- #1

Vir

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## Homework Statement

So I'm calculating the gravitational potential of a sphere at at point P. R = radius of sphere, r = distance from center of sphere to point P. I'm looking at two scenarios; r > R (1) and r < R (2). So I have the following integral:

\begin{equation} V(r) = \int \frac{-GM}{Rr} ds

\end{equation}

## The Attempt at a Solution

Now, for (1) I integrate from r-R to r+R. However for (2) I'm thinking I have to integrate from -(R-r) to R+r, but this gives me the same constants as in (1). To my understanding the potential is supposed to be constant for all r < R, but then my constants are giving me the wrong answer.

If I remove the - and integrate from R-r to R+r I get a correct answer, but this makes no sense to me. That would mean I was integrating from the center of the sphere out to the edge, effectively ignoring half of the sphere? What am I missing?