All Questions
6
questions
1
vote
2
answers
189
views
What is the gravitational field intensity of a uniformly distributed mass content in Newtonian gravity?
In an infinite universe composed of single point masses which can be simplified as a uniformly distributed mass density, what is the equation for the gravitational field intensity in Newtonian gravity?...
- 476
0
votes
1
answer
521
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How do you integrate by parts when you have a triple integral?
I'm studying how particles of equal mass behave in a spherical cluster held intact by gravity. I will assume that the mass density $\rho(R)$ of the cluster is a function of the magnitude of the ...
- 1,222
0
votes
2
answers
729
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What is the gravitational potential of a homogeneous sphere? [closed]
I am studying gravitational potentials from the book Galactic Dynamics by James Binney and Scott Tremaine. They provide the equation from where the potential of a spherical system is to be derived as:
...
- 197
1
vote
1
answer
29
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Doubt regarding solving an integration for radial flow of matter around a star in Newtonian gravity
The spherically symmetric flow of matter around a star in Newtonian gravity is governed by the equation
$$v\frac{dv}{dr}+\frac{1}{P+\rho}\frac{dp}{dr}+\frac{1}{r^2}=0$$
The equation of state is chosen ...
- 2,015
0
votes
1
answer
39
views
Finding suitable element to perform integration upon [closed]
Is there any precise (proper) method or technique to specify the element on which integration will be performed. Is it the same for all properties like moment of inertia, gravitational potential, ...
- 496
12
votes
2
answers
22k
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Gravitational potential energy of any spherical distribution
The general formula to get the potential energy of any spherical distribution is this :
\begin{equation}\tag{1}
U = - \int_0^R \frac{GM(r)}{r} \, \rho(r) \, 4 \pi r^2 \, dr,
\end{equation}
where $M(r)$...
- 7,592