# Integrating Newton's law

1. Aug 18, 2013

### Mr-R

Hello everyone,
What does it mean if I integrate Newton's law of universal gravitation with respect to r.
F= GMm/r^2 become 3GMm/r^3 . Is this the work needed to escape a gravitational pull ?

Thank you

2. Aug 18, 2013

### Staff: Mentor

Dear Mr-R. Welcome to Physics Forums.

You integrated incorrectly. Please try again.

3. Aug 18, 2013

### Astrum

This is the work-energy theorem.

$$\int ^b _a \vec{F} \cdot d \vec{r} = \Delta KE = W$$

If you integrate $\frac{GMm}{r^2}$ you get the potential energy.

Try integrating it again correctly.

4. Aug 18, 2013

### Mr-R

Oh thats quiet embarrassing. It should be = GMm/r which is the work. Thank you very much.

5. Aug 18, 2013

### Astrum

No, that's potential energy. In this case, $W = \Delta U = \frac{GMm}{r_2}- \frac{GMm}{r_1}$

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