PhysicsGravitational FieldsA-Level
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Newton's Law of Gravitation Calculator

Force between two point masses.

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Force

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Overview

Newton's Law of Gravitation describes the attractive force between any two objects with mass, establishing that the magnitude of this force is proportional to the masses and inversely proportional to the square of the distance between their centers. This principle governs the motion of celestial bodies and explains the force of weight experienced on a planet's surface.

Symbols

Variables

F = Force, G = Grav. Constant, m_1 = Mass 1, m_2 = Mass 2, r = Distance

Force
Grav. Constant
Mass 1
Mass 2
Distance

Apply it well

When To Use

When to use: Apply this formula when analyzing the gravitational interaction between two distinct bodies that can be treated as point masses or uniform spheres. It is the primary tool for determining orbital velocity, escape velocity, and surface gravity in classical physics scenarios where velocities are much lower than the speed of light.

Why it matters: This equation enabled scientists to calculate the masses of the Sun and planets and to understand the mechanics of the solar system. It remains essential for calculating the trajectories of satellites, probes, and human spacecraft in modern aerospace engineering.

Avoid these traps

Common Mistakes

  • Forgetting r is squared.
  • Using km without converting to m.

One free problem

Practice Problem

Calculate the gravitational force of attraction between the Earth and the Moon. Use the following values: Earth's mass is 5.972 × 10²⁴ kg, the Moon's mass is 7.348 × 10²² kg, and the average distance between their centers is 3.844 × 10⁸ meters.

Mass 15.972e+24 kg
Mass 27.348e+22 kg
Distance384400000 m
Grav. Constant6.674e-11 N m^2/kg^2

Solve for:

Hint: Multiply the masses and the gravitational constant first, then divide by the square of the distance.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Fundamentals of Physics by Halliday, Resnick, and Walker
  2. Wikipedia: Newton's law of universal gravitation
  3. Britannica: Newton's law of universal gravitation
  4. NIST CODATA (2018 CODATA Recommended Values of the Fundamental Physical Constants)
  5. Halliday, Resnick, Walker. Fundamentals of Physics. (Any recent edition, e.g., 10th or 11th edition)
  6. Halliday, Resnick, Walker - Fundamentals of Physics
  7. Wikipedia: General relativity
  8. Wikipedia: Quantum gravity