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6 votes
4 answers
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How do we interpret measurements of Mercury's position?

When scientists measured the position of Mercury in the 18th century, they interpreted the results assuming a Euclidean background, because they did not know general relativity. So they measured $r$ ...
Giovanni's user avatar
4 votes
0 answers
161 views

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 ...
gravitone123's user avatar
1 vote
0 answers
32 views

Help to approximately invert Post Newtonian expression [closed]

Can anyone advice how to perform some sort of Taylor series approximation to compute the inverse of the following expression for $t(v)$ i.e. to obtain $v(t)$. Thanks! $$ t(v) = t_0 - \frac{5M}{256\eta ...
cyberface's user avatar
1 vote
1 answer
64 views

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 ...
Damiano Scevola's user avatar
0 votes
0 answers
27 views

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 ...
pglpm's user avatar
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0 votes
1 answer
52 views

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}) &...
pglpm's user avatar
  • 3,743
2 votes
1 answer
64 views

Post-Newtonian Stress-Energy tensor

I am currently studying Michele Maggiore's book - 'Gravitational Waves: Volume 1: Theory and Experiments'. On pages 245 and 246, each order --- until the second order --- of the stress-energy tensor. ...
RKerr's user avatar
  • 1,161
2 votes
0 answers
70 views

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} +...
MicrosoftBruh's user avatar
2 votes
0 answers
62 views

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 ...
RKerr's user avatar
  • 1,161
1 vote
0 answers
77 views

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 ...
Alessandro_97's user avatar
1 vote
0 answers
73 views

How to do taylor expansion of metric tensor to get Lagrangian for first Post-Newtonian order? [closed]

For the two-body compact object system how to write Lagrangian after obtaining first post-Newtonian metric tensor(just gravitational field)? Considering the perturbation in the metric as $$gαβ=ηαβ+hαβ,...
Pushpraj chakravarti's user avatar
1 vote
1 answer
65 views

Mass redshift degeneracy for binary black holes at all order in post-Newtonian perturbation theory

When you compute the inspiral signals of a binary black hole to lowest order in the post-Newtonian formalism, and study how this solution propagates through an expanding spacetime, you find that the ...
konstle's user avatar
  • 758
3 votes
1 answer
145 views

Is the Laplace-Runge-Lenz vector applicable for test particle motion around black holes?

In classical mechanics , the Laplace-Runge-Lenz (LRL) vector is a characteristic feature of the Kepler problem. This enables a very simple discussion of the properties of the orbit for the problem. It ...
Richard's user avatar
  • 2,015
0 votes
0 answers
61 views

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 ...
Yuan Liu's user avatar
2 votes
1 answer
67 views

Approximation concerning gravitational waves from binary neutron star

I'm interested in studying two neutron stars orbiting each other and producing gravitational waves. In textbooks the calculation for the power of the radiation is done by considering the neutron stars ...
Ville Alanko's user avatar
1 vote
1 answer
50 views

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 ...
foolishmuse's user avatar
  • 4,717
1 vote
2 answers
271 views

Gravitational wave radiation power from dimensional analysis

Let us try to find a formula for the power emitted through gravitational waves (GW) from a binary system in quasi circular orbit. The relevant quantities are the Newton's constant $G_N$, speed of ...
Ali Seraj's user avatar
  • 950
15 votes
1 answer
759 views

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 ...
tparker's user avatar
  • 48.1k
1 vote
1 answer
77 views

At the other edge beyond Newton with General Relativity? #2

The Schwarzschild solution is derived by using the static, spherically symmetric solution $$ds^2=-B(r)dt^2 + A(r) dr^2 +\text{angular terms},$$ assuming a concentrated mass, therefore gaining $A=1/B$ ...
BarrierRemoval's user avatar
-1 votes
1 answer
148 views

Would Newton's law in the solar system be independent from a presumed different fundamental gravitational law? [closed]

A thought experiment: Let's assume the gravitational field of a black hole without any neighbors would be stronger than the Schwarzschild metric in the Newtonian limit. Now, we let a solar system (sun ...
BarrierRemoval's user avatar
11 votes
1 answer
261 views

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 ...
Daddy Kropotkin's user avatar
6 votes
2 answers
129 views

As of 2021 in how many binary systems has the period decrease due to gravitational waves been measured?

I am searching for data for the period decrease of binary systems due to gravitational waves. I am aware of three systems in which it was possible to measure this period decrease: The Hulse-Taylor ...
Benito McLanbeck's user avatar
2 votes
0 answers
217 views

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 ...
Benito McLanbeck's user avatar
0 votes
1 answer
141 views

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-...
Ben Stark's user avatar
3 votes
1 answer
71 views

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 $g_{0i}$ ...
DarkGlimmer's user avatar
0 votes
1 answer
129 views

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 ...
user avatar
5 votes
1 answer
273 views

General relativity modifies Newton's inverse square law of gravity. Why do many people do experiments to test the inverse square law?

General relativity may induce the so-called post-Newtonian correction to the inverse square law of gravity. For details, please refer to chapter 9 of Weinberg's Gravitation and Cosmology. However, ...
lewton's user avatar
  • 283
0 votes
0 answers
79 views

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 ...
JoeGlas's user avatar
  • 33
4 votes
2 answers
324 views

Newtonian approximation of the metric tensor

I was reading Dirac's General Theory of Relativity. In chapter 16, the Newtonian approximation, we start with Let us consider a static gravitational field and refer it to a static coordinate system. ...
Yiluo Li's user avatar
3 votes
1 answer
425 views

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....
user146021's user avatar
0 votes
1 answer
70 views

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 ...
Warrenmovic 's user avatar
0 votes
1 answer
71 views

Gravitional Force of Mercury in General Relativity

I have been searching everywhere for the first order GR term that describes the gravitational force of a mass. Could someone kindly show me the term that describes this?
Mathematica's user avatar
27 votes
4 answers
5k views

Why do gravitational waves circularize a binary?

I understand that a binary orbiting around one another will circularize due to the emission of GWs due to Peters equations and that highly eccentric binaries evolve faster. But GW emission also ...
Warrenmovic 's user avatar
3 votes
1 answer
191 views

When does the Post-Newtonian expansion break down?

In the book Gravitational waves Vol.1: theory and experiment by M.Maggiore, in chapter 5, page 236, the author discusses the Post-Newtonian (PN) expansion and says that it is valid for small speed and ...
mattiav27's user avatar
  • 1,335
5 votes
1 answer
610 views

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 ...
P. C. Spaniel's user avatar
3 votes
1 answer
154 views

Taking the speed of light into account during $n$-body simulation

Currently, I compute the force between two gravitational interacting particles in a simulation with $n$ bodies according to $$F = G\frac{m_1m_2}{r^2}.$$ Doing this, however, assumes that all bodies in ...
Gilfoyle's user avatar
  • 223
1 vote
1 answer
108 views

How to find the terms of Post-Newtonian approximation?

I am studying the Damour paper on the Post-Minkowskian approximation to the 2 bodies problem in General Relativity (paper) but can't really understand the explanation of the previous state of the art, ...
Mauro Giliberti's user avatar
2 votes
2 answers
111 views

What does `weakly gravitating' mean?

When relativists like Bousso (see for instance https://arxiv.org/abs/hep-th/0203101) talk about `weakly gravitating systems', what sense of weak gravity is usually meant? (1) Post-Newtonian ...
Werner Einstein's user avatar
1 vote
1 answer
310 views

Help with calculating the Ricci tensor for the PPN formalism

I'm trying to follow the calculation done by Will in his book Theory and experiment in gravitational physics, and I was hoping for some help in calculating the Ricci tensor components in Section 5.2 (...
Germ's user avatar
  • 297
1 vote
2 answers
555 views

3PN and higher order post-Newtonian Schwarzschild approximation

This expression can be found in documentation from the JPL determining the relativistic acceleration under Schwarzschild conditions in the euclidean approximation they use to calculate the orbits of ...
Agerhell's user avatar
  • 729
1 vote
3 answers
889 views

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. ...
Alex's user avatar
  • 866
3 votes
1 answer
216 views

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{...
uhoh's user avatar
  • 6,243
5 votes
1 answer
2k views

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 ...
Rumplestillskin's user avatar
5 votes
2 answers
390 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 ...
JJMalone's user avatar
  • 175
4 votes
2 answers
517 views

How to obtain components of the metric tensor?

In coordinates given by $x^\mu = (ct,x,y,z)$ the line element is given $$ (ds)^2 = g_{00} (cdt)^2 + 2g_{0i}(cdt\;dx^i) + g_{ij}dx^idx^j, $$ where the $g_{\mu\nu}$ are the components of the metric ...
Rumplestillskin's user avatar
5 votes
1 answer
668 views

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
75 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 ...
6548873432486's user avatar
2 votes
1 answer
389 views

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 ...
Aaron Wild's user avatar
11 votes
1 answer
814 views

Post-Minkowskian expansion of some quantities in Post-Newtonian theory

I'm studying Post-Newtonian theory on the book "Gravity" by Poisson and Will and I found a few formulas that I can't obtain by myself. I'm pretty sure it must be quite simple, but can't find the right ...
GRB's user avatar
  • 1,431
0 votes
1 answer
512 views

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 ...
Timmy Wright's user avatar