N. Rathnasree, Nehru Planetarium, Nehru Memorial Museum and Library
(Page under construction)
The instruments which make local (Horizon) co-ordinate measurements in the Jantar Mantar observatories are the Unnatamsa Yantra of the Jaipur observatory which measures Altitude of celestial objects, the Digamsa Yantra of the Jaipur, Ujjain and Varanasi observatories which measures Azimuth of celestial objects and the Ram Yantra of the Delhi and Jaipur observatories, which can measure both Altitude and Azimuth.
The twin cylindrical instruments the Ram Yantra at the Delhi Jantar Mantar observatory
Ram Yantra is a cylindrical instrument built in such a way that one can easily determine the location of the Sun (or other celestial objects) in the sky, in local or Horizon co-ordinates.
An object in the sky can be pin pointed by two quantities – Altitude, which is the angular height of the object above the horizon and Azimuth which can be defined as follows - take an object in the sky, and drop a perpendicular from this object to the horizon (the horizontal circle where the Earth and Sky meet) and mark this point P. Measure the angle made from direction North to the point P, moving eastwards from North. This angle is the Azimuth of the object.
The two angles Altitude and Azimuth completely specify the location of the object in the sky, in the framework, where distances to an object in the line of sight direction, are ignored. Positional Astronomy observations, dealing with timekeeping and calendar determinations, ignore this very important third dimension, which becomes noticeable when physical studies of celestial objects are of interest.
Thus, in all measurements using the Jantar Mantar observatory instruments (and related positional Astronomy), all the celestial objects are treated as being on the surface of one celestial sphere, and two dimensions suffice.
Altitude and Azimuth as visualised at Heavens-above.com
Coming back to the Ram Yantra, these are twin cylindrical instruments. The inner surface of the cylinder reflects the sky. Every point in the sky has a reflection point in the inner surface of the cylinder. The reflection point, is the top edge of the gnomon, which is the central pillar. The instrument is constructed in such a way that the height of the central pillar is equal to the radial floor length of the sectors as also equal to the outer wall height of the instrument.
Ram Yantra seems to be constructed precisely to make it very easy for any one to make local co-ordinate measurements of objects in the sky. Each of the cylindrical instruments consists of a circular wall and a gnomon at the center. The height of the walls and the gnomon, has been designed to be exactly equal to the inside radius of the building measured from the outer circumference of the thick gnomon - that is, the height of the gnomon is exactly equal to the length of the floor of the instrument measured from the outer circumference of the gnomon to the inner circumference of the wall.
The walls and floor are graduated for reading Azimuth and Altitude angles - with the Azimuth markings being a linear scale in degrees, while the Altitude markings are in tangents of degrees and therefore not linearly marked. What is needed is to observe the shadow of the gnomon - determine its center and mark it on the floor or the walls of the instrument - wherever it falls.
The instrument is divided into various sectors, so that observers can walk inside the gaps to make measurements. As this removes a half of the cylinder surface, two twin instruments are constructed with the positions of the sectors and gaps in the two being such that, where there is a gap in one instrument, there is a sector present at the corresponding location in the other instrument and vice versa. Spliced together, the two instruments make a complete cylinder.
Altitude measurement needs a little bit of trigonometry. The instrument is built in such a way that the height of the central pillar is exactly equal to the length of the floor sector. One can thus find the height of the pillar by measuring the floor sector length. Another length to be measured is the distance of the shadow edge from the central pillar. Tan Inverse of (Gnomon length/distance to the shadow) then gives the Altitude. Raja Jai Singh tried to remove the complications of these tangent conversions, by marking the altitudes for each degree incorporating the tangents involved. When the Gnomon shadow is on the top wall of the instrument - the Altitude is 0 degrees. When it is at the junction of the wall and floor it is 45 degrees and when it reaches the central pillar - the Altitude is 90 degrees.
The floor is divided into thirty sectors and thirty gaps of the same dimensions as the sectors. The gaps are for facilitating the movement of observers to read the markings and hence, the complimentary instrument is designed in such a way that, the shadow falls on a sector of one of the instruments, if it falls in the gap for the other instrument. Each of the sectors is thus spanning 6 degrees of Azimuth. The sectors are marked with six radial lines - so that each marking corresponds to a degree of Azimuth. Etched at about five feet above the raised floor of the instrument - on the gnomon itself, is a circular scale of Azimuth markings. The edge of one of the sectors is aligned to the North. This is marked as 360 degrees (in Devnagari) on the Gnomon markings. Once the center of the gnomon shadow (this is not so straightforward and is discussed later) is determined and marked with pencil - one can just read off the Azimuth - by starting with the edge marked as 360 degrees and counting the number of sectors and gaps and individual degree markings up to the center of the shadow. A little trick here, though - the shadow marks a position exactly 180 degrees away from the actual position of Sun in the sky - and therefore 180 degrees would need to be added to the Azimuth reading obtained by counting the sectors and degree lines. Thus angles of 1 degree each can just be read off from the Azimuth markings - finer graduations seem to be missing from the Delhi instrument, in its present condition, but, temporary calibrations for finer accuracy can always be achieved using tape measure placed parallel to Azimuth circles.
The walls of the instrument are also graduated similar to the floor - each of the markings representing one degree in Azimuth and one degree in Altitude.
It is the Altitude markings in tangents of scale that form the beautiful simplicity of usage of this instrument. When the shadow falls at the top of the wall of the instrument - the Altitude of Sun is zero. As one moves down from the top of the wall to the bottom, there are 45 markings on the wall giving rise to an altitude of 45 degrees for the Sun, if the shadow falls at the junction of the walls and the floor. Another 45 degrees are marked inward from the wall towards the circumference of the Gnomon - so that, altitudes between 45 to 90 degrees can be read off on the floor of the instrument. Finer graduations than a degree are marked on some of the sectors - where missing - one needs to remember that the scale is not linear any more (unlike for the Azimuth) and thus more accurate Altitude measurements (where fine graduations are missing) could be inferred by measuring accurately, the length of the shadow and knowing that the height of the gnomon is equal to the length of the floor sector.
Tan (Altitude) = Gnomon Height / Shadow Length
It is interesting to think of the accuracies possible with this instrument - a first time observer, initially, feels rather disheartened due to the uncertainties in estimating the center of the Gnomon Shadow, the blurring between the Umbra and the Penumbra and so on. But, simply because the instrument is built on such a massive scale - the errors induced by these uncertainties are minimal and wonderful accuracies (for educational purposes) can be achieved with this instrument. In the observations undertaken in all of this work, the Altitudes involved have been large enough that refraction corrections in the estimation of the correct Altitude have been ignored.
Some of the results through student observations with the Delhi Ram Yantra, from the 29th of March 2004 which was the first public observation event conducted at the Delhi Jantar Mantar observatory, in modern times, are shown below;
1. Sanskriti School - Teachers – Champa Biswas and Nidhi Kaucha and students
2. Samridhi/Sneh – Samridhi, Lady Irwin Sen. Sec. School and Sneh Kesari Nutan Marathi Sen. Sec. School.
3. Lady Irwin – Rupal Kashyap and Purnima Kashyap
4. DPS Noida – Arun Kumar, Head Physics Department
5. SBV/PBV/KB – Students of SBV Subhash Nagar, Pratibha Vikas Vidyalaya and Krishi Bihar
6. Usha Menon/VS – Usha Menon – Rolls Royce India and Dr. Vinay Sharma of Pt. GLM Sharma Hospital
7. Cheena/Dolcy – Cheena Dang – Polytechnic student and Dolcy Chabra of Imperial Academy school, Indore.
8. KDA/Hansraj/Jindal – Sivaramakrishnan, and Kartik of KD Ambani Vidyamandir, Jamnagar, Gujrat, Archit Babbar of NC Jindal public school, Delhi and Mukul Agarwal of Hansraj Public school, Delhi.
9. SKV – SKV public school, Delhi.
1. Public – Acharya Anand Sagar, Dr. Vinay Kumar, Mangal Singh and others present.
2. Sanat/Vikrant – Sanath Kumar, Nehru Planetarium and Vikrant Narang, Amateur Astronomers Association, New Delhi.
3. Sirius Group – Abhishek Tibrewal, Sapna Tibrewal, Shikha Rao, Shweta Chaurasia.
4. Samridhi/Sneh - Samridhi, Lady Irwin Sen. Sec. School and Sneh Kesari Nutan Marathi Sen. Sec. School.
Some information about an ongoing student project with a collection of a large database of observations with the Ram Yantra of the Delhi observatory, by Megha Rajoria, is here.