# Orbital speed

The speed that keeps a satellite in circular orbit, v = sqrt(G M / r). Gravity supplies the centripetal force.

Physics (university) · Part 04: Rotation and gravity · Card 9 of 11 · Last updated 2026-10-19

## Analogy

A ball that keeps missing the ground as it falls.

## Example

**Low Earth orbit**

r = 6.77e6 m
v = sqrt(3.98e14 / 6.77e6)
v = 7670 m/s

## In practice

A satellite 400 km above Earth moves at about 7.7 km/s.

## Practice

### Flashcards

- **What gives a satellite its centripetal force?** Gravity from the planet.

### 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 don't satellites fall down?

They do fall, but they also move sideways so fast that the ground curves away beneath them. At 7.7 km/s sideways, the fall matches the curve of the Earth, so the satellite stays at the same height. Astronauts feel weightless because they are in free fall.

### Does a higher orbit move faster or slower?

Slower. The speed formula v = sqrt(GM/r) falls as radius grows. Low satellites move at about 7.7 km/s, while the Moon, much farther away, moves at about 1 km/s. The period gets longer too, from about 90 minutes to 27 days.

## Related concepts

- [Centripetal force](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-3)
- [Universal gravitation](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-8)
- [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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