# Is vacuum acceleration directly proportional to distance?

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1. Aug 17, 2015

### 69911e

Do we know if the instantaneous/observed acceleration due to the vacuum is directly proportional to distance or possibly? (ignore any gravitational effects)
A~D ?
A~D^2 ?
A~D^(1/2) ?
A~D^(-2)
A~D^(Other) ?
OR
A= constant (edited as I forgot this one)

If not, is there a best guess/fit or simply not precise enough data?

Feel free to correct my question if it is simply a bad question. I didn't see this directly address in any thread; if I missed one, a link would be great.

Last edited: Aug 17, 2015
2. Aug 17, 2015

### Staff: Mentor

What do you mean by this?

3. Aug 17, 2015

### 69911e

The observed acceleration of distant objects from the supernova data or other observation.

4. Aug 17, 2015

### marcus

You could look at the Hypersine thread.

To an excellent approximation, distances are growing and are expected to continue growing as the function
sinh2/3(1.5 t) where the present is at time t = 0.8

This looks more and more like exponential growth (at a very low rate of about 1/173 % per million years) as time goes on. Eventually it will be indistinguishable from exponential growth at that rate call it H

D(t) = eHt

If you differentiate that you get the expansion speed is proportional to the distance multiplied by H and if you take the derivative again you get the acceleration is proportional to the distance multiplied by the square of H