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Suppose you could live on Jupiter without dying from anything except age, how much longer would you be able to live there compared to how long you could live on Earth?

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    $\begingroup$ Time dilation effects the extent of disagreement between observers on how much time occurs between two events, not how far apart they will be in terms of proper time. What definition of lifetime do you intend? $\endgroup$
    – J.G.
    Sep 20, 2018 at 21:49
  • $\begingroup$ I don't think Jupiter is massive enough to cause much time dilation. I bet it is a few seconds per year at most. $\endgroup$
    – zeta-band
    Sep 20, 2018 at 22:08
  • $\begingroup$ Jupiter's surface gravity is less than 3 times Earth's, so probably not a lot. Of course, Jupiter doesn't really have a "surface", so you could try living deeper inside Jupiter or something. $\endgroup$
    – user854
    Sep 20, 2018 at 23:00
  • $\begingroup$ Guy, this may be the wrong question. In any reference frame, you live as long as you live ... meaning that you can't tell the difference. A time dilation is only noticed by observers in a different reference frame than your own. $\endgroup$ Sep 21, 2018 at 2:15
  • $\begingroup$ @barrycarter: The effect depends on the gravitational potential, not the gravitational field. $\endgroup$
    – user4552
    Sep 21, 2018 at 2:23

1 Answer 1

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From the Schwarzschild metric outside a spherically symmetric mass $M$, we have that the gravitational time dilation at distance $r$ from the center is:

$$ \frac{d\tau}{dt}=\sqrt{1-2\frac{GM}{c^2}\frac{1}{r}} $$

Plug in (using SI units) $G=6.67408\times10^{-11},$ $c=299792458,$ $r_E=6371000,$ $r_J=69911000,$ $M_E=5.972\times10^{24}$, $M_J=1.898\times10^{27}$ and you get that time runs slower by $6.96085\times10^{-10}s$ per second at Earth's surface and $2.01605\times10^{-8}s$ per second at Jupiter's surface (compared to clocks out in space).

Over a lifetime, multiply those fractions by $2.5\times10^{9}s$ (about $80$ years) and you get that time has run slower by $1.75s$ on Earth and $51s$ on Jupiter.

So an observer out in space would see a clock on Jupiter reach 80 years about $49s$ later than a clock on Earth, a slight slow-motion effect.

Now, people at the surfaces would also experience slow-motion in their body chemistry and brain neurons, so they would not experience an extra $1.75s$ and $50s$. The $80$ years shown by the clocks would feel like $80$ years at both locations. This is a kind of "conspiracy of nature," if you wish.

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