# Universal gravitation

Every two masses attract with a force F = G M m / r squared, where G is 6.67e-11 in SI units.

Physics (university) · Part 04: Rotation and gravity · Card 8 of 11 · Last updated 2026-10-19

## Analogy

A very weak glue between all matter, strong only when one object is huge.

## Example

**Two masses**

F = 6.67e-11 x 1000 x 1000 / 1^2
F = 6.67e-5 N

## In practice

Two 1000 kg masses 1 m apart pull each other with about 0.00007 N.

## Practice

### Flashcards

- **How does gravitational force change if distance doubles?** It falls to one quarter.

### Interview questions

**Derive the speed of a satellite in circular orbit and use it to find the period of a satellite at radius r.**

- Gravity equals m v^2 / r
- v = sqrt(GM/r)
- Period = 2 pi r / v

## Questions people ask

### Why is gravity weak between everyday objects?

The constant G is tiny, about 6.67e-11 in SI units. Two 70 kg people 1 m apart attract with about 3e-7 N, far too small to notice. Gravity only becomes obvious when one of the masses is as huge as a planet.

### How do I get g = 9.8 from Newton's law?

Set weight mg equal to GMm over R squared and cancel m. This gives g = GM over R squared. With Earth's mass 5.97e24 kg and radius 6.37e6 m, the result is about 9.8 m/s squared. On a different planet you use its own mass and radius.

## Related concepts

- [Orbital speed](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-9)
- [Centripetal force](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-3)
- [Escape velocity](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-10)
- [Kepler's third law](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-11)

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