Questions tagged [post-newtonian]
The post-newtonian tag has no usage guidance.
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Confusion about Post-Newtonian orbital motion (Damour-Deruelle)
In their famous paper in 1985 (link), Damour&Deruelle describe the orbital motion for a binary system taking into account first-order post-Newtonian corrections (1PN). The solution is given in ...
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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 ...
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The order of the time-space components of the metric tensor in post-Newtonian expansion
In the book Gravitational waves Vol.1: theory and experiment by M.Maggiore, in chapter 5, page 239, the author announces that when we expand the metric tensor by $v \over c$, the components $g_{0i}$ ...
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Newtonian 2-Body problem
The Newtonian equations of motion for two-point masses $m$ and $m^{\prime}$ are derived from the following Lagrangian:
$$L = \frac{1}{2}m\mathbf{v}^{2} + \frac{1}{2}m^{\prime}\mathbf{v}^{\prime \, 2} +...
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Relativistic Corrections to orbital elements
Given a massive compact object $M$ and a smaller object $m$ orbiting it in an elliptical orbit where $M \gg m$, Newtonian gravity describes the orbital elements $(a, e, i, \omega, \Omega, T)$, such as ...
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Gravitational waves in the post-Newtonian expansion
I have spent some time trying to understand gravitational waves in the context of the post-Newtonian expansion.
As far as I understand it, the general relativistic equation of motion can be ...
2
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1
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Einstein-Infeld-Hoffmann (EIH) Lagrangian for a Test-Particle as Limit of Schwarzschild-Geodesic
Consider a test particle of mass $m$ which is in orbit around a spherical-symmetric body with mass $M$. It therefore has a position as described by the coordinates $r,\phi$, and its motion can be ...
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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 ...
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Question about integral with second derivative of Newtonian potential (Weinberg 9.9)
I have a question about an integration that i found in Weinberg-Gravitation (1972), specifically in 9.9 about Post-Newtonian approximation of Brans-Dicke theory. We need to solve at order $O(2)$ an ...
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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 ...
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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})
&...
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Parameterized post-Newtonian formalism of Newtonian mechanics
Please kindly advise why the parameters $\gamma$ and $\beta$ are both zero for classical Newtonian mechanics (see attached screenshot of Wikipedia (the page about Binet's equation)) instead of $\gamma ...
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How to calculate coordinate acceleration in general relativity (without going to the Newtonian domain)?
The below quote is from Gravitation and Cosmology by Weinberg. I don't understand the calculations leading to equation $(9.1.2)$. Any help or alternative resources will be helpful.
1 The Post-...
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Adding two tensors in different coordinate systems
I have difficulties understanding the following (Everything out of the book Gravity by Poisson and Clifford): We have a quantity $\mathfrak{g}^{\alpha \beta}$ called gothic inverse metric in prior ...
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Hyperbolic orbit to keplerian orbit
How do I model a two body system that is initially travelling on an unbound orbit (hyperbolic so negative semi major axis) but then becomes a bound orbit (eccentric elliptic, so positive semi major ...