Stuart,
I am not an expert in this field, but know a little based on my radio knowledge.
The things that influence the distance detection are:
Type of Radar (CW, Pulsed, Pulsed Doppler, Frequency used, etc)
Altitude of the Aircraft
Altitude of the Radar Antenna
Radar has almost unlimited actual range. We regularly use Radar to map the orbit of Satellites. Radar was used in the 1960's by NASA to check the progress of the Moon Missions.
But, most radar is "line of sight". If it is below the horizon, you can't see it.
One of the types of RADAR,"HF", are capable of "Over the horizon" detection because they can reflect off the atmosphere. So even without a direct line of sight, you can still get an echo. It will not be as good as the short range stuff. But it will tell you that way out there are a bunch of planes coming and to be prepared.
One way to increase the range and reduce the effect of ground clutter is to use airborne radar systems. The horizon is extended much further for even short wavelength signal.
where d is in kilometres and h is height above ground level in metres.
or
With d in miles and h in feet
So, an Aircraft at 35,000 feet (10600M), the horizon is 211 miles (335 km). Planes generally fly above ground level, so the detection distance might be about to 250 miles.
The inverse works as well. A ground level radar would be able to spot an aircraft out ~200 miles (300 km). Beyond this, HF over the horizon radars would need to be used and they are nowhere near as accurate because the signal bounces between the ground and the atmosphere.
Now look at a satellite orbiting at 300 miles (475 km). You could detect an object 1535 miles (2435 km) away from the ground.
So, it all depends on how high the object you're trying to track, how high is your radar installation, and what type of radar used. Oh, and whether you're paying attention.