If you have not yet changed your G string - rather unfortunate phrase - then have a look at exactly where it has sprung.
I am assuming that you mean broken.
If it is at the bridge then your bridge may have a rough edge which is chaffing the string. The same goes for the nut if the break is up the other end.
If you mean that the peg is slipping and you lose the tension on the string then crush up a piece of resin(rosin?) and sprinkle it on the peg before you replace the string.This is an old trick which works very well.
Really not a good idea to use rosin. Rosin actually degrades wood fibers among other things. Very caustic stuff. Better to use peg dope or some other similar item. Also, your pegs may need to be refit as it’s possible they or the holes are a bit worn. If your pegs are boxwood. Whatever you do, don’t try to shove the pegs in harder to prevent slippage. This can lead to cracked pegs, or worse, a crack in the pegbox. May not be a bad idea to have a good luthier give it a going over if it does turn out that the pegs or anything else on the instrument is the culprit.
Make sure you keep an eye on the humidity as well. Here in the NE US, as soon as the weather shifts to more cold and more dry, pegs start slipping. Some kind of humidifier in the case or in the instrument is very helpful for the fiddle’s general well being.
I think there might have been a discussion of the planetary pegs on the Fiddle-l mailing list, but I can’t remember for sure. They have a good archive.
Yeah, that’s the thing. My viola tunes fine, and stays put. I could tune it when I was 13, and I can tune it now. The fiddle, however, needs to go back to a fiddle tweaker for a recheck.