  Observations of open star clusters in the solar neighborhood are used to
calculate local supernova (SN) rates for the past 510 million years (Myr).
Peaks in the SN rates match passages of the Sun through periods of locally
increased cluster formation which could be caused by spiral arms of the Galaxy.
A statistical analysis indicates that the Solar System has experienced many
large short-term increases in the flux of Galactic cosmic rays (GCR) from
nearby supernovae. The hypothesis that a high GCR flux should coincide with
cold conditions on the Earth is borne out by comparing the general geological
record of climate over the past 510 million years with the fluctuating local SN
rates. Surprisingly a simple combination of tectonics (long-term changes in sea
level) and astrophysical activity (SN rates) largely accounts for the observed
variations in marine biodiversity over the past 510 Myr. An inverse
correspondence between SN rates and carbon dioxide (CO$_2$) levels is discussed
in terms of a possible drawdown of CO$_2$ by enhanced bioproductivity in oceans
that are better fertilized in cold conditions - a hypothesis that is not
contradicted by data on the relative abundance of the heavy isotope of carbon,
$^{13}$C.
