General Relativity: Curved Spaces

[SsDd]

The lecture video is embedded below.

Additionally, slides used in the lecture are embedded below, or can also be downloaded directly from here.

Questions after the lecture? Please feel free to post them in the same thread.

Click to play embedded YouTube video.

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[dougettinger]

The precession of Mercury's orbit helps to prove Einstein's GR. Do the precessions of the other planetary orbits also contribute to proving GR ? If not, then why is this the case ?

Doug Ettinger, Pittsburgh, PA 02/08/2011

[Chris Peterson]

The precession of Mercury's orbit helps to prove Einstein's GR. Do the precessions of the other planetary orbits also contribute to proving GR ? If not, then why is this the case ?

The perihelion precession of other planets due to GR has been calculated, but I don't know if it has been measured accurately. Mercury is a special case in that it orbits so fast we can fairly easily see a small shift (and the GR component is very small compared to other effects which create a much larger precession).

Trying to detect a GR-induced perihelion precession rate on the order of an arcsecond per century, embedded in a precession rate at least ten times higher from gravitational perturbations, is very difficult when orbital periods are measured in years.

[neufer]

The precession of Mercury's orbit helps to prove Einstein's GR. Do the precessions of the other planetary orbits also contribute to proving GR ? If not, then why is this the case ?

The perihelion precession of other planets due to GR has been calculated, but I don't know if it has been measured accurately. Mercury is a special case in that it orbits so fast we can fairly easily see a small shift (and the GR component is very small compared to other effects which create a much larger precession).

Trying to detect a GR-induced perihelion precession rate on the order of an arcsecond per century, embedded in a precession rate at least ten times higher from gravitational perturbations, is very difficult when orbital periods are measured in years.

Code: Select all

Sources of the precession
of perihelion for Mercury
Amount (arcsec/Julian century)   	Cause
--------------------------------------------------------------------------------
5028.83 ±0.04    Coordinate (due to the precession of the equinoxes)
530  	         Gravitational tugs of the other planets
0.0254 	       Oblateness of the Sun (quadrupole moment)
42.98 ±0.04      General relativity

5603.24 	      Total
5599.7 	       Observed

-3.54     	    Discrepancy

The other planets experience perihelion shifts as well, but, since they have lower orbital velocities, and have less eccentric orbits, their shifts are lower and harder to observe. For example, the perihelion shift of Earth's orbit due to general relativity is about 5 seconds of arc per century. The periapsis shift of binary pulsar systems have been measured, with PSR 1913+16 amounting to 4.2º per year. These observations are consistent with general relativity.>>