PA 28-200 pilot reported the throttle was unresponsive when entering the traffic pattern for landing. The pilot diverted to a longer runway; determined that they needed to shut down the engine on short final to reduce airspeed to land. The pilot landed safely and it was determined the throttle cable was broken.

Narrative

After making initial power reduction to enter the traffic pattern for ZZZ; I discovered that the throttle was not responsive. Movement of the throttle lever was not resulting in any changes in engine power; with the engine power stuck at approximately 22 inches of manifold pressure which is slightly below normal cruise power setting. I surmised that the throttle cable might have broken; preventing changes in engine power. Since I was unable to reduce or increase engine power; I realized that in order to land I would have to cut off power to the engine using the mixture lever; and would not have ability to go-around if needed. Since the engine was operating at close to cruise power I decided to divert to ZZZ1 to take advantage of the much longer runway which would enable me to carry engine power to short final before cutting the engine and using the greater length of the runway to bleed off airspeed and land safely. Upon contacting tower I explained our situation. On short final I retarded the mixture lever to cut off engine power; bled off airspeed over the runway and landed safely and uneventfully with no damage. Inspection after landing revealed that the throttle cable was in fact broken; which prevented the ability to control engine power. The aircraft is undergoing repair/replacement of the throttle cable before further flight by a qualified maintenance facility.