An earth satellite in an elliptical orbit travels fastest when it is

The satellite travels when it has a maximum distance from earth.

As per the second law of Kepler, the planet or an object moves n the eclipse such that the line between it and the sun placed at the focus sweeps out the equal areas on the equal time. The satellite orbit changes depending on the path and velocity. Hence when it's closest to earth it will move fast due to the gravitational pull.

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ANY orbiting object travels fastest when it's closest to the central body.