- #1
chef99
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Homework Statement
Two atomic clocks are synchronized. One is placed on a satellite, which orbits around the Earth at a high speed for a whole year. The other is placed in a lab and remains at rest, with respect to the earth. You may assume that both clocks can measure time accurately to many significant digits.
a) Will the two clocks still be synchronized after one year? Explain your reasoning.
b) Imagine that the speed of light was much slower 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
Δtm = Δts / √ 1- v2 / c2[/SUP] )The Attempt at a Solution
a) No, after a year, the two atomic clocks will not be synchronized. The clock on the satellite will be slightly behind the one in the lab, as the amount of time measured in the satellite's frame of reference will be slightly less than that measured from the earth’s frame of reference (the clock in the lab), because the orbiting clock is stationary with respect to the satellite’s frame of reference, whereas it is moving in relation to the earth’s frame of reference. The time dilation would be slight, however, as the satellite will likely not be moving at nearly the speed of light (the question does not specify the satellite’s speed). The faster the satellite moves, the greater the time difference.
b) If the speed of light was much slower, the results of this experiment would be dramatically different, as time dilation increases the closer an object is traveling to the speed of light. If the satellite traveled at half the speed of light, as asked in the question above, the result would be as follows:
Δtm = Δts / √ 1- v2 / c2 )
Δtm = 3.154 x107s / √ 1- 0.5c2 / c2
Δtm = 3.154 x107s / √ 1- 0.5
Δtm = 44604295.76
Δtm = 4.5 x107sThe same advent will take 4.5 x107s. This is a noticeable difference.I think I have the ideas right, I'm just not sure if I'm explaining it properly. If someone could help clarify this that would be most appreciated.[/SUB][/SUB][/SUB]