GPS satellites don't do any calculating for you, and there is no "direct connection" between the satellite and your phone. The GPS receiver in your phone is purely passive. It uses latency (usually a few dozen milliseconds) to calculate its distance from each satellite.

As long as you have access to at least 4 satellites, triangulation (quadri-angulation?) allows you to determine your precise location in all 4 dimensions, three of space and one of time.