Special Relativity: Time Dilation

In summary, the conversation discussed the fractional change in the frequency of a GPS signal due to time dilation, as described by special relativity. The fractional change is calculated using the formula 1/2 (v/c)^2, where v is the velocity of the satellite and c is the speed of light. The final result is 8.36*10^-11.
  • #1
JennV
23
0

Homework Statement



An Earth satellite used in the Global Positioning System moves in a circular orbit with period 11
hours and 58 min. The satellitle contains an oscillator producing the principal nonmilitary GPS signal. Its frequency is 1575.42 MHz in the reference frame of the satellite. When it is received on the Earth's surface, what is the fractional change in this frequency due to time dilation, as described by special relativity?

Homework Equations



Fractional change = 1/2 (v/c)^2

The Attempt at a Solution



Answer: 1/2 ( 3880m/s / c )^2 = 8.36*10^-11


Not sure if I'm even on the right track at all... some guidance would be much appreciated.
 
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  • #2
Well, you can check your logic: the fractional frequency change is [tex]\frac{\Delta\nu}{\nu}[/tex] ... so do you know how that relates to the formula you used? To time dilation?
 

1. What is time dilation in special relativity?

Time dilation is a phenomenon in special relativity where time appears to pass slower for objects moving at high speeds. This means that time is not constant in all reference frames, and can be affected by velocity.

2. How does time dilation occur in special relativity?

Time dilation occurs because of the relationship between space and time in special relativity. As an object moves at high speeds, its velocity approaches the speed of light, causing distortions in the fabric of space-time. This results in time appearing to pass slower for the moving object relative to a stationary observer.

3. How is time dilation measured in special relativity?

Time dilation can be measured in special relativity through the use of clocks. By comparing the time measured by a clock on a moving object to a clock on a stationary object, the difference in time can be calculated and used to determine the degree of time dilation.

4. Does time dilation only occur at high speeds?

No, time dilation can occur at any speed, but it becomes more noticeable as an object approaches the speed of light. Even at low speeds, there is a very small amount of time dilation, but it is not significant enough to be observed.

5. What are the real-life implications of time dilation in special relativity?

Time dilation has been proven through experiments and has real-life implications in areas such as GPS technology and particle accelerators. It also plays a crucial role in our understanding of the universe and the laws of physics governing it.

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