My John Deere LT160 battery will not keep a charge I have replaced the battery and with in 3 weeks it is dead again. I believe the problem to be a rotating short in the alternator just trying to come with a way to check it

I am not into automotive much, but a couple of things you might try. If you have a DC ammeter, you can disconnect the battery plus terminal and connect the meter in series between the battery lead and the battery(do with ignition off). If you read amperage then you have a short or a device that is staying on after the ignition switch is off and will need to be traced down. This will drain your battery over a period depending on the current draw.(that will check for leakage with the key off.
Another thing you can try is starting your tractor with everything back in its normal state and check the voltage at the battery. It should be a 12 volt system, but the alternator typically puts out about 13-14 volts DC. If the battery voltage doesn't go up after starting the tractor, the alternator probably has issues that need fixed. Try those two tests and see if it shows anything. I don't know the vintage of the tractor, but old tractors were 6 volt instead of 12 and used generators instead of alternators so if it is a 6 volt system the voltage should still go up after starting if the charging system is working, but by a couple of volts above the battery voltage rating. Try and get back to me.

This is the electrical & lighting forum related to building wiring. You may want to try here: https://www.askmehelpdesk.com/cars-trucks/