Question

HELP!!
Convince yourself that gravity vector field F =-Km*M/r^3*r, (r=xi+yj+zk) is gradient vector field on open area G =R^3\{(0,0,0)}. Find the potencial of this field.

Answer 1

If it is a gradient field, then curl F = 0. Use the polar form of curl to show that.

Then use the polar form to guess what phi has the property that
\[ F = \nabla \phi \]
if you don't know phi already

Answer 2

Here are the forms:
http://www.mas.ncl.ac.uk/~nas13/mas2104/handout5.pdf