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.
Understanding Astronautics: Orbital Velocity and Altitude
A circular orbit is a balance between two effects. Gravity pulls a spacecraft inward toward Earth. The spacecraft’s motion carries it forward.
Its path curves continuously, so it travels around Earth rather than moving in a straight line. For a given distance from Earth’s center, there is one circular speed. If the spacecraft has exactly that speed and no other forces act, its altitude stays constant.
This is an ideal model. Real orbits are affected by Earth’s uneven shape, the Moon, the Sun, and the thin outer atmosphere.
The speed rule comes from matching gravity with the inward acceleration needed for circular motion. Gravity gets weaker with distance. The needed inward acceleration depends on speed squared divided by orbital radius.
When these are set equal, the orbital speed is found by taking the square root of Earth’s gravitational parameter divided by the orbital radius. The radius must begin at Earth’s center, not at the ground.
This point causes many calculation errors. An altitude in kilometres must be converted to metres before it is combined with Earth’s radius when standard SI values are used.
A spacecraft that is too slow for its current circular altitude does not simply drop straight down. It moves into an elliptical orbit. Its starting point becomes the highest part of that ellipse, called apogee.
It then descends toward a lower point, called perigee, where it speeds up. A spacecraft that is too fast at its starting point enters an ellipse with that point as perigee and climbs to a higher apogee. This explains an important idea in spaceflight.
A forward engine burn can raise the far side of an orbit. The spacecraft gains energy, but much of that energy first appears as greater altitude rather than greater speed at the burn point.
Orbit changes therefore need careful timing. To move from a lower circular orbit to a higher one, a spacecraft commonly makes one burn to stretch its orbit outward. It coasts along the ellipse, then makes another burn near the new higher altitude to make the orbit circular.
This is called a transfer orbit. Satellites use such maneuvers when they are placed into working positions. The International Space Station needs regular boosts because traces of air in low Earth orbit create drag.
Drag removes orbital energy. The station gradually falls to a lower orbit, where its required circular speed is actually higher even though its total orbital energy has decreased.
Students should separate speed, velocity, altitude, radius, and energy. Speed gives the size of motion, while velocity includes direction. In orbit, direction changes every moment, so velocity changes even when speed remains constant.
Higher circular orbits have lower speeds, yet they take much longer to complete one trip around Earth because the path is far larger. A satellite at geostationary altitude matches Earth’s rotation period, so it remains above the same region near the equator. This result depends on choosing the correct altitude, direction, and orbital period, not merely reaching a particular 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.