Gravitation
A fuller guide to gravitational force, explaining inverse-square behaviour, centre-to-centre separation, and the difference between mass, weight, and interaction force.
Key formulas
Gravitation links masses through separation
The gravitational force between two masses depends on both masses and the square of the distance between their centres. The mass terms pull the force upward; the distance term makes the force weaken rapidly as separation grows.
This inverse-square behaviour is the heart of the topic. Doubling the separation does not halve the force. It reduces it to one quarter.
Mass is not the same as weight
Mass measures amount of matter. Weight is the gravitational force experienced in a gravitational field. The universal gravitation formula deals with interacting masses and the force between them, not with mass as a stand-alone property.
Keeping that distinction visible helps when comparing classroom gravitation problems with everyday weight calculations near Earth.
Use centre-to-centre distance
The separation in the formula is measured from the centre of one mass to the centre of the other. This matters especially in planetary or spherical-body problems where surface-to-surface distance is not the required quantity.
If the wrong distance is used, the inverse-square term magnifies the error quickly.
- Force grows with each mass.
- Force shrinks with the square of separation.
- Distance must describe the correct centre-to-centre geometry.
Worked examples and reasoning checks
If one mass doubles while the other mass and separation stay fixed, the force doubles. If the separation doubles instead, the force falls to one quarter. These proportional checks are often more valuable than the exact arithmetic when you are testing whether an answer is plausible.
In many introductory tasks the exact constant is less memorable than the relational behaviour. Knowing how the force scales with mass and distance lets you sanity-check quickly.
Common mistakes
- Using surface distance instead of centre-to-centre separation.
- Forgetting the square on the distance term.
- Confusing mass with weight in the interpretation.
- Assuming the inverse-square law means the force becomes unimportant instantly rather than reducing proportionally with distance.
How this connects elsewhere
Gravitation sits naturally beside force, potential energy, and motion topics. On this site it is best treated as an interaction model: masses, geometry, and scaling behaviour together explain why the force changes.