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What minimum launch speed is needed for a rocket to leave the surface of a solar...

What minimum launch speed is needed for a rocket to leave the surface of a solar system planet (in circular orbit) and escape the sun? Escape speed of the planet is Vesc and the planet's orbital speed is Vorb. How could launch at this speed not result in escape from the sun?

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Answer #1

To determine escape velocity for rocket we have to convert the total potential energy of rocket into zero potential energy means after that total energy of rocket is than kinetic energy of rocket

so,

where R is the radius of sun and M is mass of sun

which we putting values calculate

Vesp =617.7km/s

2) now orbital speed of sun

is less than escape velocity by lauching with speed rocket will move in circular orbit because it will never get free of potential energy of sun which provides centripetal accelartion to it to move in circular orbit.

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