
\magnification=\magstep2


$$
r(t) \quad = \quad \tilde{\omega} \thinspace a(t)
$$


$$
v(t) \quad = \quad {{d r}\over{dt}}  \quad = 
           \quad \tilde{\omega} \thinspace {{d a}\over{dt}} 
$$

$$
v \quad \equiv \quad H \thinspace r
$$

$$
H \quad = \quad {{1}\over{a}} \thinspace {{da}\over{dt}}
$$

$$
{{1}\over{H}} \quad = \quad {{a} \over {{da/dt}}}
      \quad
      = \quad
      {    {\rm size\ of\ universe}\over{\rm speed\ of\ expansion}   }
$$

$$
(m - M) \quad = \quad 5 \log_{10} d - 5
$$

$$
v \quad \sim \quad c\thinspace z
$$

\bye
