All Questions
Tagged with orbital-motion general-relativity
204
questions
19
votes
3
answers
1k
views
Can perfectly stable orbits exist in GR?
Defining "stable orbit" between two bodies as one where, in the absence of other bodies or non-gravitational forces, the distance stays between some value pair $r_{min}>0$ and $r_{max}$. ...
- 343
0
votes
1
answer
85
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Questions about speed of gravity [duplicate]
If gravity "travels" at $c$, and the sun is travelling "forward", does it mean the planets are actually orbiting various points "behind" the center of the sun? Does it ...
2
votes
3
answers
245
views
Orbit description in Schwarzschild metric
Suppose to have a restricted 2-body system (BH + star with $M_{BH}\gg M_{\mathrm{star}}$) and you want to describe the orbit of the star relative to the BH, i.e. in the Schwarzschild metric.
Usually, ...
- 169
2
votes
1
answer
50
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How to relate a gravitational plane wave to the GW from a binary system?
I have two different forms of gravitational waves that I am trying to reconcile.
A monochromatic GW with angular frequency $\Omega$ propagating in the $\textbf{n}$-direction can be expressed as
$$ ...
- 1,751
0
votes
1
answer
63
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Don't Geodesics change due to other geodesics?
So the geodesics that point towards the Earth brings space-time towards the Earth and then back out again, but then the moon has its own geodesics so wouldn't it be kind of like geodesics affecting ...
- 1,534
0
votes
0
answers
33
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Anomalistic periods of Earth and Mercury
Can any one give me a TRUE VALUE for the anomalistic periods of Earth and Mercury?
I note the previous question on the following.
I more or less implemented the method suggested above using elliptic ...
- 31
1
vote
1
answer
67
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GR correction to perihelion precession comparing with newtonian orbit
My professor did the following derivation of the formula for the perihelion precession $\delta \phi = \frac{6\pi G M}{a(1-e^2)}$, but I am missing a factor of 2. I would appreciate if someone can help ...
1
vote
1
answer
61
views
Energy of circle orbit in Schwarzschild metric
For Schwarzschild metric we have invariants:
\begin{equation}
\begin{aligned}
& r^2 \frac{d \varphi}{d \tau}=\frac{L}{m} \\
& \left(1-\frac{r_s}{r}\right) \frac{d t}{d \tau}=\frac{E}{m c^2}...
- 509
0
votes
0
answers
33
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Circular orbit in a stationary, axially symmetric spacetime
From Poisson's, A Relativists Toolkit, problem 1.12 on page 27:
"A particle moving on a circular oribit in a stationary, axially symmetric spacetime is subjected to a dissipative force which ...
- 213
0
votes
1
answer
76
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What is the expression for strong field Schwarzschild circular orbit perihelion precession?
How can you calculate how large the perihelion shift should be under Schwarzschild conditions in general relativity for minimally disturbed circular orbits in the strong field limit?
I think there is ...
- 729
1
vote
0
answers
62
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Stress-Energy Tensor for a Two Mass System
I just don't understand this tensor and would like to go through an example with you to somehow make sense of it.
I consider two spheres with masses $m_1$ and $m_2$, densities $\rho_1$ and $\rho_2$ ...
1
vote
0
answers
81
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Photon speed for an observer at the photon sphere [closed]
I am asked to compute the orbital period of a photon, in the Scwarzschild spacetime, at the photon sphere for an observer at the same radius, $r^\star=3M$. I have computed the result, $\Delta T=6\pi M$...
1
vote
2
answers
230
views
Can the Schwarzschild orbit equation be solved exactly?
The Schwarzschild orbit is
$U'' + U = 1 + \varepsilon \cdot U^2$.
I've only seen turning-point analysis that demonstrates shift of perihelion.
Is there an exact solution?
- 77
1
vote
2
answers
173
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How does the speed (and kinetic energy) necessary to orbit a black hole vary with the radius of orbit?
I understand that closer orbits around Schwarzschild black holes require faster speeds, culminating in a required speed of $c$ at the photon sphere ($r = 3M$ in Schwarzschild coordinates). I'd love to ...
- 235
0
votes
1
answer
70
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Can we correctly invoke energy conservation to explain why binary systems do collapse in GR?
I've learned that binary systems emits gravitational waves, so there is energy leaving the system in the form of waves and so the radius of the binary system must decrease as to maintain the ...
- 159