In 1925 the
American astronomer Edwin Hubble (1889-1953) proposed a very simple relationship
between the distance of a galaxy and its velocity of recession or approach (v). The Hubble
formula provides a very powerful way of determining not only distances of remote galaxies
but also the age of the Universe itself.

He stated that they were related by the
formula:

where H is Hubble's
constant and r is the distance of the galaxy from the Earth. Now clearly the value of Hubble's
constant is critical to the measurement of the distance of a given galaxy and therefore to the
measurement of the size of the Universe. **At present its
value if thought to be about 70 kms ^{-1} Mpc-^{1}.**

This means that:

The value of H
can be found by measuring the distance of another galaxy using the period-luminosity
relationship for a Cepheid variable star. The period of intensity variation is directly
proportional to the star's absolute brightness. This brightness variation is due to the balance
between gravitational attraction and the force due to radiation pressure.

It is
important to realise that the number quoted above as the value of H is the value at the
present time.

The value of H will have varied over the lifetime of the universe and will
continue to do so in the future.

The recession velocity of a given galaxy can be found
by measuring the Doppler shift of lines in its spectrum (see Figure 1). Once this is found the
distance of the galaxy can be calculated using the Hubble formula.

For a galaxy in the Virgo cluster the Doppler shift at a wavelength of 500 nm is 2 nm.

If the velocity of light in free space is 3x10

Δλ = λv/c and so v = cΔλ/λ = 3x10

v = 1.2x10

Take the Hubble constant H to be 70 kms

One Parsec = 3.26 light years = 3.0857x10

So 70 kms

Using the result worked out in the previous example we can now calculate the distance of the galaxy in the Virgo cluster.

Find the distance of the galaxy with a recession velocity of 1200 kms

Using v = Hr

r = v/H = 1200/70 = 17.14 Mpc = 17.14x3.09x10

The galaxy is therefore 56 million light years away.

This can be found by using Hubble's formula:

v = HR

R = 3x10

This is equal to 1.4x10

Assume that the radius of the universe (R) = velocity of recession of the most distant galaxies
(v) multiplied the age of the universe (t_{o}) and also that the galaxies have been moving
apart with constant velocity since the beginning of time. Written as a formula:

Take R = 1.33x10

t

It seems that Hubble's constant is probably 70 kms

Notice that since t