Gravity Formula

Gravity is the universal attractive force between any two objects with mass, decreasing with the square of distance.

The Formula

F=Gm1m2r2F = \frac{Gm_1 m_2}{r^2} (universal gravitation)

When to use: Everything pulls on everything else—but only huge things (like Earth) pull noticeably.

Quick Example

Earth pulls you down; you also pull Earth up (but it doesn't move noticeably).

Notation

GG is the universal gravitational constant (6.674×10−116.674 \times 10^{-11} N m2^2 kg−2^{-2}), m1m_1 and m2m_2 are the two masses in kilograms, and rr is the centre-to-centre distance in metres.

What This Formula Means

The universal attractive force between any two objects with mass, decreasing with the square of distance.

Everything pulls on everything else—but only huge things (like Earth) pull noticeably.

Formal View

Newton's law of universal gravitation states that every point mass attracts every other point mass with a force F=Gm1m2r2F = \frac{Gm_1 m_2}{r^2}, directed along the line joining their centres.

Worked Examples

Example 1

easy
Calculate the gravitational force between Earth (M=5.97×1024 kgM = 5.97 \times 10^{24} \text{ kg}) and a 1 kg1 \text{ kg} object at Earth's surface (r=6.37×106 mr = 6.37 \times 10^6 \text{ m}). Use G=6.674×10−11 N m2/kg2G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2.

Answer

F≈9.8 NF \approx 9.8 \text{ N}

First step

1
Apply Newton's law of gravitation: F=GMmr2F = \frac{GMm}{r^2}

Full solution

  1. 2
    Substitute: F=6.674×10−11×5.97×1024×1(6.37×106)2F = \frac{6.674 \times 10^{-11} \times 5.97 \times 10^{24} \times 1}{(6.37 \times 10^6)^2}
  2. 3
    Calculate: F=3.98×10144.06×1013≈9.8 NF = \frac{3.98 \times 10^{14}}{4.06 \times 10^{13}} \approx 9.8 \text{ N}
This calculation confirms that g≈9.8 m/s2g \approx 9.8 \text{ m/s}^2 at Earth's surface. Gravity is the attractive force between any two masses, governed by the universal law of gravitation.

Example 2

easy
A ball is dropped from rest near Earth's surface. How fast is it going after 3 seconds3 \text{ seconds}? Ignore air resistance and use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Example 3

medium
Calculate the gravitational force between two 50 kg50 \text{ kg} masses separated by 2 m2 \text{ m}. Use G=6.674×10−11 N m2/kg2G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2.

Common Mistakes

  • Using the distance between surfaces instead of the distance between the centres of mass of the two objects. - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Forgetting to square the distance rr in the denominator, which drastically changes the result. - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Confusing gg (gravitational field strength, ~9.8 m/s²) with GG (the universal gravitational constant, 6.67 × 10⁻¹¹ N m²/kg²). - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Using gravity from a keyword alone - Signal words like force, push, pull only point to a possible model; the system must match too.

Common Mistakes Guide

If this formula feels simple in isolation but keeps breaking during real problems, review the most common errors before you practice again.

Free Body Diagrams Mistakes

Why This Formula Matters

Gravity is central because forces explain changes in motion and balance. Students who can isolate a system and draw the interactions can avoid treating every force word as the same kind of cause.

Frequently Asked Questions

What is the Gravity formula?

The universal attractive force between any two objects with mass, decreasing with the square of distance.

How do you use the Gravity formula?

Everything pulls on everything else—but only huge things (like Earth) pull noticeably.

What do the symbols mean in the Gravity formula?

GG is the universal gravitational constant (6.674×10−116.674 \times 10^{-11} N m2^2 kg−2^{-2}), m1m_1 and m2m_2 are the two masses in kilograms, and rr is the centre-to-centre distance in metres.

Why is the Gravity formula important in Physics?

Gravity is central because forces explain changes in motion and balance. Students who can isolate a system and draw the interactions can avoid treating every force word as the same kind of cause.

What do students get wrong about Gravity?

Students often know a formula related to gravity but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Gravity formula?

Before studying the Gravity formula, you should understand: force, mass.

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