Space
Explainer
One equation for speed anywhere in orbit
A satellite's speed depends only on where it is and its orbit's size.
Quick check · tap an answer to continue
Lesson notes
Key points
- The vis-viva equation gives orbital speed v from distance r to the central body and the orbit's semi-major axis a.
- It comes from conserving energy: kinetic plus gravitational potential energy per kilogram stays fixed at minus GM over 2a.
- For a circular orbit r equals a, so speed simplifies to the square root of GM over r.
- Letting a go to infinity gives speed squared equals 2GM over r, which is exactly the escape speed.
Takeaway: v² = GM(2/r − 1/a) links speed, position and orbit size.
Quick check: In vis-viva, what does a circular orbit imply?
- r = 2a
- a is infinite
- r = a
In a circle distance never changes and equals the semi-major axis.
Vis-vivaSpecific energyCircular speedEscape limit
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