<p>The formula is given on <a href="https://en.wikipedia.org/wiki/Gravitational_time_dilation#Outside_a_non-rotating_sphere" rel="nofollow noreferrer">wikipedia</a>
<span class="math-container">$$t_{0}=t_{f}{\sqrt {1-{\frac {2GM}{rc^{2}}}}}=t_{f}{\sqrt {1-{\frac {r_{s}}{r}}}}$$</span></p>

<p>Here <span class="math-container">$t_0$</span> is the time measured by clock distance <span class="math-container">$r$</span> from an object whose Schwarzschild radius is <span class="math-container">$r_s$</span> as calculated by a distant observer at rest whose clock measures <span class="math-container">$t_f$</span>. </p>

<p>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.</p>

CC BY-SA 4.0
2019-06-29T18:59:54.227Z
updated question.
Muze
CC BY-SA 4.0
2019-06-29T17:43:56.103Z
2019-06-29T17:55:32.350Z
2019-06-29T17:55:32.350Z
Steve Linton
<p>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?</p>

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

<p><a href="https://i.sstatic.net/pnL6c.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/pnL6c.png" alt="enter image description here"></a></p>

CC BY-SA 4.0
2019-06-29T17:51:38.393Z
You are expected to do some research before asking questions on Stack Exchange sites. Steve has answered your question, but also see https://commons.wikimedia.org/wiki/File:Orbit_times.svg
PM 2Ring
CC BY-SA 4.0
2019-06-29T19:02:30.933Z
@PM2Ring sorry I tried and prefer the SE format, but your link helped.
Muze
<black-hole><planet><distances><time-dilation>
How does time dilation from a large body fall off?
Muze
# How does time dilation from a large body fall off?

(Asked by: username_0 on 2019-06-29)

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?

[![enter image description here](https://i.sstatic.net/pnL6c.png)](https://i.sstatic.net/pnL6c.png)

**Tags:** black-hole, planet, distances, time-dilation

> **Comments:**
> **username_1**: You are expected to do some research before asking questions on Stack Exchange sites. username_2 has answered your question, but also see https://commons.wikimedia.org/wiki/File:Orbit_times.svg  
> **username_0**: @username_1 sorry I tried and prefer the SE format, but your link helped.  

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## 1 answers

### Answer by username_2 on 2019-06-29. Score: 3 | Accepted answer

The formula is given on [wikipedia](https://en.wikipedia.org/wiki/Gravitational_time_dilation#Outside_a_non-rotating_sphere)
$$t\_{0}=t\_{f}{\sqrt {1-{\frac {2GM}{rc^{2}}}}}=t\_{f}{\sqrt {1-{\frac {r\_{s}}{r}}}}$$

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.

> **Comments:**
> **username_0**: updated question.  

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