Why is this wrong? (gravitational flux)

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The discussion revolves around the confusion between gravitational flux and gravitational potential in the context of gravitational fields. The user presents two equations for gravitational flux, leading to different expressions for gravitational acceleration, \vec{g}. They realize that the same symbol is used for both flux and potential, which are distinct concepts in physics. The user acknowledges this misunderstanding and seeks clarification on the correctness of their calculations. The conversation highlights the importance of distinguishing between similar symbols in physics to avoid errors in interpretation.
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in my notes i have..

\Phi = \int \vec{g}\cdotdA = g(4\pir2) = -\frac{GM}{r^2}(4\pir2)

which yields \vec{g}=-\frac{GM}{r^2}

here's what i did independently..

\Phi = \int \vec{g}\cdotdA = -\frac{GM}{r^2}(4\pir2)

but since \vec{g}= -\vec{\nabla}\Phi

ie...

\vec{g}=\frac{d \Phi}{dr}=\frac{4 \pi GM}{r}

but this comes out to a different answer. is this still correct?*to admins/moderators/mentors/etc: before i get in trouble again, i appologize if this is considered another homework problem. but i thought it wasn't, so i posted in this section
 
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The same symbol is used for flux and potential, but they are different physical concepts.
 
oh darn i forgot about that.. thanks
 
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