On June 5, 1872 Hall submitted an article entitled “On an Experimental Determination of Pi” to the journal Messenger of Mathematics. The article appeared in the 1873 edition of the journal, volume 2, pages 113–114. In this article Hall reported the results of an experiment in random sampling that Hall had persuaded his friend, Captain O. C. Fox, to perform when Fox was recuperating from a wound received at the Second Battle of Bull Run. The experiment involved repetitively throwing at random a fine steel wire onto a plane wooden surface ruled with equidistant parallel lines. Pi was computed as 2ml/an where m is the number of trials, l is the length of the steel wire, a is the distance between parallel lines, and n was the number of intersections. This paper, an experiment on the Buffon’s needle problem, is a very early documented use of random sampling (which Nicholas Metropolis would name the Monte Carlo method during the Manhattan Project of World War II) in scientific inquiry.
Makemake is about a fifth as bright as Pluto. However, despite its comparative brightness, it was not discovered until well after a number of much fainter KBOs had been detected. Most of the scientific hunts for minor planets are conducted relatively close to the region of the sky that the Sun, Earth's Moon, and planets appear to lie in (the ecliptic). This is because there is a much greater likelihood of discovering objects there. Makemake is thought to have evaded detection during earlier searches because of its relatively high orbital inclination, as well as the fact that it was at its greatest distance from the ecliptic at the time of its discovery--in the northern constellation of Coma Berenices.
However, the astronomers will require more HST observations in order to obtain accurate measurements in order to determine if the moon's orbit is circular or elliptical. Preliminary estimates suggest that if the moon is in a circular orbit, it finishes a circle around Makemake in 12 days or longer.
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