The range at which Radars can detect planes is a lot shorter than most people seem to believe. Ground based Radars have an effective range of something in the region of 200miles due to the earth's curvature. To get around that you either have to have air based Radars (such as the E2-Hawkeye used by US carrier groups), or more exotic/experimental types of radars which bounce off the ionosphere.
The limitations of radar are part of the reason why Aircraft have transponders - you can pick up an actively broadcasting radio from far greater range, and you're not relying on getting a clean bounce back from the aircraft. They're also the reason why carriers carry multiple E2s - a radar on the top of a mast on a ship simply can't see far enough.