All Questions
Tagged with newtonian-gravity integration
45
questions
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2
answers
298
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What is the meaning of Gravitational Potential when multiple point masses are involved?
According to Wikipedia "The gravitational potential $V$ at a distance $x$ from a point mass of mass $M$ can be defined as the work $W$ that needs to be done by an external agent to bring a unit ...
- 379
0
votes
1
answer
182
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Better understanding of the definition of Gravitational Potential as the improper integral $\frac{1}{m}\int^x _{\infty}G\frac{Mm}{x^2}dx$
According to Wikipedia "The gravitational potential $V$ at a distance $x$ from a point mass of mass $M$ can be defined as the work $W$ that needs to be done by an external agent to bring a unit ...
- 379
1
vote
1
answer
130
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Finding velocity $v$ and position $r$, given a time $t$ under the acceleration of a gravitational force [closed]
I was messing with the maths, when I tried to find the velocity as a function of time, $v(t)$, and the position, also, as a function of time, $r(t)$ under the gravity force.
$$ m \ddot{r} = -G \frac{...
- 1,525
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2
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729
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What is the gravitational potential of a homogeneous sphere? [closed]
I am studying gravitational potentials from the book Galactic Dynamics by James Binney and Scott Tremaine. They provide the equation from where the potential of a spherical system is to be derived as:
...
- 197
1
vote
1
answer
29
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Doubt regarding solving an integration for radial flow of matter around a star in Newtonian gravity
The spherically symmetric flow of matter around a star in Newtonian gravity is governed by the equation
$$v\frac{dv}{dr}+\frac{1}{P+\rho}\frac{dp}{dr}+\frac{1}{r^2}=0$$
The equation of state is chosen ...
- 2,015
0
votes
3
answers
147
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The force of gravity between a shperical shell and a particle
I am trying to understand the proof of why the force acting on a spherical shell and a particle is
$$\frac{GMm}{r^2}$$
Where M is the mass of the sphere and m is the mass of the particle.
I am looking ...
- 5
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votes
1
answer
84
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Why does this volume integral vanish?
I am stuck on this problem concerning the gravitational potential of a body. The body has a mass density $\rho(\mathbf x)$ and I have to calculate a contribution to the total gravitational potential ...
- 373
3
votes
1
answer
491
views
Better derivation for the gravitational potential energy
I was shown this derivation for the gravitational potential energy, and I'm not very happy about it assuming that $\frac{1}{\infty} = 0$. Is there a better derivation, either using a completely ...
- 73
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votes
2
answers
787
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How to calculate center of mass of a hollow hemi-sphere with some thickness?
When we calculate Center of mass (COM) of a hollow sphere, we assume that it's thickness is
infinitesimally small, but in real world, we do not have any object with zero thickness, so how can we ...
3
votes
3
answers
125
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What is wrong with this calculation of work done by an agent bringing a unit mass from infinity into a gravitational field? [duplicate]
Let us assume that a gravitational field is created by a mass $M$. An agent is bringing a unit mass from $\infty$ to distance $r < \infty$, both measured from mass $M$.
The agent is always forcing ...
- 49
0
votes
1
answer
66
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Why do I have an extra factor of 3 for self-gravity?
So, I'm trying to calculate the "acceleration" (force / mass) on a spherical object of mass $M$ and radius $R$ due to its own gravity that holds it together. So, here is what I figured. The "...
-1
votes
1
answer
356
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Integration and average in physics? [closed]
Many applications of physics theory involve computations of integrals. Examples are voltage, force due to liquid pressure, surfaces...
In some cases, when there is linear dependence between two ...
-1
votes
3
answers
1k
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Derive gravitational potential energy for this system [closed]
This is on a study guide for my Physics 221 final. I feel like I almost got it but I am off by a sign error. Here is the question:
Here is what I got so far:
Known:
$$F_g = \frac{GMm}{r^2}$$
$$U_g =...
- 101
0
votes
1
answer
39
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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
0
votes
2
answers
480
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Feynman's proof for Newton's shell theorem [closed]
I have two questions concerning this proof:
Firstly, what is the difference between the increments ds and dx? Are they not just the same thickness of the strip?
Secondly, why can the integral ...
- 406