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The speed of an electron orbiting the atom is the same every where in space measured by many observers at many locations and moving at any speed in any direction.
Based on what information?
Electrons orbit the atom at a certain speed to stay in their orbit just like the earth orbiting the sun to stay in its orbit.
Photons follow certain rules as other atomic particles do
The theory of relativity cannot be applied in some cases and for certain things such as these.