All Questions
29
questions
-4
votes
2
answers
117
views
Is Newton's gravitational acceleration centripetal instead of attractive?
In 1845 W. R. Hamilton demonstrated [1] by the use of the hodograph representation that the velocity of any Keplerian orbiter is the simple addition of two uniform velocities, one of rotation plus ...
0
votes
1
answer
120
views
How do you find the position at which three particles obey $m_1 a_1 = m_2 a_2$ if two of the particles form a composite body?
From Classical Mechanics by Kibble:
Consider a system of three particles, each of mass m, whose motion is
described by (1.9). If particles 2 and 3, even though not rigidly bound
together, are ...
1
vote
0
answers
188
views
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
1k
views
When is the effective potential equal to the total energy?
I have a question about the energy of a particle in orbit due to a gravitational attraction. The effective potential given by the gravitational force is defined to be
$$
U_{\text{eff}} = \frac{L^2}{...
- 207
1
vote
1
answer
58
views
Justification for the nature of planet's orbit in gravitational field!
In kleppner Mechanics in the chapter central force he derived the polar form of orbit for gravitational force as illustrated below: (first two equations are derived from fundamentals of central force)
...
0
votes
1
answer
43
views
Variable mass of orbiting body
Considering an object orbiting earth at radius $R$ and speed $v$, at one moment in time the mass of the object starts to decrease, what will happen to the object in terms of speed and orbit?
- 11
1
vote
1
answer
435
views
How to calculate the sphere of influence of a planet?
I'm making an orbit simulator, and to make it simpler, I'm only simulating one celestial object(planet, moon, sun) acting on each object(sattelite).
So that the sattelites and rockets can switch ...
- 13
0
votes
1
answer
296
views
Path of an object in gravitational field [duplicate]
How do you prove that path of a satellite or a planet is a second degree curve? In other words, how do you prove Kepler's law which states that planets move in elliptical paths?
0
votes
1
answer
68
views
Confusing about orbital speed [closed]
The Earth's distance from the Sun varies from $\ R_p=\ $ 1.471x$\ 10^8\ $km to $\ R_a=\ $ 1.521x$\ 10^8\ $km during the year. Determine the difference in the Earth-Sun system kinetic energy.
I have ...
- 3
0
votes
1
answer
94
views
Velocity of an orbiting body
The velocity of an orbiting body is given by:
$$v = \sqrt{\frac{Gm}{r}}$$
I was trying to derive this formula earlier but I was struggling with incorporating $G$ into my derivation.
I tried looking ...
- 324
1
vote
0
answers
108
views
If gravitation force varied with $r^{-3}$ instead of $r^{-2}$ what would happen to Kepler's laws [duplicate]
2nd law wouldn't change as it is LCAM. 3rd Law would change. But I'm confused about first law. Does any body under influence of any central force move in an ellipse?Can anyone give a simple proof/...
- 109
0
votes
1
answer
433
views
Motion of the center of mass of rigid bodies in space
For the classic two body problem, I know that the motion of the center of mass is a straight line (with respect to an inertial frame), provided that the bodies are considered as point particles.
Now ...
user84108
-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
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
15
votes
2
answers
6k
views
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