<p>Time dilation is related to differences in gravitational potential in General Relativity.</p>
<p>Observing a clock situated deep in a potential well, a distant observer would see it running slow. Vice-versa, an observer looking outwards from within a deep potential well would see distant clocks running faster.</p>
<p>The situation is complicated by orbital motion. This results in a time dilation that would be predicted by Special Relativity. Any relative motion will make a moving clock appear to run slower to an observer in a stationary frame.</p>
<p>To keep things simple, a stationary observer at a radial coordinate <span class="math-container">$r$</span> around a non-spinning black hole, would observe events far away from the black hole speed up by a factor <span class="math-container">$(1 - r_s/r)^{-1/2}$</span>, where <span class="math-container">$r_s$</span> is the Schwarzschild radius (and is the smallest radius at which a stationary observer could possibly exist).</p>
<p>However, you would only make incorrect estimates of durations and ages (by using times on your own clock) if you didn't understand General Relativity.</p>

CC BY-SA 4.0
2023-11-11T08:27:42.930Z
2023-11-11T08:27:42.930Z
ProfRob
<p>If you were on one of those planets orbiting a super massive black hole (ala Interstellar), where time is moving more slowly, would you time astronomical events differently or even the age of the universe?</p>

CC BY-SA 4.0
2023-11-11T08:39:13.483Z
Related, possible duplicate: https://astronomy.stackexchange.com/q/32440/16685
PM 2Ring
CC BY-SA 4.0
2023-11-11T08:41:51.703Z
Note that the time dilation in *Interstellar* is so high because the planet is orbiting deep within the gravitational well of a SMBH with extreme spin. The odds of such a planet existing (and being habitable) are very small.
PM 2Ring
CC BY-SA 4.0
2023-11-12T01:40:31.830Z
With sufficiently accurate clocks, a deep gravity well is not required to detect the effect: https://cdn.danielbmarkham.com/reference/original-articles/nerd-roundup/2021-10-29/resolving-the-gravitational-redshift.pdf
John Doty
<gravity><time-dilation>
If you are in a deep gravity well, where time goes by more slowly, do you see the unfolding of a cosmic event at a different rate?
Jack R. Woods
# If you are in a deep gravity well, where time goes by more slowly, do you see the unfolding of a cosmic event at a different rate?

(Asked by: username_0 on 2023-11-11)

If you were on one of those planets orbiting a super massive black hole (ala Interstellar), where time is moving more slowly, would you time astronomical events differently or even the age of the universe?

**Tags:** gravity, time-dilation
> **Comments:**
> **username_1**: Related, possible duplicate: https://astronomy.stackexchange.com/q/32440/16685  
> **username_1**: Note that the time dilation in *Interstellar* is so high because the planet is orbiting deep within the gravitational well of a SMBH with extreme spin. The odds of such a planet existing (and being habitable) are very small.  
> **username_2**: With sufficiently accurate clocks, a deep gravity well is not required to detect the effect: https://cdn.danielbmarkham.com/reference/original-articles/nerd-roundup/2021-10-29/resolving-the-gravitational-redshift.pdf  

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## 1 answers

### Answer by username_3 on 2023-11-11. Score: 6 | Accepted answer

Time dilation is related to differences in gravitational potential in General Relativity.

Observing a clock situated deep in a potential well, a distant observer would see it running slow. Vice-versa, an observer looking outwards from within a deep potential well would see distant clocks running faster.

The situation is complicated by orbital motion. This results in a time dilation that would be predicted by Special Relativity. Any relative motion will make a moving clock appear to run slower to an observer in a stationary frame.

To keep things simple, a stationary observer at a radial coordinate $r$ around a non-spinning black hole, would observe events far away from the black hole speed up by a factor $(1 - r\_s/r)^{-1/2}$, where $r\_s$ is the Schwarzschild radius (and is the smallest radius at which a stationary observer could possibly exist).

However, you would only make incorrect estimates of durations and ages (by using times on your own clock) if you didn't understand General Relativity.


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