Special Relativity: Time Dilation

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SUMMARY

The discussion centers on calculating the fractional change in frequency of a GPS signal due to time dilation as described by special relativity. The satellite's oscillator frequency is 1575.42 MHz, and its velocity is approximately 3880 m/s. The correct formula for fractional change is established as 1/2 (v/c)^2, leading to a calculated value of 8.36 x 10^-11. Participants emphasize the relationship between frequency change and time dilation, providing clarity on the application of the formula.

PREREQUISITES
  • Understanding of special relativity principles
  • Familiarity with the Global Positioning System (GPS) technology
  • Basic knowledge of frequency and oscillators
  • Ability to apply the formula for fractional change in physics
NEXT STEPS
  • Study the implications of time dilation in satellite technology
  • Learn about the derivation of the Lorentz factor in special relativity
  • Explore the effects of velocity on signal frequency in GPS systems
  • Investigate the relationship between relativistic effects and satellite positioning accuracy
USEFUL FOR

Physics students, aerospace engineers, and professionals involved in satellite technology and GPS systems will benefit from this discussion.

JennV
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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.
 
Physics news on Phys.org
Well, you can check your logic: the fractional frequency change is \frac{\Delta\nu}{\nu} ... so do you know how that relates to the formula you used? To time dilation?
 

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