The condition for an orbit to be stable is that the force of gravity pulling radially inward should equal the centripetal force required to keep the satellite in its orbit at that radius. If this radial force equilibrium were not met, the satellite would either get closer to, or farther away until the condition was satisfied. We can apply the knowledge from this section to determine the relationship between a satellite’s orbital radius r and its orbital velocity v. The result is the orbit equation for circular orbits.
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| | r | = | orbital radius (m) | | G | = | Grav. const. G = 6.67×10-11 m3/kgs | | mE | = | mass of Earth = 6 × 1024 kg | | v | = | satellite orbital speed (m/s) |
| Orbit equation
for circular orbits |
Almost everyone is familiar with weather satellites. These satellites stay above the same point on Earth so that they can image the same spot 24 hours a day. This “hovering” over the same spot is possible because the satellites are in a special kind of orbit called a
geostationary orbit. A satellite in geostationary orbit completes one orbit in exactly one day, so that its motion follows the motion of the ground underneath it. Many communications and TV broadcast satellites are also in geostationary orbits. This is why a satellite dish antenna can receive a signal 24 hours a day while pointed in a fixed direction. If the TV satellite were not in a geostationary orbit, the dish antenna would have to move around to track the satellite.
To keep up with the Earth’s rotation, a geostationary satellite must travel the entire circumference of its orbit (2πr) in 24 hours (86,400 seconds). To stay in orbit, the satellite’s radius and velocity must also satisfy the orbit equation. The combination of these two conditions determines the radius of geostationary orbit, which is 42,300 kilometers from the center of the Earth. The altitude of the orbit is 35,920 kilometers above the planet’s surface, after subtracting 6,380 kilometers for the radius of Earth itself. 
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To understand orbits, consider an object launched upwards from Earth’s surface. The faster the launch velocity the farther the object travels before coming back down again. At a launch velocity of about 8 kilometers per second, the curve of the “falling” object's trajectory matches the curvature of the planet surface. The Earth “falls away” beneath the satellite and the satellite never hits the ground but goes into orbit instead. A satellite in orbit is falling around the Earth but it never lands.
Mathematically, orbits are ellipses. A circle is special type of ellipse. Many orbits, including Earth's orbit around the Sun, are nearly perfect circles. In a circular orbit the satellite moves with constant speed. In elongated orbits, satellites do not move at constant speed. They move faster near closest approach and slower when farther away. The planets in our Solar System have orbits that are within a few percent of circular. Many comets orbit the Sun in very elongated ellipses. The aphelion or nearest point of a comet's orbit can be very close to the Sun while the perihelion or farthest point is often far beyond the orbit of Neptune. Some comets travel so far that a single orbit takes thousands of years.
A moving object approaching a planet may go into orbit, collide, or fly back into space. The outcome depends on the object's velocity vector compared to the strength of the gravitational force. 
