In 1929, Harry Edward Burton, head of the Equatorial Division at the USNO, discovered anomalies in the orbital longitude of Phobos, the larger moon of Mars. In 1939, he and Sharpless began a systematic study of the orbital behavior of Phobos and Deimos. Sharpless's photographic observations with a 40-inch Ritchey-Chrétien reflector were inferior to Burton's visual observations with a 26-inch refractor, but Sharpless was sooner ready to publish. Another USNO astronomer, Edgar W. Woolard, published on the same secular accelerations in 1944, but his work was focused on numerical rather than observational analysis. Sharpless's 1945 paper Secular accelerations in the longitudes of the satellites of Mars drawing on observations from 1879 to 1941, was the first to compute these accelerations. They provided the first evidence that Phobos's orbit was decaying and would result in its destruction. Sharpless's paper also computed much smaller accelerations for Deimos. Sharpless's work was of little interest outside his field for a decade, until Iosif Shklovsky began studying the cause of the decay in the late 1950s. Working off the hypothesis that the decay was caused by interactions with Mars's thin atmosphere, Shklovsky concluded that Phobos might be a hollow metal object as little as thick - an unambiguously artificial object. Though Shklovsky later claimed to Patrick Moore that the paper was nothing more than a practical joke, it was taken seriously by others including Carl Sagan and national science adviser Fred Singer, who commented:
If the satellite is indeed spiraling inward as deduced from astronomical observation, then there is little alternative to the hypothesis that it is hollow and therefore Martian made. The big 'if' lies in the astronomical observations; they may well be in error. Since they are based on several independent sets of measurements taken decades apart by different observers with different instruments, systematic errors may have influenced them.
Singer's speculations were correct; Sharpless's calculations were affected by differences between observations. Additionally, the orbital decay is caused not by atmospheric drag, but by solid body tidal forces not considered by Shklovsky. Nonetheless, Sharpless's work stands as the first useful calculation of Phobos's secular acceleration. Both Sharpless and Shklovsky have craters on Phobos named in their honor.
Later career and death
Sharpless published in 1946 on photographic observation of comets, work that was conducted in 1943. Suffering from emphysema, Sharpless retired from the Naval Observatory's Washington, D.C. office on January 1, 1949 and moved to its Florida office at Naval Air Station Richmond. Long in poor health, he died on October 28, 1950 in Atlanta, Georgia. He is buried in Cumberland Cemetery in Media, Pennsylvania.