All Questions
Tagged with newtonian-gravity classical-mechanics
19
questions with no upvoted or accepted answers
15
votes
2
answers
512
views
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 ...
- 9,910
4
votes
0
answers
334
views
From Newton to Kepler without infinitesimals
I've read some interesting calculus-free proofs of at least parts of the derivation of Kepler's Laws from Newton's gravitational force.
One is of course Feyman's "Lost Lecture" (which was already ...
- 131
3
votes
0
answers
139
views
Minimal value of angular momentum in a close binary
I just noticed something interesting with the angular momentum of a close stellar binary. This question is somewhat related to another question of mine, but the question here is clearly different :
...
- 7,592
2
votes
0
answers
107
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Eight-shaped orbit determination
I was playing a game on my smartphone whose goal is to draw certain orbit in presence of certain central gravitational potential. I noticed that when there are two center of force is possible to have ...
- 1,536
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
58
views
Justification for the nature of planet's orbit in gravitational field!
In kleppner Mechanics in the chapter central force he derived the polar form of orbit for gravitational force as illustrated below: (first two equations are derived from fundamentals of central force)
...
1
vote
1
answer
33
views
The potential energy of universal gravitation with dynamic mass
Everyone knows that the potential energy is generally represented by -GMm/r.
Now, consider the M will decrease or increase depending on time or the m's position (we can think m moves in v). What will ...
- 11
1
vote
0
answers
90
views
Reference Frame conceptual confusion
I am getting confused as to why a ball still feels gravity when inside a moving car. The point of a reference frame is to reinterpret all the forces acting on a particle in one frame only. Hence all ...
1
vote
0
answers
482
views
Connection between Kepler Problem and Harmonic Oscillator
Background. Take the Kepler Lagrangian as
$L^K = \frac{1}{2}\dot{q}_i\dot{q}_i + \frac{k}{q}$,
and the Lagrangian for the isotropic harmonic oscillator as
$L^H = \frac{1}{2}\dot{q}_i\dot{q}_i - \...
- 21
0
votes
1
answer
111
views
Measuring the effect of spin of a tennis ball on its trajectory
Upward spin (lift) applied to a tennis ball will shorten its trajectory.
Are mathematical calculations and actual experimental results on this available somewhere?
If not, does anyone know how to ...
- 17
0
votes
0
answers
43
views
Why is it important to release energy as quickly as possible to perform a vertical jump?
Let's assume that we create this mechanism, where we must decide if the actuating cylinders are double-acting hydraulic or pneumatic with a spring inside.
the goal is for the mechanism to suddenly ...
0
votes
0
answers
1k
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Showing The Laplace–Runge–Lenz vector (per unit mass) is constant
Given an inverse square law $\ddot{\vec{r}}=-\frac{\mu}{r^2}\hat{r}$, I define the Angular momentum per unit mass as $\vec{H}=\vec{r}\times\dot{\vec{r}}$. Showing it's constant is strightfoward. Then ...
- 137
0
votes
0
answers
37
views
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
0
votes
0
answers
102
views
Pendulum in radial gravity field
All I could find about pendulums assumes that the force on the pendulum mass $m$ is $mg$ directed downwards. The case of $m$ being attracted only by the radial gravity pull (thus replacing the "...
- 1,302
0
votes
1
answer
73
views
Falling objects with different masses
I know that free falling objects with different masses fall at the same rate but that does not explain why objects with big masses are heavier to lift? what is gravity anyway I know it isn't a force ...
