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## Q. 16.1

Astronomers use a measure of distance called the parsec, abbreviated pc, more often than the lightyear, another measure of distance. A star that is one parsec away has a parallax of one second of arc relative to the Earth’s orbit about the sun. (Parallax is the apparent displacement of a body due to its observation from two different positions.) One parsec is about 3.26 lightyears. Determine Hubble’s constant in km/s per Mpc.

Strategy We need to use conversions and the value of the Hubble constant. One Mpc is a megaparsec or $10^{6}$ pc.

## Verified Solution

We use the value just given for Hubble’s constant, 22 km/s per million lightyears, and make the conversion to Mpc.

$\frac{22 km / s }{\text { million ly }} \frac{3.26 ly }{ pc }=72 \frac{ km / s }{ Mpc }$

Hubble’s constant is quoted using either unit. Different measurements yield values between 68 and 75 $km \cdot s ^{-1} \cdot Mpc ^{-1}$. The best current estimate using all measurements is 71 $km \cdot s ^{-1} \cdot Mpc ^{-1}$, a value that we will use from now on in this text.