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If the orbit is elliptical, then by definition it is not circular.
If it is not circular, the distance of the satellite from the center of the Earth (R) must change during each orbit.
Since g is proportional to 1/R^2, the acceleration of gravity must also change between maximum and minimum values during each orbit.
Your question is why the speed changes. The speed changes in an elliptical orbit for the following reason: As the distance from the center of the earth changes, the potential energy in the Earth's gravitaional field changes. Like any falling object, the closer it is to the center of the Earth, the faster it moves. Potential energy is exchanged for kinetic energy.