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B Adorable Gravity Demo - National Medals Lab
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DaveC426913
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... of an interactive gravitational body simulator.ergospherical said:
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DaveC426913
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Hm. I'm not sure just how good it is.
I just set two massive bodies co-orbiting, which worked fine until I added a third smaller body.
The third boy seemed to orbit only one of the massive bodies, and remained unaffected by the other.
I just set two massive bodies co-orbiting, which worked fine until I added a third smaller body.
The third boy seemed to orbit only one of the massive bodies, and remained unaffected by the other.
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It would be nice to see how they coded it and what shortcuts they used (which might explain that behaviour you found for the restricted three body problem) but I couldn't find any documentation.
In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this:
$$
\partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}.
$$
The integrability conditions for the existence of a global solution ##F_{lj}## is:
$$
R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0
$$
Then from the equation:
$$\nabla_b e_a= \Gamma^c_{ab} e_c$$
Using cartesian basis ## e_I...
See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then
\begin{align}
0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\
&= \left(...
Abstract
The gravitational-wave signal GW250114 was observed by the two LIGO detectors with a network matched-filter signal-to-noise ratio of 80. The signal was emitted by the coalescence of two black holes with near-equal masses ## m_1=33.6_{-0.8}^{+1.2} M_{⊙} ## and ## m_2=32.2_{-1.
3}^{+0.8} M_{⊙}##, and small spins ##\chi_{1,2}\leq 0.26 ## (90% credibility) and negligible eccentricity ##e\leq 0.03.## Postmerger data excluding the peak region are consistent with the dominant quadrupolar...
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