Understanding the Work Needed to Escape a Gravitational Pull

[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

 

[Chestermiller]

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

Dear Mr-R. Welcome to Physics Forums.

You integrated incorrectly. Please try again.

 

[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.

 

[Mr-R]

Dear Mr-R. Welcome to Physics Forums.

You integrated incorrectly. Please try again.

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

 

[Astrum]

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

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