# Is the universe expanding faster than speed of light?

The celestial bodies like stars and galaxies are moving away from each other. How fast are they moving apart? Is that speed more than the speed of light?

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According to Hubble's law

For [proper] distances $D$ larger than the radius of the Hubble sphere $r_{\mbox{HS}}$ , objects recede at a rate faster than the speed of light ... $$r_{\mbox{HS}}=\frac{c}{H_0}$$

With $H_0=67.8\mbox{ }(\mbox{km}/{\mbox{s}})/\mbox{Mpc}$ the Hubble constant according to the Planck mission, $c=299,792,458\mbox{ m}/\mbox{s}$ the speed of light, and one Megaparsec $1\mbox{ Mpc}=3.0857\cdot 10^{22}\mbox{ m}$, we get $$r_{\mbox{HS}}=\frac{c}{H_0}=\frac{299,792,458\mbox{ m}/\mbox{s}}{67.8\cdot 10^3\mbox{ }(\mbox{m}/{\mbox{s}})/3.0857\cdot 10^{22}\mbox{ m}}=1.3644\cdot 10^{26}\mbox{ m}.$$ That's $$1.3644\cdot 10^{26}\mbox{ m}/1.3644\cdot 10^{26}\mbox{ m}= 4,421 \mbox{ Mpc}$$ or $r_{\mbox{HS}}=14.422$ billion lightyears (1 pc = 3.26156 ly).

Hence objects further away than this proper distance (what you would measure with a chain of rulers) recede faster than the speed of light. The distance is also called Hubble length.

You may find 13.8 billion lightyears elsewhere. That's calculated with $H_0=70.4\mbox{ }(\mbox{km}/{\mbox{s}})/\mbox{Mpc},$ according to the estimates of 2010, based on WMAP data, or with even older data. The exact value is not known.

Since the Hubble constant isn't really constant over time, the universe is thought to be a little younger (13.8 billion years) than the 14.422 billion years you get by just dividing the Hubble distance by the speed of light.

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