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- Homework Statement
- Earth with mass m orbits the sun (mass M) in circular path (radius R) with velocity v. If a rocket is launched from the earth,find the initial velocity that is needed so that it could leave the solar system (free from both the sun's and earth's gravity).

Note-

this process undergoes two independent steps: free from the earth's gravity, and then free from the sun's gravity.

- Relevant Equations
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I have a difficulty when making the energy-conservation-equation for the second step.

When making the equation, we need to know the exact position (measured from the sun) of the rocket after it is freed from the Earth gravitation.

But, where exactly does the rocket free from Earth gravitation? All I know is that this happens at infinity (measured from the earth).

Does this "infinity" negligible if we measure it from the sun? Why?

When making the equation, we need to know the exact position (measured from the sun) of the rocket after it is freed from the Earth gravitation.

But, where exactly does the rocket free from Earth gravitation? All I know is that this happens at infinity (measured from the earth).

Does this "infinity" negligible if we measure it from the sun? Why?