I Orbital Period In General Relativity

dsaun777
Messages
296
Reaction score
39
What is the orbital period in General Relativity using the Schwarzschild metric? In classical mechanics, it is something like
T=2pi(GnM/a3). Where a is the semi-major axis, this is for a small body orbiting a larger one. I think I have an idea but I am not 100% sure. I am interested in an outside observer far away viewing a small particle m in orbit of some mass M.
 
Physics news on Phys.org
dsaun777 said:
What is the orbital period in General Relativity using the Schwarzschild metric?
For a circular orbit, it's the Kepler's Third Law expression with the Schwarzschild ##r## plugged in as the orbital radius. Note that this is the case even though ##r## is not the same as the physical distance from the center of mass of the central body.
 
  • Like
Likes cianfa72 and PeroK
PeterDonis said:
For a circular orbit, it's the Kepler's Third Law expression with the Schwarzschild ##r## plugged in as the orbital radius. Note that this is the case even though ##r## is not the same as the physical distance from the center of mass of the central body.
Yeah, its the areal radius found by integrating over the radial coordinate from r to rs dr using the metric components related to radial coordinates.
 
dsaun777 said:
Yeah, its the areal radius
Yes, but...

dsaun777 said:
found by integrating over the radial coordinate from r to rs dr using the metric components related to radial coordinates.
...no, that's not what the areal radius is. The areal radius is ##r = \sqrt{A / 4 \pi}##, where ##A## is the surface area of the 2-sphere labeled by ##r## that is centered on the central mass.
 
In this video I can see a person walking around lines of curvature on a sphere with an arrow strapped to his waist. His task is to keep the arrow pointed in the same direction How does he do this ? Does he use a reference point like the stars? (that only move very slowly) If that is how he keeps the arrow pointing in the same direction, is that equivalent to saying that he orients the arrow wrt the 3d space that the sphere is embedded in? So ,although one refers to intrinsic curvature...
I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
Thread 'Dirac's integral for the energy-momentum of the gravitational field'
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(...

Similar threads

Replies
5
Views
2K
Replies
13
Views
4K
Replies
4
Views
2K
Replies
42
Views
5K
Replies
3
Views
1K
Replies
16
Views
3K
Replies
4
Views
2K
Replies
3
Views
1K
Back
Top