bluemoonKY said:
When Neil Tyson spoke of cosmic rays that were lethal, I don't think he was talking about cosmic rays from the sun. I think he was talking about cosmic rays from Supernovas and neutron stars.
There are two major sources of radiation, solar and cosmic (meaning from beyond the solar system). Solar radiation obviously originates with the sun, and we can detect that (to an extent) in advance. Cosmic radiation, however, can come from any direction, and is impossible to detect in advance. Both could prove fatal to unprotected astronauts. Even in 1969 they knew the effects of solar radiation could prove fatal. The astronauts were very lucky, and it also explains in part why there have been no manned-missions beyond the protective magnetic field of Earth since 1973.
Even in the protective magnetosphere of low-earth orbit, the astronauts on the ISS are still exposed to "5 to 12 μ Gy (0.5 to 1.2 milli rads) per hour" which equates to "44 to 105 milli Gy (4.4 to 10.5 rads)" annually. That is 11.5 ± 4 times the background radiation we experience on the surface of the planet in the US. The NASA source below also has numerous other publications which can be referenced concerning both solar and cosmic radiation in space.
On the surface of Mars the daily radiation dose ranges from between 200 to 220 μ Gy per day, or 12 ± 0.5 times higher than the normal background radiation on the surface of Earth in the US. That is not a large enough dose of radiation to prove fatal, it is very close to what astronauts currently experience on the International Space Station. Mars offers no protection from solar or cosmic radiation spikes. With sufficient warning, astronauts could get to a protective shelter in the event of a solar flare or coronal mass ejection. However, there is no way to warn the astronauts about an impending spike in cosmic radiation, for example, from a gamma-ray burst.
Solar and cosmic radiation is certainly one of the biggest technological challenges we have to face in our exploration of manned space missions.
Sources:
Deadly Solar Flares Pose Threat To Astronauts While On Moon - Daytona Beach Morning Journal, July 15, 1969
International Space Station Internal Radiation Monitoring (ISS Internal Radiation Monitoring) - NASA, International Space Station Mission Pages
Radiation Measurements on Mars - NASA/JPL, from August 2012 to June 2013
Background Radiation - Wikipedia