1570 movement?

[Sunshine]

So, I have somewhat of an understand of the different vintage Rolex movements but I am far from being an experienced. LOL.. Going through some of my grandfathers old watches I found an older 34mm non date holding a 1570 movement. We have also have had for years an original 5513 case and case back. My question is are all 1570 movements the same in size? For instance will the movement fit in my 5513 case? I feel like this was my grandfathers plans and just never got around to it. I hate to think I have a nice 5513 case sitting around not being used and plus it would be something extra to have from my grandfather. Thanks for any advice.