Escape Velocity & Synchronous Orbits

Test yourself

Escape Velocity

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

Illustrative background for Equations for escape velocityIllustrative background for Equations for escape velocity ?? "content

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.
Illustrative background for Calculation for escape velocityIllustrative background for Calculation for escape velocity ?? "content

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}}
Illustrative background for Earth's escape velocityIllustrative background for Earth's escape velocity ?? "content

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.

Illustrative background for Satellites Illustrative background for Satellites  ?? "content


  • 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.
Illustrative background for Calculation Illustrative background for Calculation  ?? "content


  • 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 the take the cubed root to find r.

Jump to other topics

1Measurements & Errors

2Particles & Radiation


4Mechanics & Materials


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)

Go student ad image

Unlock your full potential with GoStudent tutoring

  • Affordable 1:1 tutoring from the comfort of your home

  • Tutors are matched to your specific learning needs

  • 30+ school subjects covered

Book a free trial lesson