Orbital velocity is the sideways speed a spacecraft needs so that it keeps falling around Earth instead of falling into it. In a circular orbit, gravity provides the centripetal force that bends the spacecraft's path. This idea matters because every satellite, space station, and crewed spacecraft must reach the right speed for its altitude.
Lower orbits require higher speed, while higher orbits require lower speed.
Key Facts
- Circular orbital speed: v = sqrt(GM/r)
- Orbital radius is measured from Earth's center: r = R_E + h
- Earth's mean radius is R_E = 6.37 x 10^6 m
- Earth's gravitational parameter is GM = 3.986 x 10^14 m^3/s^2
- At about 400 km altitude, the circular orbital speed is about 7.7 km/s
- At geostationary altitude, about 35,786 km, the circular orbital speed is about 3.1 km/s
Vocabulary
- Orbital velocity
- Orbital velocity is the speed an object needs to stay in a stable orbit at a given distance from the body it is orbiting.
- Circular orbit
- A circular orbit is an orbit with a constant radius where gravity continuously provides the centripetal acceleration.
- Altitude
- Altitude is the height of an object above Earth's surface, not its distance from Earth's center.
- Orbital radius
- Orbital radius is the distance from Earth's center to the orbiting object, equal to Earth's radius plus altitude.
- Geostationary orbit
- A geostationary orbit is a circular orbit above Earth's equator where a satellite takes one day to orbit and appears fixed over one point on Earth.
Common Mistakes to Avoid
- Using altitude h instead of orbital radius r in v = sqrt(GM/r) is wrong because gravity and circular motion depend on distance from Earth's center, so r = R_E + h.
- Thinking higher satellites move faster is wrong because circular orbital speed decreases as orbital radius increases.
- Forgetting unit conversions is wrong because using kilometers in a formula with GM in m^3/s^2 gives a speed with incorrect units.
- Assuming an orbit needs constant engine thrust is wrong because an ideal circular orbit is maintained by gravity, while engines are mainly used to change orbits or correct disturbances.
Practice Questions
- 1 A satellite orbits 400 km above Earth. Use R_E = 6.37 x 10^6 m and GM = 3.986 x 10^14 m^3/s^2 to calculate its circular orbital speed in km/s.
- 2 A satellite is in a circular orbit at an altitude of 20,200 km. Calculate its orbital radius and circular orbital speed using v = sqrt(GM/r).
- 3 Explain why a satellite at 35,786 km altitude moves more slowly than a satellite at 400 km altitude, even though it travels around a much larger circle.