Poisson's equation for gravitational field

In summary, the conversation revolves around the proof of Poisson's equation for a gravitational field, specifically the independence of Gauss's Law on the choice of a closed surface surrounding a point mass. The use of the divergence theorem is suggested and explained, with the final step being the proof for any closed surface. There is also a mention of using infinitesimal masses and the correct application of the divergence theorem. Overall, the conversation is seeking clarification on how to prove the independence of Gauss's Law using the divergence theorem.
  • #1
Sphinx
8
0
Hello everyone!
I have a question concerning the proof of Poisson's equation for a gravitational field.
My question is how can i prove that Gauss's Law is independent of the choice of the closed surface surrounding the point mass?
Thanks in advance
 
Physics news on Phys.org
  • #2
Did you try using the divergence theorem?
 
  • #3
Yes, but this is the last step of the proof , my difficulty resides in proving that the integral doesn't depend on the closed surface
 
  • #4
It would easier to help you if you actually showed what you did.
 
  • #5
You can either use the divergence theorem (the thing is that if you can prove it for a sphere you can prove it for any closed surface), or become hardcore (for no reason) and work with infinitesimal masses.
 
Last edited:
  • #6
∫ƒ.ds over a closed surface =∫div(f) dΩ over the corresponding volume =∫div(f) dΩ over a sphere enclosing the volume =∫ƒ.ds over the surface of the sphere
is that correct??
 
  • #7
Yes, so what is your question?
 
  • #8
I didn't see how to use the div theo, but know it's clear.
Thank u very much Orodruin & ChrisVer
 

What is Poisson's equation for gravitational field?

Poisson's equation for gravitational field is a mathematical expression that describes the relationship between the distribution of mass or energy in a given space and the resulting gravitational field. It is often used in physics and astronomy to calculate the gravitational potential or force at any point in space.

What is the significance of Poisson's equation for gravitational field?

Poisson's equation is significant because it provides a way to mathematically model the gravitational effects of mass or energy. This allows scientists to make predictions about the behavior of celestial bodies and to understand the structure of the universe.

How is Poisson's equation for gravitational field derived?

Poisson's equation is derived from Newton's law of universal gravitation and Gauss's law of gravity. It can also be derived from the general theory of relativity, which describes the relationship between mass and gravity in terms of the curvature of space-time.

What are the assumptions made in Poisson's equation for gravitational field?

Poisson's equation assumes that the gravitational field is caused by a static distribution of mass or energy, that the gravitational force is proportional to the inverse square of the distance between two objects, and that the gravitational potential is a continuous function.

How is Poisson's equation used in practical applications?

Poisson's equation is used in a wide range of practical applications, including satellite orbit calculations, mapping of gravitational fields on other planets, and predicting the motion of celestial bodies. It is also used in geophysics to study the Earth's gravitational field and in cosmology to model the large-scale structure of the universe.

Similar threads

I Gravity inside an exponential mass disk
    • Classical Physics
Replies
16
Views
842
I Understanding Physical Processes: EM, Gravitational, Mechanical & Entropic
    • Classical Physics
Replies
1
Views
624
Gravitational equipotential multiple choice problem
    • Introductory Physics Homework Help
Replies
4
Views
768
B How many electrons to make a stable gravitational object?
    • Classical Physics
Replies
5
Views
1K
I Gravitational potential energy
    • Classical Physics
2
Replies
46
Views
2K
I Potential energy and the gravitational field of a collapsing cloud of gas
    • Special and General Relativity
Replies
1
Views
234
I Simple case of Gauss' law for gravity
    • Classical Physics
Replies
10
Views
1K
I Reaction force of and its relation to normal force and friction
    • Classical Physics
Replies
20
Views
2K
I Pushing a rod in a magnetic field
    • Classical Physics
Replies
15
Views
524
B Gravitational force between two masses
    • Classical Physics
Replies
11
Views
1K

Hot Threads

Recent Insights

Back
Top