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Author Topic: What is the profile of an elliptical orbit around a black hole?  (Read 1466 times)

Offline jeffreyH

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Kepler's second law states that equal areas of the orbit are swept out in equal amounts of time. If we add time dilation into the equation how can we then describe the elliptical orbital speed of a body at the perihelion and aphelion? At its nearest approach it should speed up just when time dilation is strongest and at the furthest point it should slow down where time dilation is weakest.


Offline evan_au

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Kepler's law assumes that the orbit will be an ellipse, and the major axis of the ellipse will be stationary in space.

However, relativity predicts that the major axis of the orbit will precess (change direction over time). This was first detected in the orbit of Mercury. Many astronomers had tried to explain this effect, until Einstein explained it with general relativity.
As our Solar System has many planets, the gravitational tug of the other planets has a much stronger effect than the relativistic effects. However, when the effects of the other planets, and tidal bulges were taken into account, there was still an "anomalous" (unexplained) precession of perihelion.

This effect has now been detected in orbiting pulsars.

But Kepler's law of equal areas still applies to each elliptical orbit (provided you don't measure the areas too precisely).

Offline yor_on

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It's a question of what you locally measure versus what a far observer observes. And if you go by relativity all frames of reference are equally correct, joined through Lorentz transformations. There is no simple answer to it, as long as you want it to be a container, in where all observation have a exact fit, 'immediately compared'. Although the discrepancies you consider here should be extremely small as long as we don't get into relativistic regimes, considering mass and 'relative speeds'. And how you will describe it is observer dependent, that doesn't state that you can have two opposite descriptions relativistically, causality must be observed. You can translate the last into a statement of 'c'.
« Last Edit: 19/03/2015 11:58:33 by yor_on »

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