What Is the Escape Speed from the Sun to Mercury at 25 Million Kilometers?

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The discussion focuses on calculating the escape speed from the Sun to Mercury when a spaceship is positioned 25 million kilometers away from the Sun. The relevant equation involves gravitational force and kinetic energy, specifically Gm1m2/radius plus the distance from the Sun. It is clarified that escape speed is typically defined from a gravitating body to infinity, rather than to another celestial body. The participants confirm that the equation provided is appropriate for calculating escape speed from the Sun alone. Understanding these principles is essential for solving the problem accurately.
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Homework Statement



I need to what the escape speed from the sun to mercury would be if the spaceship is 25 mil km away from the sun.

Homework Equations





The Attempt at a Solution


Basically, all need to know is if I can do this:
Gm1m2/radius of sun+ 25 mil km away from sun=1/2 mv^2.

Also, as you get farther away you can decrease your speed. Correct?
 
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What is "escape speed from the Sun to Mercury"? The escape speed is usually defined from some location near a gravitating body to infinity, not to another body.
 
Oh sorry, I meant just from the sun.
 
Then your equation is correct.
 
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