Hello all,

The specific question I have is whether the acceleration of universal expansion on a small scale (such as the acceleration rate at which space is increasing between two objects) is similar to the rate at which space increases between objects when they are attracted to a large gravitational mass?

I think that the question I just posed could be interpreted a few different ways so let me frame what I mean:

There are 2 baseballs in space accelerating towards earth in a straight line trajectory one baseball is slightly closer to earth so it is accelerating more rapidly towards earth. To an outside observer ignoring earth and just looking at the 2 balls, the space in between the balls would be increasing, and because one ball is closer to the large mass the rate of acceleration is also increasing.

Similarly, I have read that objects in our universe are expanding away from one another and that the rate of acceleration away from one another is also increasing, but I have not read about an equation or relationship (if known or able to be determined) about whether the changes in rates of acceleration behave in a way similar to gravity.

For example, going back to the baseball example, but with universal expansion~ if the space in between 2 galaxies is increasing because of universal expansion, is the rate of increase in acceleration between the 2 galaxies by an outside observer able to be explained mathematically in a way consistent with an unknown gravitational force? One example would be, we could pretend that at the edge of the known universe that there is a gravitational force pulling on both galaxies (know this is probably not true), but if it was true, would the universal expansion (aka rate of distance change between the galaxies) be consistent with the traditional f=Gxm1xm2/d^2?

Also, a second question that is simpler. Are objects at the edge of the universe accelerating away more rapidly than those close (after accounting for gravity pulling those objects back?).