**4.2. Measuring the Hubble Constant**

As stated previously, the expansion of the universe follows the Hubble
law given by Eq. (6). Observationally, we measure the recession
velocity as a redshift, *z*, in the light from the supernova
(*v*_{r} = *cz*). Since every type Ia supernovae has
about the same absolute
magnitude, Eq. (26), the apparent magnitude provides an indirect measure
of its distance. Therefore, for nearby supernovae (*z*
0.3) the
Hubble Law is equivalent to a relationship between the redshift and the
magnitude. Inserting (26) into (24), using (6), and applying to the
current epoch, yields the *redshift-magnitude relation*

(27) |

Defining the *z* = 0 intercept as

(28) |

we can write equation (27) as

(29) |

As shown in Fig. 1, low-redshift data can be
used to find and
Eq. (28) to solve for the Hubble constant. Studies on type Ia supernova
[12]
consistently suggest a value for the Hubble constant of
about 63 km s^{-1} Mpc^{-1}.

The result for *H*_{0}, found from low-redshift supernovae,
tends to set the lower bound when compared with other methods for obtaining
*H*_{0}. For example, if the distances to enough galaxies
can be
accurately found, then the Hubble law can be used directly to obtain a
value of *H*_{0}. This has partly been the goal of the
*Hubble Space Telescope Key Project*.
[13]
This project has shown that a
careful consideration of the type Ia supernova results in combination
with the other methods for obtaining *H*_{0} produces what
has become a widely accepted value for the Hubble constant

(30) |

The value given in Eq. (30) is the one that we shall adopt in this paper.