Gravitational Field Strength Calculator
Force per unit mass.
Formula first
Overview
This equation defines gravitational field strength as the gravitational force exerted per unit mass on a small test object at a specific point. It demonstrates that the acceleration due to gravity depends solely on the mass of the source body and the square of the distance from its center, independent of the test object's mass.
Symbols
Variables
g = Field Strength, G = Grav Constant, M = Mass, r = Distance
Apply it well
When To Use
When to use: Apply this formula when calculating the local acceleration of gravity on a planetary surface or at a specific altitude in space. It assumes the central body is a uniform sphere and requires the distance r to be measured from the center of mass, not the surface altitude.
Why it matters: This principle is fundamental for predicting orbital trajectories and ensuring the safety of satellite deployments. It also allows planetary scientists to compare physical conditions across different worlds, influencing how we design technology for lunar or Martian exploration.
Avoid these traps
Common Mistakes
- Using r instead of r².
- Mixing km and m.
One free problem
Practice Problem
Calculate the gravitational field strength on the surface of Mars, given its mass is 6.39 × 10²³ kg and its radius is 3.39 × 10⁶ m.
Solve for:
Hint: Plug the mass and radius into the formula g = GM/r² and ensure you square the radius.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Halliday, Resnick, Walker. Fundamentals of Physics. 10th ed. John Wiley & Sons, 2014.
- Wikipedia: Gravitational field
- NIST CODATA 2018
- Halliday, Resnick, and Walker, Fundamentals of Physics, 11th Edition
- Halliday, Resnick, Walker, Fundamentals of Physics
- NIST CODATA
- Wikipedia: Earth radius
- Wikipedia: Standard gravity