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.
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