User:Spacepotato/Aryabhata's measurement of the Earth

In his only surviving work, the Aryabhatiya, Aryabhata states that the Earth has a diameter of 1,050 yojana ( The Aryabhatiya of Aryabhata: An Ancient Indian Work on Mathematics and Astronomy, tr. with notes by Walter Eugene Clark, Chicago: Univ. of Chicago Press, 1930, p. 15.) Unfortunately, the length of the yojana is not known precisely, and estimates of its value differ widely:
 * "The yojana is a standard Indian unit of distance whose exact value in terms of modern units is not known (and may have been somewhat variable), but it is approximately on the order of ten kilometers." (Kim Plofker, Mathematics in India, Princeton, 2008, p. 69)
 * "yojana A unit of distance, probably somewhere between five and ten kilometers." (Plofker, p. 315)
 * Monier-Williams's Sanskrit-English dictionary remarks that the work yojana means yoking, and can also mean the distance traversed in one harnessing. When the word is used as a measure of distance, it suggests values of 2.5, 4, 5, or 18 English miles, but "more correctly...about 9 miles". (p. 858, A Sanskrit English Dictionary, M. Monier-Williams, reprint ed., Motilal Banarsidass, 2005; first ed. published by Oxford University Press, 1899)
 * The yojana is "estimated by different authorities at from four and a half to rather more than ten miles English." (p. 39, Translation of the Sûrya-Siddhânta: a text-book of Hindu Astronomy, Ebenezer Burgess, American Oriental Society, 1860.
 * Aryabhata himself states that a yojana equals 8,000 nṛ [meaning, 8,000 times the height of a man]. (Clark, p. 15.)

However, one may read in various places around the Web, and even in print, that Aryabhata estimated the circumference of the Earth to be 24,835 miles, sometimes with the addition that this is "within 0.2%". The source of this may be the MacTutor History of Mathematics archive, which writes: Aryabhata gives a systematic treatment of the position of the planets in space. He gave the circumference of the earth as 4 967 yojanas and its diameter as 1 581 1/24 yojanas. Since 1 yojana = 5 miles this gives the circumference as 24 835 miles, which is an excellent approximation to the currently accepted value of 24 902 miles. ("Aryabhata the Elder",, accessed 2010-IV-23) This is problematic in two ways, viz., that Aryabhata is misquoted, and that there is no justification for the equation of 1 yojana to 5 miles. The diameter and circumference figures in this quote come not from Aryabhata but from Bhaskarachaya's Siddhanta Siromani (p. 122, Translation of the Súrya siddhánta by B.D. Sástri, and of the Siddhánta Siromani by L. Wilkinson, Calcutta: C. B. Lewis, 1861.)