Question

Two atomic clocks are synchronized while on Earth before one is launched (within a GPS satellite) into a medium-altitude Earth orbit. The satellite orbits the Earth at an altitude of 22,000 km, with an orbital velocity of 15,000 km/hr. After 1000 orbits, estimate the time difference between the two atomic clocks? (Assume that only special relativity effects are present.)

ANS: (~4 x 10-3s)

Answer 1

Answer on Question #42932, Physics, Relativity

Two atomic clocks are synchronized while on Earth before one is launched (within a GPS satellite) into a medium-altitude Earth orbit. The satellite orbits the Earth at an altitude of 22,000 km, with an orbital velocity of 15,000 km/hr. After 1000 orbits, estimate the time difference between the two atomic clocks? (Assume that only special relativity effects are present.) ANS: $(4\cdot 10^{-3}$

Solution

$15000km/hr\approx 4.17km/s$ Let us find how much slower the clock is going on the satellite

$\frac{\delta t^{\prime}}{\delta t}=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=\frac{1}{\sqrt{1-(4.17\cdot 10^{3}/3\cdot 10^{8})}}\approx 1+10^{-8}$

Now let us find how much time would it pass for satelite clock. We assume length of orbit is $l=2\pi(R_{earth}+H_{altitude})$. Hence

$t=S/v=\frac{2\cdot(22000+6300)\cdot\pi\cdot 1000}{4.17\cdot 10^{3}}\approx 42641.28s$

Therefore, difference in time is

$42641.28\cdot 10^{-8}\approx 4\cdot 10^{-3}$

http://www.AssignmentExpert.com/