How a satellite stays in orbit
A man-made satellite is an object launched to orbit the Earth. It does not fall to the ground because the Earth's gravitational pull acts as the centripetal force that keeps it moving in a circle. If it moved too slowly gravity would pull it down; too fast and it would fly off into space.
Key formula / 关键公式
Gravity = centripetal force: GMm / r² = mv² / r
Orbital (linear) speed: v = √(GM / r)
where M = mass of Earth, r = distance from Earth's centre. The required speed depends only on r, not on the satellite's mass.
Types of orbit
- Geostationary satellite: orbits directly above the equator with a period of exactly 24 hours, so it appears fixed above one point on Earth. Used for communication and TV broadcasting. Its orbital radius is about 4.2 × 10⁷ m.
- Low Earth / polar orbit satellite: orbits at a few hundred kilometres with a much shorter period, passing over the poles. Used for weather monitoring, Earth imaging and GPS support.
Escape velocity
To leave the Earth's gravitational field completely, an object needs the escape velocity v = √(2GM / r). For Earth this is about 1.1 × 10⁴ m s⁻¹ (11 km s⁻¹). Notice it is √2 times the orbital speed at the same radius.
Worked example / 例题
Find the orbital speed of a satellite at r = 8.0 × 10⁶ m from Earth's centre (M = 6.0 × 10²⁴ kg, G = 6.67 × 10⁻¹¹).
v = √(GM/r) = √[(6.67 × 10⁻¹¹ × 6.0 × 10²⁴) / (8.0 × 10⁶)]
= √(4.0 × 10¹⁴ / 8.0 × 10⁶) = √(5.0 × 10⁷) ≈ 7.1 × 10³ m s⁻¹.
Remember / 记住
- Lower orbits need higher speeds and have shorter periods.
- Orbital speed does not depend on the satellite's mass.
- Escape velocity = √2 × orbital speed at the same radius.