<p>A simple way to calculate the gravitational time dilation on the surface of a planet comes by assuming that</p>
<ul>
<li>the planet is spherically symmetric</li>
<li>other sources of gravitational potential (a star, a moon) are negligible on the surface of the planet</li>
</ul>
<p>In that case, the time experienced by the person on planet 1 is related to the time experienced by the person on planet 2 by</p>
<p><span class="math-container">$${\Delta \tau_1 \over \Delta \tau_2} = \frac{\sqrt{1-\frac{2GM_1}{c^2R_1}}}{\sqrt{1-\frac{2GM_2}{c^2R_2}}}$$</span></p>
<p>On a planet, the factor <span class="math-container">${2GM \over c^2R}$</span> is usually very small, so the formula can be approximated to</p>
<p><span class="math-container">$${\Delta \tau_1 \over \Delta \tau_2} = (1-\frac{GM_1}{c^2R_1})(1+\frac{GM_2}{c^2R_2})$$</span></p>
<p>This is valid if the two planets are still with respect to each other. If they are moving at a substantial speed also SR time dilation should be considered. In any case, the effect is really small.</p>

CC BY-SA 4.0
2021-08-08T19:38:27.920Z
Just to extend this a little, if the density of the planets is the same, then surface acceleration is proportional to R, (and mass is proportional to R^3).  Thus if the second planet has double the gravity, it would have double the radius, and eight times the mass.  Plugging in the values for Earth mass and radius gives a ratio of 1.00000000209 times slower on the planet with more gravity.
James K
CC BY-SA 4.0
2021-08-08T07:24:23.950Z
2021-08-08T07:24:23.950Z
Prallax
<p><strong>How slow would you age on a double gravity planet?</strong></p>
<p>Gravity of the planet A is 10 units. If you are taken from planet A to planet B where gravity is double that of A, i.e. 20 units. How slowly would you age as compared to being on planet A, and how?</p>

CC BY-SA 4.0
2021-08-08T00:03:03.193Z
BTW, gravitational time dilation on a planet is quite small. Eg, the difference in the time rate between the Earth's surface and its centre is $\approx 3.48×10^{-10}$, so over a century a clock at the centre of the Earth would be slow by ~1.1 seconds compared to a clock on the surface.
PM 2Ring
<planet><gravity><general-relativity><age>
How slow would you age on a double gravity planet?
Sazzad Hissain Khan
# How slow would you age on a double gravity planet?

(Asked by: username_0 on 2021-08-07)

**How slow would you age on a double gravity planet?**

Gravity of the planet A is 10 units. If you are taken from planet A to planet B where gravity is double that of A, i.e. 20 units. How slowly would you age as compared to being on planet A, and how?

**Tags:** planet, gravity, general-relativity, age
> **Comments:**
> **username_1**: BTW, gravitational time dilation on a planet is quite small. Eg, the difference in the time rate between the Earth's surface and its centre is $\approx 3.48×10^{-10}$, so over a century a clock at the centre of the Earth would be slow by ~1.1 seconds compared to a clock on the surface.  

---

## 1 answers

### Answer by username_2 on 2021-08-08. Score: 5 | Accepted answer

A simple way to calculate the gravitational time dilation on the surface of a planet comes by assuming that

* the planet is spherically symmetric
* other sources of gravitational potential (a star, a moon) are negligible on the surface of the planet

In that case, the time experienced by the person on planet 1 is related to the time experienced by the person on planet 2 by

$${\Delta \tau\_1 \over \Delta \tau\_2} = \frac{\sqrt{1-\frac{2GM\_1}{c^2R\_1}}}{\sqrt{1-\frac{2GM\_2}{c^2R\_2}}}$$

On a planet, the factor ${2GM \over c^2R}$ is usually very small, so the formula can be approximated to

$${\Delta \tau\_1 \over \Delta \tau\_2} = (1-\frac{GM\_1}{c^2R\_1})(1+\frac{GM\_2}{c^2R\_2})$$

This is valid if the two planets are still with respect to each other. If they are moving at a substantial speed also SR time dilation should be considered. In any case, the effect is really small.

> **Comments:**
> **username_3**: Just to extend this a little, if the density of the planets is the same, then surface acceleration is proportional to R, (and mass is proportional to R^3).  Thus if the second planet has double the gravity, it would have double the radius, and eight times the mass.  Plugging in the values for Earth mass and radius gives a ratio of 1.00000000209 times slower on the planet with more gravity.  

---

