Anonymous
Anonymous asked in Science & MathematicsPhysics · 2 months ago

# need help fast!?

GPS satellites orbit the earth at a speed of approximately 3900 m/s, compared to our speed on the earth's surface of 460 m/s at the equator. This means that the clocks on the satellites must be adjusted by ___ x10 ___ seconds each day to match the clocks on the earth's surface.

Relevance
• The GPS clocks are adjusted for speed and for the difference in gravity. They are not adjusted each day.  Instead, the frequency of the clocks was set before the satellite was launched.

The adjustment for speed is a factor of 6.469 x 10^-11.  Since the question asks for the "each day" adjustment, just multiply by the number of seconds per day.

Answer = 5.589 x 10^-6 seconds  per day.  <== BUT you better check to make sure this is correct!

It's worthwhile, if you're interested, to study the way the GPS clocks are REALLY set and adjusted.  Maybe someday if you go to college and study physics and systems engineering.

• time dilation

t' = t/γ

γ = 1/√(1–(V²/c²))

γ = 1 + (V²/2c²) for small v

γ = 1 + (V²/2c²) = γ = 1 + ((3900-460)²/2(3e8)²) = 1+6.6e-11

1 day = 24x3600 = 86400 s

divide above by that to get new value in seconds. correction is

86400 – 86400 / (1+6.6e-11)

which is approx

86400 – 86400 (1–6.6e-11)

or

6.6e-11 sec