Changes
Jump to navigation
Jump to search
Line 19:
Line 19: − + + + + + + + + + + + + +
Added derivation
The formula that depends on [[surface gravity]] is simpler:
The formula that depends on [[surface gravity]] is simpler:
<math>v_{escape} = \sqrt{2gR}</math> where ''g'' = surface gravity.
<math>v_{escape} = \sqrt{2gR}</math> where <math>g</math> is the [[acceleration]] due to gravity at the surface.
===Derivation===
Consider an object of mass <math>m</math> trying to escape from a [[planet]] of mass <math>M</math>. The energy required to do this is in the form of [[kinetic energy]], and is converted completely into gravitational potential energy. Hence:
<math>\frac{1}{2} m v^2 = \int^{\infty}_{R} \frac{GMm}{r^2} dr</math>
Performing the integration gives:
<math>\frac{1}{2} v^2 = \frac{GM}{R}</math>
Rearranging gives the result above.
== See also ==
== See also ==
(username removed)