All Questions
Tagged with celestial-mechanics classical-mechanics
29
questions
3
votes
1
answer
420
views
Feynman's Lost Lecture: what is the significance of $\frac{d\mathfrak{v}}{d\theta}=-\frac{GMm}{\left|\mathfrak{L}\right|}\hat{\mathfrak{r}}?$
My question pertains to a fact used by Richard Feynman in his so-called
Lost Lecture. http://books.wwnorton.com/books/Feynmans-Lost-Lecture/.
I have only skimmed the book, so I have much more to learn ...
- 2,015
-2
votes
1
answer
115
views
Spirals in newtonian celestial mechanics?
I know Kepler's laws, Newton's laws, and that conic sections are the trajectories of noncolliding two point masses. But I wonder about a point mass A eventually colliding with point mass B.
In ...
- 926
1
vote
3
answers
1k
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Does it take energy (in joules) to keep the moon in orbit around the Earth?
If energy is force times distance and I use the Newtonian formula to calculate the force between the earth and the moon
$$ F=\frac{G m_1 m_2}{r^2} , $$
then multiply it by the circumference of the ...
- 163
1
vote
0
answers
53
views
Sign of the action for the harmonic osccilator?
I am confused about the derivation of the action $S(x,\mathbf{J})$ for a harmonic oscillator as given at page 219 in "Galactic Dynamics", J.Binney-S. Tremaine, 2nd Ed. 2008. The part of the derivation ...
15
votes
2
answers
512
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Regularization: What is so special about the Coulomb/Newtonian and harmonic potential?
I wanted to know if the procedure for regularization of the Coulomb potential outlined in Celletti (2003): Basics of regularization theory could be generalized to arbitrary polynomial potentials. So ...
- 9,890
-2
votes
1
answer
223
views
Impact of Moon's gravitational pull on Earth [closed]
What speed does the Moon's gravitational pull impart to Earth?
0
votes
1
answer
247
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Problem: Spectroscopy of a binary system
The Problem is:
For a binary system (2 Stars) with Orbital Period of $P =4.822 days = 416620.8 second$ and inclination $i=90$ and with speeds very less than $3 .10^8 m/s$. Their orbital planes around ...
- 115
0
votes
0
answers
37
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How can I measure the stability of a many body gravitational system?
Suppose I have an N body planetary system interacting via gravity. Suppose I know the positions and momenta at t=0. How do I know if this system is stable (indefinitely)? By stable I mean the ...
- 1,601
1
vote
1
answer
165
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Stability of the classical helium atom
Let us forget about quantum mechanics and confine ourselves to classical mechanics.
The Hamiltonian for a classical helium atom would be
$$ H = \frac{p_1^2 + p_2^2}{2m } - \frac{Z}{r_1} - \frac{Z}{...
- 4,122
3
votes
2
answers
897
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What is the "associated scalar equation" of equations of motion?
In an essay I am reading on celestial mechanics the equations of motion for a 2 body problem is given as:
$$\mathbf{r}''=\nabla(\frac{\mu}{r})=-\frac{\mu \mathbf{r}}{r^3}$$
Fine. Then it says the "...
- 1,517
0
votes
1
answer
51
views
What does an $n$-body system with constant $T$ and $U$ look like?
Can someone give an example of a system where the kinetic $T$ and potential $U$ energy are constant (but not zero)?
Here's what I have in mind: Say you have $n-1$ satellites of negligible mass ...
- 1,517
3
votes
0
answers
447
views
Story about a mathematician, a dinner party, and the three-body problem
I remember dimly hearing a story, coincidentally also at a dinner party, and I was trying recently to track the details down with no success. I was hoping someone here might have also heard this story ...
- 139
12
votes
3
answers
893
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What could cause an asymmetric orbit in a symmetric potential?
My question can be summarized as:
Given a potential with a symmetry (e.g. $z\rightarrow-z$), should I expect orbits in that potential to exhibit the same symmetry? Below is the full motivation for ...
- 18.5k
2
votes
1
answer
1k
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Angular momentum components as independent integrals of motion
I was told that in order to solve the Kepler problem (6 degrees of freedom in total) you have to proceed, step by step, to reduce those degrees of freedom using the integrals of motion. You do so ...
- 65