# The Greatest Time Traveler

1. Nov 10, 2009

### sciroccokid

The greatest time traveler we have so far, Sergei Krikalyov, spent 803 days in space, orbiting the earth at 17,000 miles per hour. As a result of this he has traveled 1/48 of a second into the future.

I am curious how much gravity affected the calculation of Sergei Krikalyov's fraction of a second time travel to the future?

2. Nov 10, 2009

### tiny-tim

Hi sciroccokid!

From the PF Library on time dilation (substitute "Krikalyov" for "clock" ) …

Gravitational time dilation in static metric:

$$\sqrt{\frac{g_{00}(clock)}{g_{00}(observer)}}\ \simeq\ \sqrt{\frac{1\ -\ 2U(clock)}{1\ -\ 2U(observer)}}\ \simeq\ 1\ -\ U(clock)\ +\ U(observer)\ =\ 1\ -\ \Delta\,U$$

Schwarzschild (static metric) gravitational potential at distance r from mass M:

$$U\ =\ \frac{2GM}{rc^2}\ =\ \frac{2gr}{c^2}$$

3. Nov 10, 2009

### sciroccokid

Thank you Sir. However, you have not taken into account the fact that you are of a vastly superior intellect then I. Is there any way to answer that equation, with some thing like "1/30 of earth's gravity."

Sergei was traveling at 17,000 mph & traveled 1/48 of a second into the future after 803 days. I suppose we could find the "altitude" somewhere.

Can any one out there find the solution to this?

4. Nov 10, 2009

### tiny-tim

Hi sciroccokid!
I'm only a little goldfish.

I just know where to look things up.
I was expecting you would tell us what the altitude was …

once you have that, just mulitply it by g/c2, where g = 9.81 m/s2.

5. Nov 10, 2009

### sciroccokid

The altitude is about 173 Mi (278km)...

6. Nov 11, 2009

### clamtrox

Lets check: for the time delay due to special relativity, we have

$$\Delta t = (\gamma -1) T$$

where T = 803 days and $$\gamma \simeq 1 - v^2/2c^2$$. This gives the result $$\Delta t = 0.02 \sec$$ which is what you quoted. This means that time passes more slowly for the astronaut, meaning that he 'travels into the future'.

Now, for gravitational time dilation you have

$$\Delta t \simeq -\Delta U T \simeq -0.004 \sec,$$

so special relativity makes him travel 0.02 seconds into the future and general relativity makes the rest of the world travel 0.004 seconds into the future.

7. Nov 11, 2009

### clamtrox

Notice btw, how the time dilation due to SR is proportional to v^2, and the time dilation due to GR is proportional to r (on small speeds and distances), meaning that the magnitude of the effects would be reversed for example in an aeroplane.

8. Nov 11, 2009

### Elvin12

Can you please clarify more on that please? How can he make the whole world travel to future?

9. Nov 11, 2009

### tiny-tim

Welcome to PF!

Hi Elvin12! Welcome to PF!
He means the surface of the Earth, not the whole universe. The stronger gravity dilates time more, and so a clock on Earth will go very slightly more slowly than a clock on the spaceship.

This is the opposite effect to the special relativity effect … so speed makes the Earth clock go faster than the spaceship clock.
Hi clamtrox!

I think "travel into the future" is a bit misleading when he's actually getting comparatively yonger (and will remain so when he comes back to Earth)…

though it enables him to travel into the future without dying!

I think it's clearer to say that speed makes him age slightly less, but the weaker gravity makes him age very slightly more.

10. Nov 11, 2009

### clamtrox

Did you know that in the future we're all going to die?!!?

-Stephen Colbert

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