A rocket is in circular orbit around the earth; the radius is 1.16 R earth. To p

Question

A rocket is in circular orbit around the earth; the radius is 1.16 R earth. To put the rocket into an escape orbit, its engine is fired briefly in the direction tangent to the orbit, changing the rocket's velocity by Delta V. Calculate the minimum value of Delta V to escape from Earth orbit. Tries 0/25 A rocket is in an elliptical orbit around the earth; the radius varies between 1.16 R earth and 1.32 R earth. To put the rocket into an escape orbit, its engine is fired briefly in the direction tangent to the orbit when the rocket is at perigee, changing the rocket's velocity by Delta V. Calculate the minimum value of Delta V to escape from Earth orbit. Tries 0/25

Explanation / Answer

At distance r from the center of the earth the potential energy is PE = -G M m / r At infinity the potential energy is zero (and the speed can also be zero) 1/2 m v^2 = G M m / r where v is the speed of the rocket at distance r and v is the required speed of the rocket to reach infinity Then V = v - v0 where v0 is the speed of the rocket in orbit m v0^2 / r = G M m / r^2 speed of rocket in orbit v0^2 = G M / r In other words, total energy of rocket at distance r is E = 1/2 m v0^2 - G M m / r and at infinity E (total) = 0

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