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## Homework Statement

We have an object with much smaller mass than compared to the sun.

This object is at rest when released at 1AU from the sun. After a week how far is the mass from the sun.

## The Attempt at a Solution

So I look at the gravitational potential energy and set it equal to kinetic energy.

[itex] \frac{-GMm}{r}=\frac{m(v)^2}{2} [/itex]

the v should be an r dot. now I take the square root of both sides. and then multiply both sides by dt then move the r from the left side to the right side and then integrate bothe sides. this will give me r(t). and then for the bounds I use r=1au and then I can solve for r final. after using t=0 and t=1 week for the time. i will put the time in seconds. this seems somewhat reasonable.