Escape Velocity

Previous: Newton’s Laws

How fast must an object travel to escape a gravitational potential well? At the escape velocity, or faster.

escape-velocity

G = Gravitational constant, 6.67300 × 10-11 m3 kg-1 s-2
M = Mass of the planet (or whatever it is)
r = distance of the object from the center of mass of the planet

This formula is obtainable by simply following these steps:

  1. Mechanical energy = Kinetic energy + Gravitational potential energy
  2. Mechanical energy = 0. This gives us the condition that the kinetic energy counterbalances exactly the gravitational potential energy, namely, the object has just the minimum velocity required to overcome the gravitational potential of the planet (this is the escape velocity).
  3. We simply isolate the velocity from:

kineticequalspotentialG

See how m cancels from each side, and the escape velocity does not depend at all on the mass of the object! The escape velocity near the surface of Earth is =  11.2 km/s

Next: Ellipse

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2 Responses to Escape Velocity

  1. Pingback: Newton’s Laws | The Quantum Red Pill Blog

  2. Pingback: Ellipse | The Quantum Red Pill Blog

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