All Questions
Tagged with post-newtonian gravity
16 questions
2
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0
answers
62
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Formulating the dynamics of mass distribution in Newton-Cartan gravity
I am a mathematician following the lectures of Schuller about General Relativity, in particular this lecture. My main motivation is to understand how do we use Einstein field equation to model a ...
0
votes
0
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33
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Order of magnitude of time derivatives of gravitational potential and gravitational vector potential on Earth
[This question is connected with this one. Since the estimation and measurement of spatial gradients and time derivatives have very different levels of difficulties, I thought it best to ask two ...
- 3,833
0
votes
1
answer
59
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Order of magnitude of gravitational vector potential & its gradient on Earth
In post-Newtonian approximation of gravitation, the metric on and around the Earth is taken to have the expression
$$
\begin{bmatrix}
-1+\frac{2}{c^2}U+ \frac{2}{c^4}(\psi-U^2) + \mathrm{O}(c^{-5})
&...
- 3,833
1
vote
1
answer
56
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Under PPN Formalism, would the gravity of a mass double as its velocity approaches $c$?
I'm looking at the answer Michael gave to my question. Does this imply that under parameterized post-Newtonian formalism, under the $β1$ factor for kinetic energy, the gravity of a mass doubles as it ...
- 4,861
15
votes
1
answer
774
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What's wrong with Abraham's proposed force law in Nordström's first theory of gravity?
Nordström's 1912 proposed theory of relativistic gravity posited that the gravitational potential field $\phi$ and the matter density field $\rho$ are both scalar fields, simply related by the wave ...
- 49.4k
11
votes
1
answer
289
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What is the current status of the convergence of the post-Newtonian approximation?
In the very well written article by C. Will, On the Unreasonable Effectiveness of the post-Newtonian Approximation in Gravitational Physics, he states:
The one question that remains open is the ...
- 2,770
0
votes
2
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177
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Does Newton's Theory with Retarded potentials give rise to the motion of perihelion of Planets
If we take into account the retarded potentials and the motion of the Sun(due to the planet), does Newton's Gravitational theory give rise to the motion of Perihelion of planets (qualitatively, not ...
user300251
3
votes
1
answer
504
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Precession of perihelion of Mercury?
I have a few questions about precession of Mercury and GR corrections. Feel free to any that you can:
GR is used to correct precession caused by Sun on Mercury by time dilation and length contraction....
- 143
5
votes
1
answer
757
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What's the difference between a post-Minkowskian approximation and a post-Newtonian one?
I'm studying the book Gravity by Poisson & Will. Specifically, I'm interested in the post-Newtonian and post-Minkowskian approximations showed in chapters 6-10. The problem I'm having is ...
- 4,737
1
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3
answers
952
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How to get space component of weak field (linearized) metric?
For Minkowski space with a weak gravitational field the metric takes the form
$$
ds^2 = (1+2\phi/c^2)c^2dt^2 -(1-2\phi/c^2)(dx^2+dy^2+dz^2),
$$
where $\phi$ is the Newtonian gravitational potential.
...
- 886
3
votes
1
answer
229
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Experimental limits on non-Newtonian gravitational force at length scales larger than 1 meter?
This answer from 2012 shows some information on an exponential term characterized by relative strength and range parameters $\alpha$ and $\lambda$,
One potential tested here is here
$$V(r)=-G\frac{...
- 6,101
5
votes
1
answer
2k
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What are modern solar system applications of GR where approximation methods fail? [closed]
It is often stated that general relativity (GR) provides the most accurate description of gravitational phenomenon. In most undergraduate and even graduate textbooks this idea is reinforced by ...
- 1,998
5
votes
2
answers
402
views
Light dispersion in gravitational theories
GR predicts no Ricci curvature in vacuum (or at least when we can ignore the cosmological constant). Would theories that violate this lead to observable light dispersion in solar system tests of ...
- 175
5
votes
1
answer
709
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Derivation of Post-Newtonian (PN) expression for acceleration in Schwarzschild geometry
The expression for the acceleration of a near-earth satellite as presented in the IERS Technical note is given by
\begin{equation} \label{eq:problemeq} \tag{1}
\frac{d^2\mathbf{r}}{dt^2} = \frac{GM_E}{...
4
votes
0
answers
76
views
Gravitational force for a binary of point particles with GR term
i'm trying to simulate the two body problem with 2 equal masses and I want to account for general relativistic effects. I know that the difference in the gravitational force would be an additional ...
- 113
0
votes
1
answer
517
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Definition of "nonlinear" in the context of perturbation of gravity
What exactly is the definition of a nonlinear perturbation when applied to a background spacetime metric?
I have seen so called "linear perturbations" which look like
$$ds^2 = -(1+2\Phi)dt^2 ...
- 13