In today's Guardian there an article titled "Satellite launch accident provides unexpected test of Einstein’s theory" - http://www.theguardian.com/science/across-the-universe/2015/nov/25/satellite-launch-accident-test-einsteins-relativity. This refers to the Galileo 5 and 6 navigation satellites, which are inadvertently orbiting the Earth twice a day and changing their altitude by 8500km on each orbit. What's so special about this set up that makes it particularly well suited to testing GR?
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The Guardian article is over dramatising a bit. GPS satellites normally orbit at an approximately fixed altitude and orbital speed so their gravitational time dilation is constant. Because Galileo 5 and 6 are in elliptical orbits their time dilation is constantly varying. The variation is partly due to changes in altitude and partly due to changes in the orbital speed. Because of this variation checking that GR correctly predicts the time dilation all through the orbit is a more thorough test.
However this is not testing anything new. Gravitational time dilation was first demonstrated in the Pound-Rebka experiment in 1959 and although obviously experiments have become increasingly precise since then they're really just checking the same thing. Precision tests are important since even the slightest deviation from the predictions of GR could indicate new physics. However few of us will be lying awake at nights waiting for the results.
If you're interested to know more there is an article describing the experiment on the European Space Agency website.
answered Nov 26, 2015 at 7:48