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A magnetic fields generally fall off as 1 / r^3 rather than 1 / r^2 for gravity. How does time dilation fall off from a large body?

Where would the gravity and magnetic field line be in this chart provided from comments?

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    $\begingroup$ You are expected to do some research before asking questions on Stack Exchange sites. Steve has answered your question, but also see commons.wikimedia.org/wiki/File:Orbit_times.svg $\endgroup$ – PM 2Ring Jun 29 '19 at 17:51
  • $\begingroup$ @PM2Ring sorry I tried and prefer the SE format, but your link helped. $\endgroup$ – Muze Jun 29 '19 at 19:02
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The formula is given on wikipedia $$t_{0}=t_{f}{\sqrt {1-{\frac {2GM}{rc^{2}}}}}=t_{f}{\sqrt {1-{\frac {r_{s}}{r}}}}$$

Here $t_0$ is the time measured by clock distance $r$ from an object whose Schwarzschild radius is $r_s$ as calculated by a distant observer at rest whose clock measures $t_f$.

This is however, dependent on how the distant observer decides which ticks of your clock occur at the same time as which ticks of theirs, for which there are a number of perfectly reasonably choices, each of which gives a distinct answer. This formula is for what are called Schwarzschild coordinates, but there are other coordinate frames. Each one forces the distant observer to do a different calculation based on when they receive light signals from the close-in clocks ticks, in order to decide at what time the tick happened.

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  • $\begingroup$ updated question. $\endgroup$ – Muze Jun 29 '19 at 18:59

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