Atomic Clock Time Dilation Experiment

[HarleyM]

Homework Statement

Two atomic clocks are synchronized. One is placed on a satellite which orbits around the Earth at high speeds for a whole year. The other is placed in a lab and remains at rest with respect to the earth. You may assume both clocks can measure time accurately to many significant digits.

a)Will the two clocks stil be synchronized after one year?
b) imagine the speed of light is much lower than its actual value. How would the results of this experiment change if the speed of light was only twice the average speed of the satellite? Explain your reasoning using a calculation.

Homework Equations

Δt_m = Δt_s/√(1-v²/c²)

The Attempt at a Solution

a) I calculated the Δt_m using a theoretical velocity (3x10³m/s) and a theoretical Δt_s 3.1x10⁷ (about how many seconds per year)

When calculated using Δt_m = Δt_s/√(1-v²/c²) I find no time dilation.. 3.1x10⁷/0.9999999999= 3.1x10⁷

but the fact that the clocks can go to many significant digits worries me, I think they may not be synchronized after the experiment because of the obvious time dilation that will inevitably take place.. any input here would be awesome!

b) using the same theoretical #'s, and changing the speed of light of course, I determined much more time dilation would occur as expected, as objects approach the speed of light time dilation becomes very significant.

Δt_m=3.1x10⁷/√(1-1x10^-6)
=31,000,015.5 s

significant time dilation as speed becomes closer to speed of light, or in this case speed of light becomes closer to speed of satellite.

Does everything seem logical and ok?

Thanks !

 

[rollcast]

Time dilation does occur for satellites in orbit.

Look up GPS satellites and you should get more info about the effects of it on time keeping while in orbit.

http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Relativity

That should give you a bit of info.

 

[cupid.callin]

Two atomic clocks are synchronized. One is placed on a satellite which orbits around the Earth at high speeds for a whole year. The other is placed in a lab and remains at rest with respect to the earth. You may assume both clocks can measure time accurately to many significant digits.

When calculated using Δt_m = Δt_s/√(1-v²/c²) I find no time dilation.. 3.1x10⁷/0.9999999999= 3.1x10⁷

Average speed of a satellite is about 10³m/s in orbit
Going by this value, we find that γ ≈ 1
so i don't think there is much difference and that there is any atomic clock that will be able to calculate that ...

 

[HarleyM]

SO yes, there is time dilation, but it is not detectable even by the most sensitive of atomic clocks?

 

[cupid.callin]

SO yes, there is time dilation, but it is not detectable even by the most sensitive of atomic clocks?

Lets say it is not detectable by nearly all of the atomic clocks we have till now !

 

[HarleyM]

ok, thank you very much for your help ! :)

 

[alexg]

What you haven't taken into account is time dilation due to GR. While the clock in orbit will experience time dilation relative to the grounded clock due to the differential velocity, the clock on the ground will experience time dilation relative to the orbiting clock due to the gravitational field.

 

[cupid.callin]

What you haven't taken into account is time dilation due to GR. While the clock in orbit will experience time dilation relative to the grounded clock due to the differential velocity, the clock on the ground will experience time dilation relative to the orbiting clock due to the gravitational field.

Yes, 10³m/s is the velocity of satellite wrt earth

 

[alexg]

Looking at the real world GPS, they actually run faster than clocks on earth. Gravitational time dilation is greater than SR time dilation.

From wiki:

For example, the relativistic time slowing due to the speed of the satellite of about 1 part in 10^10, the gravitational time dilation that makes a satellite run about 5 parts in 10^10 faster than an Earth based clock

 

[Billowz]

You may assume both clocks can measure time accurately to many significant digits.

Did they not include this in the question so that you would be able to mention the fact that there is Time dilation that is noticeable between the clocks? Similar to the early experiments with atomic clocks and airplanes?

I know next to nothing about Physics, just trying to learn myself and that was how I read the question.

 

[HarleyM]

thats how I interpreted it as well, but I believe I got the question right. I guess its all about how you explain the answer.