Communications satellites are geostationary. It means they are located directly above the equator about 22,000 miles high. Because they rotate with the earth they remain apparently fixed over a particular place on the equator.
So to communicate with a particular satellite you need to aim your parabolic antenna at it. So you have to point your antenna exactly in the direction of the satellite.
This means we have a fixed point in the sky that we can aim at and confirm that our aim is correct from multiple different locations on the earth. So with a little trigonometry it should be possible to determine the shape of the earth using this data.