PhysicsGravitational FieldsA-Level

Newton's Law of Universal Gravitation Calculator

This law states that the gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the dis...

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Gravitational Force

Formula first

Overview

The force is always attractive, acting along the line joining the centers of the two masses. This inverse-square relationship means that doubling the distance between the two bodies reduces the gravitational force to one-quarter of its original value. It serves as the foundation for understanding planetary orbits, satellite motion, and the formation of celestial structures.

Symbols

Variables

F = Gravitational Force, G = Gravitational Constant, M = Mass of first object, m = Mass of second object, r = Distance between centers

Gravitational Force
Variable
Gravitational Constant
Variable
Mass of first object
Variable
Mass of second object
Variable
Distance between centers
Variable

Apply it well

When To Use

When to use: Use this equation when calculating the force of gravity between any two massive objects where the separation distance is significantly greater than the radii of the objects.

Why it matters: It explains why planets orbit the Sun, why moons stay in orbit, and how we can calculate the mass of celestial bodies.

Avoid these traps

Common Mistakes

  • Forgetting to square the radius (r) in the denominator.
  • Measuring r from the surface of a planet rather than from its center.
  • Confusing the gravitational constant G (6.67 × 10^-11) with the acceleration due to gravity g (9.81 m/s²).

One free problem

Practice Problem

Calculate the gravitational force between two 1000 kg masses separated by a distance of 10 meters.

Gravitational Constant6.67e-11
Mass of first object1000
Mass of second object1000
Distance between centers10

Solve for:

Hint: Plug the values into F = GMm/rθ. Remember that rθ is 100.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica.
  2. Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics.
  3. AQA/Edexcel A-Level Physics Specification: Gravitational Fields