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Sidereal day of Aryabhata

Activity objectives

  • Learn about the difference between sidereal and solar days
  • Gain an idea of ancient Indian astronomy
  • Use Stellarium to determine the duration of a sidereal day
 
Background
           
Indian astronomy has a history that spans several thousand years but it is the period around the 5th – 6th century CE where it is said to have reached its greatest heights. This is when the most famous Indian astronomer, Aryabhata (476–550 CE), flourished. His greatest mathematical and astronomical work, the Aryabhatiya, represented the pinnacle of astronomical knowledge at the time.
Picture
                                                                                       Aryabhata: Taken from https://en.wikipedia.org/wiki/Aryabhata#/media/File:2064_aryabhata-crp.jpg
 
Amongst Aryabhata’s most important astronomical achievements was the correct interpretation of the apparent daily motion of the stars, which he attributed to the rotation of the Earth about its axis rather than the rotation of the celestial sphere itself, the correct scientific interpretation of eclipses, and the accurate determination of the duration of a sidereal day.
 
A sidereal day is the time it takes for the Earth to completed one revolution about is axis with respect to the fixed stars. A solar day on the other hand, is the time it takes for the Sun to return to our local meridian (due South for the Northern hemisphere and due North for the southern hemisphere). The solar day is what we are more used to (more precisely the mean solar day), and it lasts 24 hours. The sidereal day is a little shorter and the following figure illustrates why.
Picture
                                                                                                                                                    Solar and sidereal day
 
At point 1, the sun lies at our local meridian. At point 2, the Earth has completed one revolution with respect to the fixed stars but because of its motion relative to the Sun, the Sun has still not reached our local meridian. In order to achieve this (at point 3), the Earth must spin for a little longer than 24 hours. So, the solar day is slightly longer than the sidereal day and this is due to our motion around the Sun.
 
Implementation in Stellarium
 
Start Stellarium and in the Date/Time Window, set the date to: 500 / 01 / 01. This is around the time when Aryabhata lived.
 
Next, set the location in the Location Window to Patna in India. This is where Aryabhata lived for part of his life.
 
Set the local time to 10:30 pm and locate the star Canopus (you can obviously use any star to perform this). Determine the exact time when Canopus crosses the local meridian (i.e. when it is exactly South with an azimuth of 180 degrees).
 
Next, set the date to: 500 / 01 / 02 (i.e. exactly a day later) and find the time when Canopus has an azimuth of 180 degrees.
 
Use the difference in the two times to estimate the duration of a sidereal day.
 
Aryabhata determined the sidereal day to be 23 hours, 56 minutes, and 4.1 seconds.
 
Compare the value you obtained to that of the great Indian astronomer.
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  • MY SCIENCE WALKS
  • SHORT BIO
  • STELLARIUM RESOURCES
    • Introduction
    • Astronomy and the Odyssey
    • Circumference of the Earth (Eratosthenes)
    • Circumference of the Earth (Posidonius)
    • Distance to the Sun (Aristarchus)
    • Size of the Moon (Aristarchus)
    • Distance to the Moon (Hipparchus)
    • Lunar eclipse of Alexander the Great
    • Journey of Pytheas
    • Babylonian Cycles
    • Direction to Mecca
    • Great Conjunction of 1166
    • Medieval supernovas
    • Chinese pole star
    • Sidereal day of Aryabhata
  • NAVIGATING WITH THE STARS
  • ANTIKYTHERA MECHANISM
  • BOOKS & COURSES
    • An Introduction to the Physics of Sports
    • The Physics of Sports course
    • Every Night Astronomy
    • Scientific Secrets of Athens
    • Scientific Secrets of Edinburgh & Glasgow
    • Textbooks in Greek
  • TRAVEL BLOG
  • Contact Me