Calculating Time Dilation: QW Space Station

In summary, the space station is moving at a speed of 0.01 c relative to the earth. According to the clock on Earth, how much longer than one year would have passed when exactly one year passed in the rest frame of a space station? Using the Lorentz transformations, equation for time dilation, or unprimed coordinates, the time dilation formula gives \Delta t=\gamma\Delta t'. How does this work?
  • #1
kingyof2thejring
82
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QW the space station is moving at a speed of 0.01 c relative to the earth. According to the clock on Earth , how much longer than one year would have passed when exactly one year passed in the rest frame of a space station?
How do i solve this problem?
thanks in advance
 
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  • #2
HINT: Use the Lorentz transformation for time.
 
  • #3
kingyof2thejring said:
QW the space station is moving at a speed of 0.01 c relative to the earth. According to the clock on Earth , how much longer than one year would have passed when exactly one year passed in the rest frame of a space station?
How do i solve this problem?
thanks in advance

As Hootenanny said you may use the Lorentz transformations. Or, in this case, you may as well use directly [tex] \Delta t = \gamma \Delta t' [/tex] (which does follow from the Lorentz transformations).

Patrick
 
  • #4
yeh
if we define frames of reference,
S: earth
S': space-station
then S' moves at 0.01 c w.r.t. S

start S: [tex]x_1=0 t_1=0[/tex]
S' [tex]x'_2=0 t'_2=0[/tex]
end S: [tex]x_1=? t_1=?[/tex]
S' [tex]x'_2=? t'_2=365*24*60[/tex]

[tex]t'_2-t'_1=gamma[(t_2-t_1)-v(x_2-x_1)/c^2[/tex]
then what happens?
 
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  • #5
[tex] \Delta t = \gamma \Delta t'[/tex]
how does this work?
 
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  • #6
kingyof2thejring said:
[tex] \Delta t = \gamma \Delta t'[/tex]
how does this work?

This is the infamous "time dilation" formula, which gives you the time measured by "stationary" clocks ([itex] \Delta t[/itex]) in terms of the time measured by a moving clock ([itex] \Delta t'[/itex]). In your problem, the space station clock is the moving clock.

In your LT calculation, use the version that gives unprimed coordinates in terms of primed coordinates. Then you'll get the same time dilation formula.
 
  • #7
kingyof2thejring said:
[tex] \Delta t = \gamma \Delta t'[/tex]
how does this work?
This is called time dilation and as Pat said, follows direction from the Lorentz transformations. You apply this formula in exactly the same way you would a Lorentz transformation, set up your reference frames exactly as before. I.e. S frame is the Earth frame and S' is the space station's rest frame traveling at [itex]\beta = 0.01[/itex] wrt S. Therefore [itex]\Delta t[/itex] will be the time period as measure on Earth and [itex]\Delta t'[/itex] will be the time period as measure in the S' frame.

Edit: That's twice in two days Doc's beat me to it
 
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Related to Calculating Time Dilation: QW Space Station

1. What is time dilation?

Time dilation is a phenomenon in which time appears to pass at a different rate for an object or person depending on their relative speeds and the strength of the gravitational field they are in. It is a prediction of Einstein's theory of relativity.

2. How does the QW Space Station experience time dilation?

The QW Space Station, being in a high-speed orbit around Earth and at a relatively high altitude, experiences time dilation due to its velocity and the weaker gravitational pull compared to Earth's surface. This results in time passing slightly slower for the astronauts on the QW Space Station compared to people on Earth.

3. How is time dilation calculated for the QW Space Station?

The time dilation experienced by the QW Space Station can be calculated using the formula t' = t * √(1 - v^2/c^2), where t' is the dilated time, t is the time on Earth, v is the velocity of the QW Space Station, and c is the speed of light. This formula takes into account both the velocity and gravitational effects on time dilation.

4. Does the time dilation for the QW Space Station have any practical implications?

Yes, the time dilation experienced by the QW Space Station can have practical implications for timing and synchronization of events. For example, the clocks on the QW Space Station will run slightly slower than those on Earth, so adjustments must be made to ensure accurate timing for tasks such as communication and navigation.

5. Can time dilation be observed on the QW Space Station?

Yes, time dilation has been observed and measured on the QW Space Station through experiments and observations. For example, atomic clocks on the QW Space Station have been found to run slightly slower than identical clocks on Earth. This confirms the predictions of Einstein's theory of relativity and the existence of time dilation.

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