Flying Clocks on Jets and in space

Scientists have flown clocks in jet aircraft and on orbiting spacecraft and measured the slowing of their onboard clocks by comparing them to clocks on the ground.

Around the world in 40 hours.

Compare watches with a friend as you leave San Francisco on a round-the-world tour by jet. When you return you compare watches again, They will agree to within the accuracy of the watches. So it seems that Newtons idea that clocks run at the same at all speeds and in all locations is correct.

However this very experiment was done in 1971 using very accurate atomic clocks (cesium beam) flying around the world strapped to the wall in coach class in a 707 airliner.

The experimenters were J.C.. Hafele of Washington University, and Richard Keating of the U.S. Naval Observatory.

Images: experimenters, 707, atomic clock

Use this one it is simpler

In another experiment, on November 22, 1975 a U.S. Navy P3C Orion aircraft flew back and forth for 15 hours at altitudes between 25,000 and 35,000 feet (7,600 meters to 10,600 meters) over Chesapeake Bay. The experimenter was Carroll Alley the plane flew at 270 knots or 140 m/s and clocks were compared on the plane and on the ground by laser signal.

The clocks lost 5.6 nanoseconds during this 15 hour flight, as predicted by Special Relativity. The plane flew at 4.7 x 10^-7 c.

If we imagine a version of this experiment in which the plane flew around in a circle over us for the same 40 hours it took to fly around the world then the following calculation can be done.

In 40 hours of flying at 550 miles per hour the flying clock ran slower and measured less time than the clock on the ground.

calculation gamma = 1/(1-v^2/c^2)^0.5 with v = 550 and c = 700,000,000

gamma = 1+ 3 * 10^-13

40 hr. = 1.5 * 10^5 s so it takes longer by 4.5 * 10 ^-8 s or 45 nanoseconds.

Atomic clocks can easily measure this time difference.

Calculator to do this? ala RonH your weight on other worlds.

Frequent Flyer Seconds enter the number of frequent flyer miles you have flown in your life ( between 0 and 100,000,000) print out the number of seconds your watch has lost as viewed by a stationary observer on the ground.

convert m miles into hours h into seconds t then multiply by 3 * 10^-13

55,000 miles will save you 0.1 microsecond

There is another effect from general relativity that also affects this experiment, clocks run slow when the acceleration is higher, so near the surface of the earth where the acceleration of gravity is higher than in an airplane clocks run slower, this effect was also observed during the round the world flight, but we're not dealing with general relativity on this web page.

GPS clocks in space

GPS

There are 24 satellites orbiting the earth as part of the Global Positioning Satellite navigation system.

These satellites have atomic clocks on board,

Receivers on earth use signals from these satellites to determine the location of the receiver on the earth. The satellites circle the earth twice per day at an altitude of 20,000 km and at a speed of 14,000 km/hr or 3.9 km/s or 3.9 * 10^3 m/s

Because the atomic clocks are moving relative to the surface of the earth, and because the satellites are in orbit high above the earth the clocks must be adjusted for the effects of special relativity as well as general relativity.

A moving clock appears to run slow in special relativity. The GPS satellites are orbiting at a speed that is fast enough to make the clock lose 7,000 nanoseconds a day. This would lead to an error in the location of the receiver on the ground of 7000 feet or about 1.5 miles per day.

A moving clock appears to run fast when it is in a lower gravity environment. The clocks run fast so that they gain about 45,000 nanoseconds a day due to general relativity. The combination of the gain from general relativity and the loss for special relativity would create an error of about 38,000 ns or 7 miles per day if corrections were not made.

The first GPS satellite was launched without the relativity correction program operating. The data showed that Einstein's theories predicted the changing clock rates of the GPS satellites within the errors of the measurements. The engineers then turned on the correction program.

 Scientific Explorations with Paul Doherty © 2005 8 May 2005