Anyone can participate in the challenge, which will be open from April 29 to June 29, 2015, NASA said.
Galactic cosmic rays (GCRs), high-energy radiation that originates outside the solar system are a major issue facing future space travellers venturing beyond low-Earth orbit.
These charged particles permeate the universe and exposure to them is inevitable during space exploration.
Because missions to Mars will require crews to remain beyond the protection of Earth's magnetic field and atmosphere for approximately 500 days and potentially more than 1,000 days, learning how to protect human explorers from the effect of exposure to GCRs is a high priority.
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"We are very impressed with the enthusiasm and sheer number of people from the public who showed interest in solving this very difficult problem for human space exploration," said Steve Rader, NASA deputy manager of the Center of Excellence for Collaborative Innovation.
"We look forward to seeing what people will come up with in this next challenge to find the optimal configuration for these different protection approaches," said Rader.
While the five winners selected in the first challenge did not identify a solution that ultimately solves the problem of GCR risk to human crews, the first place idea did provide a novel approach to using and configuring known methods of protection to save substantial launch mass and lower launch costs over multiple missions.