(naive?) interpretation of Hubble's Law

From my understanding, the Hubble constant $H_0$ calculates from observed redshifts $z$ of distant galaxys against their proper distance $D$. The current value appears to be 67.80(77) ${\frac{km}{s}}Mpc^{-1}$.

Does this mean that at a distant of 1 Mpc space expands with a rate of 67.80(77) ${\frac{km}{s}}$? Breaking it down to a more comprehensible scale => $H_0 = 2.197 \times 10^{-18} {\frac{m}{s}} m^{-1}$. So every ~15 minutes ($\approx$ 1000 sec) one meter expands by the size of one proton (assuming $r_{proton} \approx$ 1 fm)

Is this a right image that I got out of it?

Bonus question:

Calculating the Hubble constant via the redshift, I assume one only wants those velocity contributions due to the expansion of the universe, and not those from the real movement of the galaxies within in cluster or so. How do you account for that?

• This expansion of space doesn't happen for gravitationally bound systems, so the naive picture is deceptive and it breaks the equivalence principle. A massive body can detect acceleration against the background spacetime, but it can't detect constant motion like this one. – CuriousOne Jan 31 '16 at 19:14
• the bonus question must be asked in a new page because it requires experts in astronomical observations. The first is common and had been asked many times – user46925 Jan 31 '16 at 19:33
• or modify this page to keep only the bonus question. The answer to the 1st is something like this : "the expansion doesn't affect in the same way low and high density regions. When there is a high density of matter, like in a galaxy, the gravity is stronger and there is no expansion. Else space expands as you wrote." – user46925 Jan 31 '16 at 19:46
• So the expansion of the universe only occurs on large scales and can't be applied to higher density regions(?). But what's about the Big Rip theory. It states that at one point the expansion of space could be faster than the speed of light and no interaction between anything is possible anymore (understandable), but also that atoms and subatomic particles, [are] progressively torn apart by the expansion of the universe, which than doesn't make sense if expansion only appears on large scales. Is the big rip theory possibly just wrong? – rtime Jan 31 '16 at 20:26
• there will be no witness from us, why not ? imagine a very strong expansion, some will call this a new inflation. At some point, one must stop to infer the (un)possibilities :) – user46925 Jan 31 '16 at 21:21