If you're dreaming about your summer vacation, check out the new travelers' guide from O'Reilly, The Geek Atlas: 128 Places Where Science & Technology Come Alive ($29.99), by John Graham-Cumming. This unique resource covers 128 interesting destinations around the globe where major breakthroughs in science, mathematics, or technology occurred--or are happening now. In this excerpt you'll learn about India's Samrat Yantra, the largest sundial in the world at over 27 meters high. A discussion of the celestial coordinate systems is also included in this excerpt (adapted for the web).
Chapter 24. Jantar Mantar, Jaipur, India
An Enormous Observatory in Stone
In 1728 the Maharaja Sawai Jai Singh II commissioned the building of an observatory as part of the newly founded city of Jaipur. The Jantar Mantar observatory (Figure 24-1) was renovated in 1901 and is now a popular Jaipur tourist attraction and respite from the noise and heat of the city that surrounds it.
Figure 24-1. Part of Jantar Mantar
The Samrat Yantra is the largest sundial in the world at over 27 meters high, and is capable of telling the time, day or night, with an accuracy of about two seconds. Its design is slightly different from that of classical sundials, which consist of a stick (called the gnomon) that creates a shadow and a flat scale on which the time is read. The Samrat Yantra's gnomon is a huge triangle made of local stone. The gnomon's upper face is angled at 27° (the latitude of Jaipur), and the gnomon follows the local meridian, with the highest point pointing to geographical north. The shadow cast by the gnomon falls on a pair of marble-faced curving quadrants on the east and west sides of the Samrat Yantra. The quadrants are curved so that, unlike on a normal flat sundial, the hours are spaced equally apart.
The reason that the Samrat Yantra and the other instruments at Jantar Mantar are so enormous is that Jai Singh wanted to obtain the greatest accuracy possible. Because of the Samrat Yantra's massive size, its shadow can be seen moving at the rate of about 6 centimeters per minute. You can use the Samrat Yantra to tell the time at night by observing the position of a star from one of the quadrants and moving until the star just touches the top of the gnomon.
Another instrument, the Shasthansa Yantra, is essentially a darkened chamber with a pinhole through which the Sun's rays enter the chamber when the Sun is at its zenith. Inside the chamber is a scale that can be used to measure the declination and diameter of the Sun.
The most stunning instrument at the observatory is the Jai Prakash (also known as the Mirror of the Heavens). The Jai Prakash is a bowl-shaped instrument over 5 meters across whose interior is divided into marble-covered surfaces. You can enter the Jai Prakash in the spaces between the interior surfaces.
Suspended in the middle of the Jai Prakash is a metal plate with a small hole in the center for observing stars at night. During the day the plate casts a shadow on the interior of the bowl. At night an observer can find a star through the hole in the plate using a sighting device, and read the position of the star off the interior of the bowl. To make reading positions easy, there are actually two bowls with complementary surfaces and spaces for observers.
Another instrument, the Kapala Yantra, is an earlier, smaller version of the Jai Prakash that consists of a single bowl and lacks the easy access afforded by the spaces added to the later model.
The Ram Yantra consists of a pair of complementary cylinders that are used to measure the altitude and azimuth of celestial objects such as stars. In the center of each cylinder is a pole that has the same height as the cylinder's radius. During the day, the pole casts a shadow that can be used to determine the position of the Sun. At night, celestial bodies can be sighted over the top of the pole, and their positions can be read from the scales set into the floor and walls.
Other instruments are used to calculate the Hindu calendar (the Raj Yantra), locate the 12 signs of the zodiac (the Dhruva Yantra), find the altitude of celestial bodies (the Unnsyhsmsa Yantra), find the angle of any celestial body relative to the Equator (the Chakra Yantra), and observe heavenly bodies that are transiting the local meridian (the Dakshina Yantra). There is also a set of 12 additional sundials (the Rashivalayas Yantra).
When talking about the position of celestial objects, there are two major coordinate systems: the equatorial and the horizontal. Both work on the concept of a celestial sphere. Since the Earth is roughly spherical, it's convenient to think of the stars as being positioned on the inside surface of a sphere sharing the same center as the Earth.
This celestial sphere is used to find the position of any celestial body, and the two coordinate systems work by using spherical coordinates. Spherical coordinates require three pieces of information: the distance to the celestial object, and a pair of angles relative to fixed axes. It's the determination of the two axes that defines the equatorial and horizontal coordinate systems.
The equatorial coordinate system is the most widely used and is based on projecting the Earth's poles and Equator onto the sphere. An imaginary line drawn through the Earth's axis of rotation (through the north and south poles) will intersect with the celestial sphere at the celestial north and south poles. The usual way of finding the northern celestial pole is to locate the star Polaris, which is very close to the imaginary pole; the southern celestial pole is found from the Southern Cross.
The plane that cuts through the Earth's Equator can be extended out to the celestial sphere, creating a celestial equator in line with the Earth's.
The equatorial coordinate system, then, is just a projection of the Earth's latitude and longitude measurements onto the celestial sphere. On the celestial sphere, latitude is called declination and is the angle from the celestial equator; longitude is called the right ascension.
On Earth, longitude is measured from the Greenwich Meridian, but in the equatorial coordinate system it is measured from where the Sun crosses the celestial equator on the March equinox (the Sun crosses the equator again during the December equinox, but going in the opposite direction).
Because the equatorial coordinate system is defined by the celestial equator and a point on it, it does not depend on the observer's location on the Earth's surface. The horizontal coordinate system, on the other hand, depends on the observer's latitude and longitude.
The position of any celestial object in the horizontal coordinate system is given by two angles: the altitude and the azimuth. The altitude is the angle of the object from the observer's horizon. An altitude of 0° indicates that the object is on the horizon, and an altitude of 90° indicates that the object is directly overhead (this is called the zenith).
The azimuth is the angle from a line parallel to the horizon that points due north. An azimuth of 0° indicates that the object is due north; 180° means that it is due south.
The horizontal coordinate system has the advantage that it is easy to observe--just find due north and the horizon, and you can determine the altitude and azimuth. Its great disadvantage is that it changes over time (as the Earth rotates) and from place to place.
The instruments at Jantar Mantar use both coordinate systems, and the Kapala Yantra can be used to convert between them.
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