January 2 – Soviet spacecraft Luna 1 is launched by a Vostok rocket from the Baikonur Cosmodrome; the first man-made object to attain escape velocity, it is intended to impact Earth's Moon, but an error causes it instead to become the first spacecraft to fly by the Moon and the first man-made object to enter heliocentric orbit.
May 28 – Jupiter AM-18 rocket launches two primates, Miss Baker and Miss Able, into space from Cape Canaveral in the United States along with living microorganisms and plant seeds. Successful recovery makes them the first living beings to return safely to Earth after space flight.
June 25 – A KH-1 Corona satellite, believed to be the first operational spy satellite, is launched as science mission "Discoverer 4" from Vandenberg Air Force Base, California, aboard a Thor-Agena rocket.
July 7 – At 14:28 UT Venusoccults the star Regulus. The rare event (which will next occur on October 1, 2044) is used to determine the diameter of Venus and the structure of Venus' atmosphere.
August 7 – The United States launches the Explorer 6 satellite from the Atlantic Missile Range in Cape Canaveral.
August 14 – Explorer 6 sends the first picture of Earth from orbit.
September 14 – Soviet spacecraft Luna 2 becomes the first man-made object to crash on Earth's Moon.
September 19 – Giuseppe Cocconi and Philip Morrison establish the scientific rationale for SETI with the publishing of their seminal paper "Searching for Interstellar Communications" in Nature.
October 7 – Russian probe Luna 3 sends back the first images of the far side of Earth's Moon.
October 13 – The United States launches Explorer 7.
First femur of Arlington Springs Man is found on Santa Rosa Island, California, by Phil C. Orr. The remains are subsequently dated to 13,000 years BP, making them potentially the oldest known human remains in North America.
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McLaughlin, Thomas P.; etal. (May 2000). "A Review of Criticality Accidents"(PDF). CSRIC. Los Alamos National Laboratory. p.96. Archived from the original on 2007-09-26. Radiation doses were intense, being estimated at 205, 320, 410, 415, 422, and 433 rem.74 Of the six persons present, one died and the other five recovered after severe cases of radiation sickness.
Johnston, Wm. Robert (2005-09-14). "Vinca reactor accident, 1958". Database of radiological incidents and related events – Johnston's Archive. Retrieved 2012-07-02.
Gould, R. Gordon (1959). "The LASER, Light Amplification by Stimulated Emission of Radiation". In Franken, P. A.; Sands, R. H. (eds.). The Ann Arbor Conference on Optical Pumping, the University of Michigan, 15 June through 18 June 1959. p.128. OCLC02460155.