# Triple integral to find the gravity inside a solid sphere

1. Nov 4, 2008

gravity inside a solid sphere

1. The problem statement, all variables and given/known data
I'm having a hard time setting up a triple integral to find the force of gravity inside a solid sphere. I've done a similar proof in physics before with gravity inside a spherical shell, but it only required a single integral. In this problem the answer must be derived using a triple integral.

2. Relevant equations
Newton's law of gravity:

|$$\vec{F_{grav}}$$|= $$\frac{GmpdV}{r^{2}}$$

3. The attempt at a solution
I believe i found a way to set up the triple integral using spherical coordinates on another physics forum thread, but I don't understand how to get the integrand. Can someone please explain the way the intergrand was derived in the following integral?

Last edited: Nov 5, 2008
2. Feb 2, 2017

### JOE SUPPLE BRUNS

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/sphshell.html#wtls

3. Feb 2, 2017

4. Feb 5, 2017

### JOE SUPPLE BRUNS

• Poster reminded to watch the attitude, and not to post in all capital letters (yelling)
THANK FOR NOTICING . ALSO SEE GRAVITATION CHAPTER IN HALLIDAY RESNICK INTRO PHYSICS USED TEXTBOOKS

5. Feb 5, 2017

### JOE SUPPLE BRUNS

THIS PROOF IS FOR INVERSE SQUARE MATH EQUATIONS.
DIVIDE BY DISTANCE r BETWEEN
CENTER OF MASS 1 AND
CENTER OF MASS 2
SQUARED.
YOUR WEIGHT F ON PLANET EARTH SURFACE IS
m2 = PLANET EARTH MASS

r = 6378 KM = 4000 MILES = NOT 0 KM = NOT 0 MILES =
PLANET EARTH RADIUS + HEIGHT OF m1

NOW CALC F = WEIGHT

ALSO APPLIES TO ELECTRIC FORCE
INVERSE SQUARE MATH EQUATION

EXCEPT
GRAVITY IS ONLY ATTRACTION FORCE BUT
ELECTROSTATIC CAN BE
ATTRACTION FORCE OR
REPULSION FORCE

6. Feb 5, 2017

### Farang

Has your shift button stuck or are you normally a loud person?

7. Feb 8, 2017

### TeethWhitener

Here's a link to the page on how to use the open practice problem forums: