I’m probably missing something obvious here but I can’t figure out what.(adsbygoogle = window.adsbygoogle || []).push({});

Consider a galaxy, starting at an initial distance of ##D_0##, recessing with a constant velocity. After a time Δt, we’d measure a larger distance ##D_{t}##. From this scenario I’d conclude that the Hubble value based on this object is calculated by:

$$H = \frac{D_t – D_0}{Δt} \cdot \frac{1}{D_0}$$

That is, the velocity, which is obtained by the first fraction, divided by the initial distance ##D_0## of the galaxy gives the Hubble value when the galaxy was at distance ##D_0##

Now, from what I understand, the scale factor ##a## is how large the reached distance ##D_t## is relative to the initial distance ##D_0##. Thus; ##a = \frac{D_t}{D_0}##

Furthermore, the rate of change of the scale factor ##\dot a## is how much the distance has increased per unit of time, relative to the initial distance ##D_0##. So ##\dot a## could be calculated by adding the velocity (a distance per unit time) to the initial distance ##D_0## and dividing that by ##D_0##:

$$\dot a = (\frac{D_t – D_0}{Δt} + D_0) \cdot \frac{1}{D_0}$$

When combining these formulations for ##H##, ##a## and ##\dot a## I’d get: ##H+1 = \dot a##.

This is obviously not true since it should be ##H = \frac{\dot a}{a}##.

What am I missing?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Determining H value from scalefactor

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**