ok, i was REALLY bored. i decided to try to derive the newtonian analogue of GR with absolute space and time-no space-time.
i started like this:
you have a piece of matter. this piece is the center of an imaginary sphere(not in the i sense, but in the sense of not existing). the gravity would cause a volume reduction. this could be seen by having the edge of the sphere be composed of matter.
[math]V=\frac{4}{3}{\pi}r^3[/math]
[math]\frac{dV}{dt}=4{\pi}r^2{\frac{dr}{dt}}[/math]
[math]a{\frac{dV}{dt}}=4{\pi}GM\frac{dr}{dt}[/math]
now, i know acceleration has something to do with curvature, but i'm not sure how to express it. the acceleration causing curvature can be seen by means of the first law of motion.
how do i get rid of the [math]\frac{dV}{dt}[/math] and the [math]\frac{dr}{dt}[/math]? how do i use the a to make a term for curvature? i am pretty sure i need an r term in there as well. would [math]\frac{dr}{dt}[/math] be the same as v=at?