- #1

- 9

- 0

- Thread starter llandau
- Start date

- #1

- 9

- 0

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

If the radius of the sphere is R, then its volume is [itex](4/3)\pi R^3[/itex] and the density is [itex](3/4)m/(\pi R^3)[/itex]. That means that the mass of the sphere below radius r is [itex](3/4)m/(\pi R^3)(4/3)\pi r^3= m(r/R)^3[/itex]. The force on an object of mass M then is [itex]-Gm(r/R)^3M/r^2= -Gmr/R^3[/itex].

So the force is proportional to r and the potential energy is [itex]-Gmr^2/(2R^3)[/itex].

- #3

- 9

- 0

You have been helpful, thanks (I believe you lost an M, but it really doesn't matter).

- Replies
- 3

- Views
- 4K

- Replies
- 5

- Views
- 8K

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 9

- Views
- 12K

- Last Post

- Replies
- 1

- Views
- 768

- Last Post

- Replies
- 3

- Views
- 3K

- Last Post

- Replies
- 1

- Views
- 7K

- Last Post

- Replies
- 10

- Views
- 5K

- Last Post

- Replies
- 2

- Views
- 28K