Gravitational Potential Calculator
Work done per unit mass from infinity.
Formula first
Overview
Gravitational potential is a scalar quantity representing the potential energy per unit mass at a specific location within a gravitational field. It defines the work done per unit mass by gravity to move an object from an infinite distance to a specific point, resulting in a negative value as energy is released during the approach.
Symbols
Variables
V = Potential, G = Grav Constant, M = Mass, r = Distance
Apply it well
When To Use
When to use: Apply this formula when analyzing the energy environment around spherical celestial bodies like planets or stars. It is essential when the distance from the source of gravity changes significantly, rendering the local g ≈ 9.81 approximation invalid.
Why it matters: This equation is the foundation for calculating escape velocities and the energy required for orbital maneuvers. It helps engineers determine the fuel needed for spacecraft to climb out of a planet's 'gravity well' and traverse the solar system.
Avoid these traps
Common Mistakes
- Dropping the negative sign.
- Using r² instead of r.
One free problem
Practice Problem
Calculate the gravitational potential on the surface of Earth. Assume Earth has a mass of 5.97 × 10²⁴ kg and a radius of 6,371,000 meters.
Solve for:
Hint: Multiply the gravitational constant by the mass of the Earth, then divide by the radius and add a negative sign.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Halliday, Resnick, and Walker, Fundamentals of Physics
- Britannica: Gravitational potential
- Wikipedia: Gravitational potential
- NIST CODATA (2018) for the value of G
- Halliday, Resnick, and Walker, Fundamentals of Physics, 11th Edition (2018) for unit definitions and dimensional analysis
- Halliday, Resnick, Walker - Fundamentals of Physics, 10th Edition
- AQA A-Level Physics — Gravitational Fields