Why is this wrong? (gravitational flux)

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SUMMARY

The discussion centers on the calculation of gravitational flux and its relationship to gravitational potential. The user presents two equations for gravitational flux, \Phi = \int \vec{g}\cdot dA and \Phi = -\frac{GM}{r^2}(4\pi r^2), leading to the gravitational field \vec{g} = -\frac{GM}{r^2}. However, confusion arises when the user derives \vec{g} = \frac{d \Phi}{dr} = \frac{4 \pi GM}{r}, resulting in a discrepancy. The user acknowledges the distinction between flux and potential, indicating a misunderstanding of the concepts involved.

PREREQUISITES
  • Understanding of gravitational potential (\Phi) and gravitational field (\vec{g})
  • Familiarity with vector calculus, specifically divergence and gradients
  • Knowledge of the law of universal gravitation and its mathematical representation
  • Basic principles of flux in physics
NEXT STEPS
  • Study the mathematical derivation of gravitational potential and field equations
  • Learn about the divergence theorem and its application in gravitational contexts
  • Explore the relationship between flux and potential in electromagnetism for comparative understanding
  • Review advanced vector calculus techniques relevant to physics problems
USEFUL FOR

Physics students, educators, and anyone interested in gravitational theory and its mathematical foundations will benefit from this discussion.

iScience
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in my notes i have..

[itex]\Phi[/itex] = [itex]\int[/itex] [itex]\vec{g}\cdot[/itex]dA = g(4[itex]\pi[/itex]r2) = -[itex]\frac{GM}{r^2}[/itex](4[itex]\pi[/itex]r2)

which yields [itex]\vec{g}[/itex]=-[itex]\frac{GM}{r^2}[/itex]

here's what i did independently..

[itex]\Phi[/itex] = [itex]\int[/itex] [itex]\vec{g}\cdot[/itex]dA = -[itex]\frac{GM}{r^2}[/itex](4[itex]\pi[/itex]r2)

but since [itex]\vec{g}[/itex]= -[itex]\vec{\nabla}[/itex][itex]\Phi[/itex]

ie...

[itex]\vec{g}[/itex]=[itex]\frac{d \Phi}{dr}[/itex]=[itex]\frac{4 \pi GM}{r}[/itex]

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
 
Last edited:
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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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