The US space organization on Tuesday said it would acknowledge entries until April 27, 2018.
Bottom line: NASA's Parker Solar Probe - launching summer 2018 - will travel closer to the sun than any spacecraft yet.
By using Venus' gravity to steer its trajectory closer to the Sun with each pass, the probe saves vital fuel and battery power while bringing itself as close as 3.83 million miles from the surface of the Sun-a distance far closer than the planet Mercury and seven times closer than any other spacecraft has ever ventured.
"The spacecraft will also carry my name to the sun, and your name, and the names of everyone who wants to join this voyage of extreme exploration", the Star Trek actor said in a promotional video.
The Parker probe is scheduled to launch on July 31.
NASA just launched what it calls the "Hot Ticket" program to allow members of the general public to participate in the solar probe mission by having their names included in a tiny memory card that will be placed in the probe. "This mission will answer questions scientists have sought to uncover for more than six decades", Mr. Zurbuchen said.
According to NASA, the Parker Solar Probe will be the first ever spacecraft traveling to Sun and it will be launched this summer.
The size of a small auto, it can travel from Washington DC to Tokyo in under a minute, NASA said.
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Studying the effects of the Sun on Space and the planetary system is known as heliophysics.
The Sun is roughly 93 million miles away from Earth, and to get the probe to its desired destination, NASA has selected the second most powerful and among the most reliable rockets now in the human arsenal: the United Launch Alliance Delta IV Heavy.
And, the Parker Solar Probe could help researchers crack some of the biggest mysteries of our universe. "This incredible spacecraft is going to reveal so much about our star and how it works that we've not been able to understand", said project scientist Nicola Fox of the Johns Hopkins Applied Physics Laboratory.
This was the first time NASA named a spacecraft for a living individual.
The announcement was made at a ceremony at the University of Chicago, where Parker serves as the S Chandrasekhar Distinguished Service Professor Emeritus, Department of Astronomy and Astrophysics.
In the 1950s, Parker proposed a number of concepts about how stars - including our Sun - give off energy. Professor Parker has an huge contribution in the field of heliophysics, especially related to the solar corona and the solar winds. It will orbit the star at a distance of just under 4 million miles, and it will have to endure temperatures of nearly 2,500 degrees Fahrenheit.
Eugene Parker also theorised an explanation for the superheated solar atmosphere, the corona, which is - contrary to what was expected by physics laws - hotter than the surface of the Sun itself.