-3/3-potential-energy/study-guide/JOHf0KeXoaldDqpO "fv-autolink") pairs gravitation with the electric force on purpose. Both are inverse square laws with the same mathematical shape, just with charges instead of masses. The big difference is that gravity only attracts, while electric forces can attract or repel.

## On the AP Exam

Expect the law of gravitation in multiple-choice ratio problems (how does F change when mass or distance changes?) and in free-response questions about orbits. The 2022 Long FRQ Q2 gave two identical moons orbiting a planet and asked you to reason about the gravitational forces in the system, including the case where the moons' masses are significant rather than negligible. The skill being tested is setup and reasoning, not memorizing G. You'll need to write F = Gm₁m₂/r² with the correct masses and distances for the specific pair of objects, apply Newton's third law to force pairs, and often equate gravitational force to the centripetal force mv²/r for circular orbits. Watch the classic trap of using surface-to-surface distance instead of center-to-center distance for r.

## Law of Gravitation vs F = mg (weight near a planet's surface)

F = mg is a shortcut version of the full law of gravitation that only works near a planet's surface, where r barely changes. The value g is really Gmₚ/r² evaluated at the planet's radius. Use mg when you're standing on Earth doing a free-body diagram; use Gm₁m₂/r² when distance changes, when you're comparing planets, or when you're analyzing orbits. They're the same physics at two different zoom levels.

## Key Takeaways

- The law of gravitation, F = Gm₁m₂/r², says every pair of masses attracts with a force proportional to the product of the masses and inversely proportional to the square of the center-to-center distance.
- G is the universal gravitational constant (6.67 × 10⁻¹¹ N·m²/kg²) and is not the same as g, which is the local gravitational field strength like 9.8 m/s² near Earth's surface.
- By Newton's third law, two objects exert equal-magnitude gravitational forces on each other no matter how different their masses are.
- Gravity is a conservative force, which is why a system of two masses has gravitational potential energy, the focus of learning objective 3.3.A in Unit 3.
- For orbit problems, set the gravitational force equal to the net centripetal force (Gm₁m₂/r² = mv²/r) and solve for whatever the question asks.
- Always measure r from center to center, not from surface to surface; this is one of the most common point-losing mistakes on FRQs.

## FAQs

### What is the law of gravitation in AP Physics 1?

It's Newton's law stating that every object attracts every other object with a force F = Gm₁m₂/r², proportional to the product of the masses and inversely proportional to the square of the distance between their centers. It's covered in Topic 3.3 of Unit 3.

### Does a planet pull harder on its moon than the moon pulls on the planet?

No. By Newton's third law, the forces are exactly equal in magnitude and opposite in direction. The moon accelerates more because it has less mass, but the forces themselves are identical. The 2022 FRQ on two moons orbiting a planet rewarded exactly this reasoning.

### What's the difference between G and g?

G is the universal gravitational constant, 6.67 × 10⁻¹¹ N·m²/kg², and it's the same everywhere in the universe. Lowercase g is the gravitational field strength at a specific location, like 9.8 m/s² at Earth's surface, and it equals Gmₚ/r² for that planet and distance.

### How is the law of gravitation different from F = mg?

F = mg is the special case of the full law for objects near a planet's surface, where the distance r is roughly constant. The full law, F = Gm₁m₂/r², works at any distance and is what you need for orbits, comparing planets, or anything where r changes.

### What happens to gravitational force if the distance between two objects doubles?

The force drops to one quarter of its original value, because gravitation follows an inverse square law. Triple the distance and the force becomes one ninth. These ratio questions are AP multiple-choice favorites.

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