A rocket must accelerate to at least 25,039 mph (40,320 kph) to completely escape Earth's gravity and fly off into space (for more on escape velocity, visit this article at kidsplanet.com and this one at Northwestern University).
Earth's escape velocity is much greater than what's required to place an Earth satellite in orbit. With satellites, the object is not to escape Earth's gravity, but to balance it. Orbital velocity is the velocity needed to achieve balance between gravity's pull on the satellite and the inertia of the satellite's motion -- the satellite's tendency to keep going. This is approximately 17,000 mph (27,359 kph) at an altitude of 150 miles (242 km). Without gravity, the satellite's inertia would carry it off into space. Even with gravity, if the intended satellite goes too fast, it will eventually fly away. On the other hand, if the satellite goes too slowly, gravity will pull it back to Earth. At the correct orbital velocity, gravity exactly balances the satellite's inertia, pulling down toward Earth's center just enough to keep the path of the satellite curving like Earth's curved surface, rather than flying off in a straight line.
The orbital velocity of the satellite depends on its altitude above Earth. The nearer Earth, the faster the required orbital velocity. At an altitude of 124 miles (200 kilometers), the required orbital velocity is just over 17,000 mph (about 27,400 kph). To maintain an orbit that is 22,223 miles (35,786 km) above Earth, the satellite must orbit at a speed of about 7,000 mph (11,300 kph). That orbital speed and distance permits the satellite to make one revolution in 24 hours. Since Earth also rotates once in 24 hours, a satellite at 22,223 miles altitude stays in a fixed position relative to a point on Earth's surface. Because the satellite stays right over the same spot all the time, this kind of orbit is called "geostationary." Geostationary orbits are ideal for weather satellites and communications satellites.
The moon has an altitude of about 240,000 miles (384,400 km), a velocity of about 2,300 mph (3,700 kph) and its orbit takes 27.322 days. (Note that the moon's orbital velocity is slower because it is farther from Earth than artificial satellites.)
* To get a better feel for orbital velocities at different altitudes, check out NASA's orbital velocity calculator.
* To learn more about orbits and other topics in space flight, check out JPL's Basics of Space Flight Learners' Workbook.
* A detailed technical treatment of orbital mechanics can be found at this site.
In general, the higher the orbit, the longer the satellite can stay in orbit. At lower altitudes, a satellite runs into traces of Earth's atmosphere, which creates drag. The drag causes the orbit to decay until the satellite falls back into the atmosphere and burns up. At higher altitudes, where the vacuum of space is nearly complete, there is almost no drag and a satellite can stay in orbit for centuries (take the moon as an example).
Satellites usually start out in an orbit that is elliptical. The ground control station controls small onboard rocket motors to provide correction. The goal is to get the orbit as circular as possible. By firing a rocket when the orbit is at the apogee of its orbit (its most distant point from Earth), and applying thrust in the direction of the flight path, the perigee (lowest point from Earth) moves further out. The result is a more circular orbit