Aryabhata’s Computation of the Earth’s Perimeter

One of the most important astronomers and mathematicians, Aryabhata, was born in 476 CE. He belonged to Pataliputra, which is present-day Patna.

His major work includes Aryabhatiya, which also introduced the number zero and place value system, and other concepts like trigonometry. Aryabhatiya is divided into four chapters, containing 13 introductory verses and 108 verses. 

Considered astounding even today, Aryabhata estimated the circumference of the Earth as 24835 miles (39968.058 km) as per modern units. He calculated the planet’s diameter to be 1050 yojanas. This calculation was followed for many years without being changed.

Aryabhata

The founder of zero and the place value system, the great astronomer and mathematician Aryabhata was born in 476 CE and lived up to 550 CE. He was an inhabitant of Pataliputra, which is present-day Patna in Bihar. He received his education from the University of Nalanda. 

This mathematician put forward concepts such as algebra, trigonometry, sidereal periods, Heliocentrism, cube root, square root, areas of triangles, the volume of spheres, and many more.

He was also a great astronomer who described the occurrence of the lunar and solar eclipses, developed approximations for Pi, and attempted to calculate the Earth’s circumference.

Aryabhata’s Computation of Earth’s Perimeter

1. He considered two places on the same latitude, say X and Y. These were determined using the principle that sites on the same stretch have the same length of the shadow at the same local time.
2. The time difference between these places is measured with the help of a water clock. Let the difference be q minutes. A one-degree change in longitude communicates a time difference of 4 minutes (obtained from the period of Earth’s rotation). Hence, the time difference is q/4 degrees in longitude.
3. The terrestrial distance between X and Y is measured. Let us call it p Km. Now, q/4 degrees corresponds to p Km. From this, 360 degrees corresponds to p*360*4/q Km. This is the circumference of the latitude.
4. As an astounding expert in trigonometry, Aryabhata must have used his sin table to calculate the circumference of the Earth.
5. Though this method is somehow based on assumptions, despite the assumed and imprecise measuring devices, Aryabhata was able to calculate the Earth’s circumference accurately. 
6. However, some people argue that another way Aryabhata calculated the circumference of the Earth is by noticing shadows and taking terrestrial distances between two longitudes. This way, he calculated Earth’s circumference to be 4967 yojanas, where one yojana is equal to five miles, making the circumference 24835 miles.

Eratosthenes’s Measurement of Earth’s Circumference

A Greek polymath, Eratosthenes was also a poet, mathematician, geographer, and music theorist. He is best known for calculating the circumference of the Earth. He estimated the circumference perfectly by assuming Earth as a sphere in space. He made the first projection of the world using parallels and meridians. Some terminologies used by him are still used in modern times.

Eratosthenes recognised that ships slowly disappeared as they crossed the horizon. He also observed a curved reflection of the Earth on the Moon during a lunar eclipse and the changing positions of stars. 

He focused on the Egyptian city, Swenet, on the Nile River during the summer solstice at noon one day every year. He found that the Sun came directly up to his head as the rays were straight.

Later, he struck a pole in Alexandria again at the summer solstice. This time, he noticed that the Sun was not directly over his head but more towards the south. Seeing the curve of the Earth and stretching between two places, he calculated the Earth’s circumference.

Conclusion

The astounding mathematician and astronomer Aryabhata was born in 476. He is a significant figure in the field of mathematics and science. His notable ideas revolutionised various concepts. He also provided explanations on the lunar eclipse, value of pi, diameter of Earth, etc. 

Aryabhata calculated the circumference of the Earth by taking into account the shadows and considering the distance between two longitudes. He found that the Earth’s circumference was 4967 yojanas. One yojana is equal to five miles, which makes the Earth’s circumference 24835 miles.