Satellites

Orbits Gravitational Potential Escape Velocity

1. Satellite Basics

Natural Satellites

  • Moon (Earth's natural satellite)
  • Moons of other planets (e.g., Jupiter's Galilean moons)

Artificial Satellites

  • Also known as man-made satellites
  • Examples:
    1. International Space Station (ISS) - Research facility, ~90 minute orbit
    2. Hubble Space Telescope - Astronomy, ~95 minute orbit
    3. Molniya satellites - Communications, elliptical orbit (12 hour period)

2. Orbital Mechanics

v = √(GM/r)

Orbital Speed Derivation

  1. Centripetal force = Gravitational force
  2. mv²/r = GMm/r²
  3. Solve for v: v = √(GM/r)
  4. Common Mistake: r is distance from center of mass, not surface

Low Earth Orbit (LEO)

  • Altitude: 160-2000 km
  • Period: ~90 minutes
  • Examples: ISS, Hubble, Iridium

Geostationary Orbit

  • Altitude: ~35,786 km
  • Period: 24 hours
  • Used for communications/weather

3. Gravitational Potential

Key Concepts

  • Symbol: Φ (Phi)
  • Unit: J/kg
  • Approaches zero at infinite distance
  • Negative because gravity is attractive

Φ = -GM/r

4. Escape Velocity

Definition

Minimum speed needed to escape gravitational field without further propulsion

vesc = √(2GM/r)

Moon Example

MMoon = 7.342×10²² kg
RMoon = 1,737 km
vesc ≈ 2.38×10³ m/s