Expanding Universe

In the early 1900's (1910's), an important discovery was made by V. M. Slipher. Slipher found that distant galaxies were receding from the Earth, actually he found that distant galaxies showed redshifts. A redshift is a shift in the measured wavelength of some spectral feature to a value greater than its value as measured in a stationary Terrestrial laboratory. The redshift, z, is defined as

Redshift ===> z = [W(observed)-W(rest)] / W(rest)

That is, the redshift is the relative change in the wavelength of the spectral feature. If the observer and the source are in relative motion, then z will be nonzero. If there is no relative motion then, z = 0. Typical measurements

Hubble demonstrated that the larger the redshift, z, the greater the distance to the object. This can be easily seen in the above where the sources with the smaller redshifts present larger images on the sky. Since we know that angles (apparent sizes of objects on the sky) decrease as you move an object farther away roughly as angle ~ size/distance, smaller appearing objects must be farther away.

Hubble found what is referred to as Hubble's Law. Algebraically, we have that

Hubble's Law ===> z proportional to distance

Interpreting the redshift as being due to motion, i.e., the Doppler shift let's re-state the Hubble Law in its more familiar form. For small speeds, the Doppler shift is

Doppler shift ===> z = speed of recession / speed of light

so that,

Hubble's Law ===> v = constant x D = Hubble's constant x D = H(now) x D

Hubble's Law is interpreted as being due to the expansion of the Universe and is one of the three fundamental observations that we have about the Universe