All Questions
Tagged with newtonian-gravity classical-mechanics
15
questions
10
votes
4
answers
953
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The converse of Newton's shell theorem
The shell theorem states that a spherically symmetric body $S$ of mass $m$ has a gravitational field identical to that of a point particle $P$ of mass $m$ located at the center of $S$.
We can ask the ...
- 4,576
15
votes
2
answers
6k
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Conservative central force and stable orbits
I saw a question a few days ago which referred to Bertrand's theorem. So, I now know that stable, closed orbits only occur when the potential function is $\frac{-k}{r}$ or $\tfrac{1}{2}kr^2$.
If ...
- 2,075
4
votes
1
answer
2k
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How does Newton's 2nd law correspond to GR in the weak field limit?
I can only perform the demonstration from the much simpler $E = mc^2$.
Take as given the Einstein field equation:
$G_{\mu\nu} = 8 \pi \, T_{\mu\nu}$
... can it be proved that Newton's formulation ...
user756
7
votes
1
answer
1k
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Lyapunov stability of circular orbits
I'm studying Classical mechanics on Arnold's "Mathematical Methods of Classical Mechanics". In a problem I am asked to find for which $\alpha$ the circular orbits in the central field problem are ...
- 260
4
votes
5
answers
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Does mass affect speed of orbit at a certain distance?
Does the mass of both the parent object, and the child object affect the speed at which the child object orbits the parent object?
I thought it didn't (something like $T^2 \approx R^3$) until I saw ...
- 6,927
0
votes
2
answers
318
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Constant of gravity in earth fixed coordinate system
I have this problem:
If the constant of gravity is measured to be $g_0$ in an earth fixed
coordinate system, what is the difference $g-g_0$ where $g$ is the
real constant of gravity as measured ...
user714
32
votes
11
answers
5k
views
In reverse time, do objects at rest fall upwards?
I want to develop a game where time runs backwards, based on the idea that physical laws are reversible in time. However, when I have objects at rest on the earth, having gravity run backwards would ...
- 422
9
votes
1
answer
614
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Marvin the Martian vs. the Death Star: how much energy will they actually need to disintegrate the Earth?
According to a detailed analysis by Dave Typinski, Marvin the Martian’s Illudium Q-36 Explosive Space Modulator will require $1.711 \cdot 10^{32}~\text{J}$ to shatter the Earth into a gravitationally ...
- 360
6
votes
1
answer
2k
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Conservation of spin angular momentum in a close binary system
Consider a simple model of a close stellar binary, of mass $m_1$ and $m_2 < m_1$, moving on circular orbits around the system's barycenter (no eccentricity, to simplify things). Both star's ...
- 7,592
6
votes
5
answers
2k
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Energy of Falling chain
Can someone explain this solution for the motion of a falling chain?
My Question is based on the above mentioned question on PSE. Suppose we have a chain attached on one end, while the other end is ...
- 1,466
4
votes
1
answer
3k
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On the Stability of Circular Orbits
Bertrand's Theorem characterizes the force laws that govern stable circular orbits. It states that the only force laws permissible are the Hooke's Potential and Inverse Square Law. The proof of the ...
- 357
3
votes
2
answers
855
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Bertrand's theorem
I found in Goldstein's Classical Mechanics that the condition for closed orbits is given by $\frac{d^2 V_{eff}}{dr^2}>0$.(bertrand's theorem). Can somebody explain to me, how this inequality is ...
- 1,880
2
votes
2
answers
2k
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Why does Friction act Parallel to the Surface (Microscopic Level)?
If we assume an object (blue layer) sliding towards the right across a surface (black layer). According to Newton's 3rd Law, the frictional force would act to the left (resisting the object's relative ...
user226894
1
vote
0
answers
188
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Physical interpretation of the symmetry for the Runge-Lenz vector
In the post What symmetry causes the Runge-Lenz vector to be conserved?, and based on the results of https://arxiv.org/abs/1207.5001, it was it was discussed that the Runge-Lenz vector is the ...
- 3,915
1
vote
1
answer
614
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What's the amount of deviation of cellestial orbits from perfect ellipses
It's well known that the planets don't orbit the sun in perfect circles and the characteristics of the elliptical orbits which serve as better approximations to their motion have been calculated ...
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