Orbital speed
The speed that keeps a satellite in circular orbit, v = sqrt(G M / r). Gravity supplies the centripetal force.
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Analogy
A ball that keeps missing the ground as it falls.
Example
r = 6.77e6 mv = 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.