How A Satellite Can Prove Einstein's Theory Of Relativity

When rockets misfire their payloads, scientists use the misplaced satellites to prove the Theory of Relativity. How do they do it?

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Wayward satellites repurposed to test general relativity (Nature)
"Two satellites that were accidentally launched into the wrong orbit will be repurposed to make the most stringent test to date of a prediction made by Albert Einstein's general theory of relativity - that clocks run more slowly the closer they are to heavy objects."

What is relativity? (How Stuff Works)
"Einstein proposed the theory of special relativity, which boils down to this: The laws of physics are the same in all inertial frames, and the speed of light is the same for all observers."