Section 2.7: Applications of Satellites
Satellites are artificial objects placed in orbit around celestial bodies for various practical purposes. Their applications span communications, navigation, observation, and scientific research.
Used for transmitting television, radio, internet, and phone signals globally. Often placed in geostationary orbit for constant coverage of a region.
GPS satellites enable precise location tracking and navigation for civilian and military use. Typically in medium Earth orbit (MEO).
Used to monitor climate, predict weather, track storms, and collect environmental data. Often placed in low Earth orbit (LEO) for higher resolution imaging.
Satellites for astronomy, astrophysics, and space exploration. Examples include Hubble Space Telescope and probes studying other planets.
Example 1
A communication satellite orbits Earth at 3.6×10^7 m (geostationary). Calculate the required orbital period to remain stationary relative to Earth's surface.
Orbital period for geostationary orbit: T = 24 hours = 86400 s (by definition of geostationary orbit).
Example 2
A GPS satellite orbits at 2×10^7 m. Find its approximate orbital speed assuming circular orbit.
v = √(GM/r) ≈ √(6.674×10^-11 * 5.972×10^24 / 2×10^7) ≈ 3.45×10^3 m/s
Practice Problems
- Calculate the orbital period of a LEO satellite at 500 km above Earth.
- Find the speed of a geostationary satellite at 3.6×10^7 m.
- Determine the altitude for a satellite to orbit Earth with period 12 hours.
- A weather satellite takes images of the equator every 90 minutes. Find its orbital radius.
- Compare velocities of LEO and MEO satellites.
- Compute the centripetal acceleration of a GPS satellite.
- Explain why communication satellites are placed in geostationary orbit.
- Estimate the orbital speed of a scientific satellite at 1×10^6 m above Earth.
- Calculate the orbital period of a satellite around Mars at radius 2×10^6 m.
- Explain advantages of satellites in sun-synchronous orbits for Earth observation.