7.2.5

Escape Velocity & Synchronous Orbits

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Escape Velocity

Escape velocity is the velocity needed for an object to escape a planet's gravitational pull.

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Equations for escape velocity

  • The escape velocity, ve, needed for an object to leave the gravitational influence of a planet can be estimated by equating the expressions:
    • KE=12mv2KE = \frac12 mv^2
    • GPE=mΔV=0(GMmRP)=GMmRPGPE = m\Delta V = 0 - (-\frac{GMm}{R_P}) = \frac{GMm}{R_P}
  • Where M is the mass of the planet, RP is the radius of the planet and m is the mass of the satellite.
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Calculation for escape velocity

  • When an object is removed from a planet’s gravitational pull, it loses kinetic energy equal to the gravitational potential energy it gains.
  • The kinetic energy lost is equal to the potential energy gained when the object is moved an infinite distance from the planet and has zero velocity.
    • 12mve2=GMmRP\frac12 m v_e^2=\frac{GMm}{R_P}
    • ve2=2GMRPv_e^2 = \frac{2GM}{R_P}
    • ve=2GMRPv_e = \sqrt{\frac{2GM}{R_P}}
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Earth's escape velocity

  • For the Earth, RP = 6.4 × 106 m and M = 6.0 × 1024 kg.
  • This gives ve of approximately 11 km/s.

Synchronous Orbits

A geosynchronous orbit has a period of exactly one day.

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Satellites

  • A satellite in a geosynchronous orbit remains at the same point above the Earth at all times.
  • These satellites can be used for weather mapping and observation as they can watch the same place for long periods of time.
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Calculation

  • By definition, a geosynchronous orbit has a period of one day, this can be used to calculate the radius of the orbit.
    • r3=GmT2/4π2r^3=GmT^2/4{\pi}^2
  • Remember to convert the period into seconds and then, take the cubed root to find r.

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1Measurements & Errors

2Particles & Radiation

3Waves

4Mechanics & Materials

5Electricity

6Further Mechanics & Thermal Physics (A2 only)

7Fields & Their Consequences (A2 only)

8Nuclear Physics (A2 only)

9Option: Astrophysics (A2 only)

10Option: Medical Physics (A2 only)

11Option: Engineering Physics (A2 only)

12Option: Turning Points in Physics (A2 only)

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