All Questions
7
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Why is there a *minimum* energy for a particle to be captured in a $r^{-3}$ potential?
I was stuck in a central force problem from David Morin's Book "Introduction to Classical Mechanics".
The problem states that suppose there is a particle of mass $m$ moving under the ...
- 11
1
vote
2
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675
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How do we find the average value of gravitational potential energy over one orbit?
We just completed orbital dynamics in my university astrophysics class. The textbook we are using is Carroll and Ostlie. In the textbook, it is mentioned that the average gravitational potential ...
6
votes
2
answers
2k
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Bertrand's theorem and nearly-circular motion in a Yukawa potential
The question has arisen as a result of working on part b of problem 3.19 in Goldstein's Classical Mechanics book.
A particle moves in a force field described by the Yukawa potential $$ V(r) = -\frac{...
- 1,031
1
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2
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79
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Problem involving gravitational potential energy [closed]
Two uniform solid spheres of equal radii $R$, but mass $M$ and $4M$ have a centre separation of $6R$. The two spheres are held fixed. A projectile of mass $m$ is projected from the surface of the ...
3
votes
4
answers
710
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Rocket Leaving Earth's Gravitational Field
I stumbled across this seemingly simple question that really stumped me on further thought:
A rocket is intended to leave the Earth's gravitational field. The fuel in its main engine is a little ...
1
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3
answers
8k
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What makes an orbit stable or unstable?
I have an assignement, where I have a given central potential $V(x)=-\frac{K}{6r^6}$ and object with an angular momentum $L$.
I've calculate the radius of a circular orbit, which I've done by ...
- 69
0
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2
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3k
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How to show that the gravitational potential energy of a two particle system is -2 times the total kinetic energy, without using the virial theorem?
Consider a two-particle system with identical masses, orbiting in circles about their center of mass. I'm supposed to prove that:
$$U_p = -2U_k$$
With $U_p$ potential energy of the system, and $U_k$ ...
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