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Q: Did Shapley used the distribution of globular clusters in the galaxy to determine that the Sun was not at the center of the Milky Way?
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What is the diameter of the Shapley supercluster?

Super clusters do not have defined boundaries, not a defined shape. A ballpark figure would put the diameter at about 100 million light years, but extending to about 250 million light years at the extreme. See related link for a pictorial of the cluster


Who was the first astronomer to get a reasonable idea of the size and shape of the galaxy?

Shapley


Who was George E. Hale and what did he discover?

George Ellery Hale (June 29, 1868 - February 21, 1938) was an American solar astronomer, born in Chicago. He was educated at MIT, at the Observatory of Harvard College, (1889-90), and at Berlin (1893-94). As an undergraduate at MIT, he invented the spectroheliograph, with which he made his discoveries of the solar vortices and magnetic fields of sun spots. In 1890 he was appointed director of the Kenwood Astrophysical Observatory; he was professor of Astrophysics at Beloit College (1891-93); associate professor at the University of Chicago until 1897, and full professor (1897-1905). He was coeditor of Astronomy and Astrophysics, 1892-95, and after 1895 editor of the Astrophysical Journal. Hale was a driven individual who worked to found a number of significant astronomical observatories, including Yerkes Observatory, Mount Wilson Observatory, Palomar Observatory, and the Hale Solar Laboratory. At Mount Wilson, he hired and encouraged Harlow Shapley and Edwin Hubble toward some of the most significant discoveries of the time. He was a prolific organizer who helped create a number of astronomical institutions, societies and journals. Hale also played a central role in developing the California Institute of Technology into a leading research university.