# Kepler's law

#### rlmurra2

Suppose the Sun's gravity were turned off, and the planets would leave their nearly circular orbits and fly away in straight lines described by Newton's first law. Would Mercury ever be farther away from the Sun than Pluto? If so, how long would it take for Mercury to acheive this passage?

I know this problems must have something to do with Kepler's laws, b/c its out of that section of the book. But I'm guessing you would have to find the tangential velocity first, or at some point?

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#### daveed

well you do have the relationship t^2 ~ r^3....
meaning that the relationship between period and radius is not linear... if you want that ratio, then period would have to increase faster than radius
and, well the path of a planet is linearly related to radius, so... if period increases faster, that means that the farther you get out there,

the slower you go...

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