A geostationary orbit is a special orbit where a satellite appears to hang over one fixed point on Earth. This matters because antennas on the ground can point in one direction and stay connected without tracking the satellite across the sky. Geostationary satellites are widely used for television, internet links, telephone relays, and weather monitoring.
The orbit works only at a specific height above Earth and only above the equator.
Key Facts
- Geostationary altitude is about 35,786 km above Earth's surface.
- Orbital radius for geostationary orbit is about 42,164 km from Earth's center.
- The orbital period must match Earth's rotation: T = 23 h 56 min 4 s.
- For a circular orbit, gravity supplies centripetal force: GMm/r^2 = mv^2/r.
- Orbital speed is v = sqrt(GM/r), about 3.07 km/s for geostationary orbit.
- A geostationary orbit must be circular, prograde, and have inclination i = 0 degrees.
Vocabulary
- Geostationary orbit
- A circular equatorial orbit where a satellite stays above the same point on Earth's surface.
- Orbital period
- The time it takes a satellite to complete one full orbit around Earth.
- Inclination
- The angle between a satellite's orbital plane and Earth's equatorial plane.
- Centripetal acceleration
- The inward acceleration needed to keep an object moving in a circular path.
- Sidereal day
- The time Earth takes to rotate once relative to distant stars, about 23 hours 56 minutes 4 seconds.
Common Mistakes to Avoid
- Using exactly 24 hours for the period, because the correct orbital match is Earth's sidereal rotation of about 23 h 56 min 4 s.
- Placing a geostationary satellite above any latitude, because only an equatorial orbit can keep the satellite fixed over one point on Earth's surface.
- Thinking the satellite is not moving, because it is actually traveling around Earth at about 3.07 km/s while matching Earth's rotation.
- Confusing altitude with orbital radius, because altitude is measured above Earth's surface while orbital radius is measured from Earth's center.
Practice Questions
- 1 A geostationary satellite orbits 35,786 km above Earth's surface. If Earth's radius is 6,378 km, what is the satellite's orbital radius from Earth's center in kilometers?
- 2 Use v = 2πr/T with r = 42,164 km and T = 86,164 s to estimate the orbital speed of a geostationary satellite in km/s.
- 3 Explain why a satellite in a 24-hour orbit with a 20 degree inclination is not geostationary, even if its period is nearly correct.