I had a thought before and I'm not sure if this is meaningful to ask or even possible to ask but I'd figure it's worth a shot. Is it meaningful to take the position derivative of acceleration due to gravity? I'd imagine, at least intuitively, this sounds like it's possible. As you move along space, the acceleration you'd experience would be greater as you approach the mass which is creating the gravitational field. Or is that just nothing more than taking the gradient of the gravitational field?