Time taken for Earth to orbit Sun

The famous Hindu mathematician, Bhaskaracharya, in his treatise Surya Siddhanta, calculated the time taken for the earth to orbit the sun to nine decimal places (365.258756484 days).

Bhaskaracharya rightly calculated the time taken by the earth to orbit the sun hundreds of years before the astronomer Smart. His calculations was - Time taken by earth to orbit the sun: ( 5th century ) 365.258756484 days.

Today’s accepted measurement is 365.2564 days. Therefore, assuming that today’s figures are correct, it means that Bhaskaracharya was off by only 0.0002%.

Bhaskaracharya wrote Siddhanta Shiromani in 1150 AD when he was 36 years old. This is a mammoth work containing about 1450 verses. It is divided into four parts, Lilawati, Beejaganit, Ganitadhyaya and Goladhyaya. In fact each part can be considered as separate book. The numbers of verses in each part are as follows, Lilawati has 278, Beejaganit has 213, Ganitadhyaya has 451 and Goladhyaya has 501 verses.

Bhaskara has given a very simple method to determine the circumference of the Earth. According to this method, first find out the distance between two places, which are on the same longitude. Then find the correct latitudes of those two places and difference between the latitudes. Knowing the distance between two latitudes, the distance that corresponds to 360 degrees can be easily found, which the circumference of is the Earth. For example, Satara and Kolhapur are two cities on almost the same longitude. The difference between their latitudes is one degree and the distance between them is 110 kilometers. Then the circumference of the Earth is 110 X 360 = 39600 kilometers. Once the circumference is fixed it is easy to calculate the diameter. Bhaskara gave the value of the Earth’s circumference as 4967 ‘yojane’ (1 yojan = 8 km), which means 39736 kilometers. His value of the diameter of the Earth is 1581 yojane i.e. 12648 km. The modern values of the circumference and the diameter of the Earth are 40212 and 12800 kilometers respectively. The values given by Bhaskara are astonishingly close.