1. The problem statement, all variables and given/known data
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.
3. 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.
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.
3. 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.
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