A special kind of curve
Calculus shows that the curve swept out by a satellite has to be a conic section. The exact nature of this curve depends on the velocity at which the satellite is released from the launcher, at its injection point. Once the satellite is in orbit, its velocity depends only on its altitude and not its mass, according to Galileo’s law of falling bodies, which states that all bodies in a vacuum fall in the same way.
Imagined by Jean-Pierre Penot (CNES) and Bernard Nicolas, illustrated by Bernard Nicolas
Below a certain velocity, a satellite cannot stay in orbit and will fall to the ground. There is also a velocity, called the circular orbital velocity, at which the satellite’s altitude is constant and the orbit is therefore a circle. This velocity depends on the altitude of the injection point.
Imagined by Jean-Pierre Penot (CNES) and Bernard Nicolas, illustrated by Bernard Nicolas
|
If the orbital velocity is still higher, the ellipse gets even more elongated until it becomes an open-ended curve, called a parabola. This change occurs at a velocity called the escape velocity, beyond which the orbit becomes a hyperbola and the satellite overcomes the pull of Earth’s gravity and flies off into space.
These general orbital characteristics apply to all celestial bodies.
These general orbital characteristics apply to all celestial bodies.
Circular orbital velocities and escape velocities for an Earth satellite
| Altitude of injection point | Circular orbital velocity | Escape velocity |
| 200 km | 7,784 kps (28,024 kph) | 11,009 kps |
| 400 km | 7,663 kps (27,607 kph) | 10,845 kps |
| 800 km | 7,452 kps (26,827 kph) | 10,539 kps |
| 36,000 km | 3,075 kps (11,069 kph) | 4,348 kps |
