Relativistic Effects on Satellite Clock as Seen from Earth

The general theory of relativity implies time contraction due to the Earth's gravitational field. A clock on a satellite appears to run faster when observed from the surface of the Earth.
The special theory of relativity predicts time dilation. A clock on a fast-flying satellite appears to run slower when observed from a stationary position on Earth.
It is possible to observe the combined effect of general and special relativity on an atomic clock on board a GPS satellite.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


General and special relativity effects are stronger near the Earth's surface than they are on an orbiting satellite. Also the speed of the satellite must be greatest at its minimum height, so that centrifugal force can cancel the stronger gravitational attraction. As the height increases, both effects decrease nonlinearly according to the Lorenz factor from special relativity and following the Schwarzschild solution of the Einstein field equations from general relativity. But the two effects are opposite, so there is a height (about 3200 km above the Earth) where they cancel; the clock is seen to be working correctly at this point when observed from the Earth's surface. A GPS (Global Positioning System) satellite system is an example and practical proof of both of Einstein's theories. GPS receivers are made to receive 10.23 MHz code. But GPS satellites must broadcast this code on the frequency 10.22999999543 MHz to cancel relativistic effects. The effect (a time difference about 38 μs/day) is apparently insignificant, but it must be taken into account or there would be a 11.5 km/day position measurement error. The errors are marked at the approximate heights of International Space Station (ISS), GPS satellites (GPS), and geostationary satellites (GEO) in the plot.
[1] Wikipedia. "Time Dilation." (Apr 26, 2013) en.wikipedia.org/wiki/Time_dilation.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+