ASTRONOMY FUNDAMENTALS - Chapter 8, Exercise 1 Solution
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Applying Hubble's Law

PROBLEM
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Using Hubble's Law (v = H0 x D) with a Hubble constant of H0 = 70
km/s/Mpc, calculate the real recession velocity of a galaxy measured to
be 150 Mpc away.

SOLUTION
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Hubble's Law: v = H0 x D

Substitute the given values:
    v = 70 km/s/Mpc x 150 Mpc

The Mpc units cancel out, leaving km/s:
    v = 70 x 150 km/s
    v = 10,500 km/s

ANSWER: The galaxy's real recession velocity is 10,500 km/s.

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WHY THIS WORKS AS AN ANSWER

Hubble's Law is a direct proportionality: recession velocity scales
linearly with distance, with the Hubble constant as the real
proportionality factor connecting the two. Since H0 is given in units
of km/s per Mpc, multiplying it by a distance in Mpc directly cancels
the Mpc units, leaving a real velocity in km/s - no additional unit
conversion is needed as long as the distance is expressed in the same
distance unit (Mpc) the Hubble constant is defined against.

This result also illustrates the real, defining feature of Hubble's
Law itself: a galaxy twice as far away would have exactly twice the
recession velocity (assuming the same H0 value), which is precisely
the real, linear pattern that led Hubble - and, two years earlier,
Lemaître - to conclude the universe itself must be expanding, rather
than galaxies moving away from a single fixed point for some other
reason.