Did Gravity Impact the Time Travel of Sergei Krikalyov?

[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?

 

[tiny-tim]

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

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:

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

 

[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 anyone out there find the solution to this?

 

[tiny-tim]

Hi sciroccokid!

Thank you Sir. However, you have not taken into account the fact that you are of a vastly superior intellect then I.

I'm only a little goldfish.

I just know where to look things up. ​

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.

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.

 

[sciroccokid]

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

 

[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.

 

[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.

 

[Elvin12]

and general relativity makes the rest of the world travel 0.004 seconds into the future.

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

 

[tiny-tim]

Welcome to PF!

Hi Elvin12! Welcome to PF!

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

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.

… 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.

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.

 

[clamtrox]

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

-Stephen Colbert