Jantar Mantar

Objective behind Jantar Mantar Project was to study various instruments at the Jantar Mantar observatory at Delhi and to figure out methods to restore the markings on the instruments so that the instruments can be reused to take astronomical observations. MSF | IAYM

What is Jantar Mantar? • Jantar Mantar is a big astronomical observatory built by Sawai Jai Singh. The first Jantar Mantar was constructed in the 18th century. • Its construction came about due to heated disagreements between Hindu and Muslim astrologers failing to reach conciliation due to inaccurate astronomical tables at a time when Emperor Muhammad Shah had to leave for a journey and thus wanted an auspicious date. • Jai Singh thus requested Emperor Muhammad Shah to allow him to undertake the responsibility of constructing this observatory, which was given to him seeing his passion for math and astronomy. MSF | IAYM

How does Jantar Mantar work on spherical trigonometry? • The instruments at the 5 Jantar Mantars all work on the principles of Spherical Trigonometry. • Yantras like the Ram Yantra can measure Altitude and Azimuth of the sun and stars while the Jai Prakash Yantra can measure Right Ascension and Declination. MSF | IAYM

The Jai Prakash Yantra The Jai Prakash Yantras are used to locate the position of stars based on two different coordinates measurements systems, the horizontal and celestial equatorial systems. MSF | IAYM

Reconstructing the Jai Prakash Yantra 1. LOCATING THE POLE STAR • Since the hemisphere is a reflection of the celestial sphere, the directions are also reversed i.e. the North of the hemisphere is actually the geographical south and so on. • To locate the pole star, take the latitude angle of the place. • We know that the angle between the image of the Pole Star in the hemisphere and the surface of the hemisphere will be equal to the latitude of the place. Putting Ɵ=28.38˚ N, r=4.165 m, we find the location of the Pole Star on the hemisphere. MSF | IAYM

Reconstructing the Jai Prakash Yantra Pole Star Radius of hemisphere Ɵ- latitude angle Image of Pole Star Meridian MSF | IAYM

Ram Yantra Introduction The Rama Yantra can be used to measure both the position of the sun and stars. It is based on the horizon and zenith system. It consists of two complimentary instruments. MSF | IAYM

Re-marking on Ram Yantra • For measuring azimuth, readings are marked at equal distances along the circumference of the gnomon of Ram Yantra. • For measuring altitude, readings are marked on the flans and walls of the Yantra. • The readings on the walls can be marked using the formula: l tan θ = R where l is the distance from the top of the wall • The radius is known to be 7.52metres and θ is varied from 0.1,0.2…up to 45 degrees to obtain l. • Similarly, the readings on the flans can be marked using the formula: R tan θ = l' • The height of the central pillar is known to be equal to radius R and the value of θ is varied from 45.1,45.2 …up to 90 degrees. • Thus, the Ram Yantra can be re-marked and brought into usable condition again. MSF | IAYM

Samrat Yantra The Samrat Yantra (Supreme Instrument) is the crowning glory of the observatory. It, in essence, is a sundial. Its principal purpose is to conduct solar time-reading duties. It is also able to trace the path of stars, reveal the duration of day-night, and verify the location of the Pole Star. MSF | IAYM

Construction Pole Star Gnomon Ɵ Ɵ 90-Ɵ Ɵ Ɵ Celestial Equator MSF | IAYM

Re-marking of Samrat Yantra • To restore the Samrat Yantra and bring it to usable condition again, the readings on the quadrants and the gnomon have to be re-marked. • The radius of the quadrants is known to be 15.09metres. • Using the formula, and varying the values of Ɵ as 0.1,0.2….up to 90 degrees, the lengths of arcs at various angles can be found out. • Thus, the right ascension at different positions of the sun can be determined using these markings. • Right Ascension is also called hour-angle as the local time of a place can be determined using the right ascension. • For this purpose, the readings also have to be marked in hours, angles and minutes also, other than degrees. MSF | IAYM

Present condition of Delhi Jantar Mantar MSF | IAYM

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Jantar Mantar

by Anjani on Apr 12, 2010

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