# Day – 2 C. K. Raju session

-Preethi and Sanjeev

C.K.Raju started the session with a short summary of yesterday’s session.

Models of Christian Chauvinist History:

He explained that many people wrongly mix up Indian astronomy with astrology, which is often seen as a pseudoscience.  He highlighted that India had a scientific theory that the Earth is a spherical body that floats freely in space without any physical support. This was important for a good calendar and needed for understanding the concept of day and other observed phenomena. He pointed out that this concept was known in India long before it became widely accepted among Europeans. That Indians opposed the false claim in religious texts that the earth was supported by a tortoise or Sheshnag, etc.

In contrast with the Europeans who did not challenge the Bible that the earth was flat. He explained the Greek belief that the Atlas holds up the Earth. He uses this as an example of how ancient Greek ideas were more superstitious than scientific.

He mentioned  that Indians were using trigonometry as early as the 5th century. The accuracy of these trigonometric values were needed for accurate calculation of the Earth’s radius as well as for navigation.

The European scholars took precise trigonometric values from Indian sources, but were unable to use them effectively and did not give proper credit to where they received this information.

Position and Motion on a Sphere

As we are talking about a spherical object we need to learn about the position and motion on a sphere. Motion refers to the change in position of an object over time. Position refers to where the small object (“ a point”) is on the sphere. Since space is also spherical we would also need this for the position of a star, sun, moon, etc.

He explained that both Latitude and Longitude are angles that are measured in degrees on the sphere.

What is angle?

He enquired on what is the definition of an angle. An angle is defined in NCERT Class 6 as two rays which originate from a common point. He asked questions like why an angle is denoted by putting an arc between two straight lines? Why are we using a protractor to measure an angle? Why is the protractor a semi-circle? If you had protractors of different sizes then will they measure the same angle?

We are only taught to measure angles only on paper. Then how would we measure these angles of latitude and longitude made by imaged straight lines at the center of the earth? We would need to make holes in earth and measure the angle it made at the Earth’s core?

He gave the definition of the angle in the Hindi text book and pointed out that it was quite complicated, because this is not how angle was measured in India and the language lacked the terms needed. Instead he stated that angle is defined as a ratio of arc length to either the circumference (degrees) or to the radius. When an angle is measured relative to the radius of the circle, it is measured in radian. When the circumference is divided into 360 pieces (or more) then the length can be measured by how many of these pieces are covered by the arc giving the angle in degrees. The circumference and radius of the circle are proportional i.e. they track with the size of the circle. Hence the measured angle does not depend on the size of the protractor.

This allowed for making measurements on the surface of the earth rather than dig inside :). This is still not an easy task as it involves long curved distances. Further, to convert these distances into an angle of the longitude and latitude, we need to know the circumference of the earth.

He explained that the earth rotates about an axis. The point which the axis passes through the earth is called North and South poles. A great circle is a circle whose center is the same as the center of a sphere. On earth, a circle through poles is a great circle. All longitudes are great circles. In the latitudes the only great circle is the equator. He explained to the children with an orange cut in the center to show the largest circle will be at the equator or center.

Sexagesimal system for times and angles

We were taught that 1 day consists of 24 hours, 1 hour consists of 60 minutes, and 1 minute consists of 60 seconds. But the Indian system is full of sexagesimal, a day consists of 60 ghati(24 mins) , 1 ghati consists of 60 pala, 1 pala of 60 vipala, etc.

Likewise, an angle consists of degree, 1 degree is 60 minutes, 1 minute is 60 seconds, 1 second is 60 thirds.

12°34’24’’13’’’ = 12 degrees, 34 minutes, 24 second, 13 thirds

When we measure in the stop watch it no longer uses a consistent sexagesimal system as the minutes and seconds are in sexagesimal, but after that it uses 100 divisions.

What is a day?

A simple definition of a day is a time from sunrise to sunrise. More precisely, this is a civil day. A simplest calendar would be to count civil days (Robinson Cruso calendar) from a given starting point (epoch).

In Indian tradition, the usual starting day or epoch is the start of kaliyuga. (This is the astronomy Kaliyuga, time when all planets were in conjunction i.e. the first point of aries that occurs rarely. The Maya calendar also begins almost at the same epoch. In the Gregorian calendar, kaliyuga, starts in 3102 BC = -3101 CE (The difference of one year is because the christian calendar does not have a zero or negative number). The Mayan calendar starts at 3112 BC. The difference of only 10 years in 3000 years.

How do we know the starting date?

The start of kaliyuga is -3101 CE. The difference of one year is because the christian calendar does not have a zero or negative number.

Ahargana and Julian days

The notation of ahargana (day count) is a very ancient notion in India. E.g. It is found in the Surya Siddhanta. But in western thought the corresponding notion of julian days is very recent. It appeared in the west in 16th c. In the 16th century, Jesuit missionaries were based in kochi. We collected knowledge from Indian mathematics and astronomy texts with the help of local Syrian Christians. The translating and sending this knowledge back to Europe to prominent people such as christoph clavius, Tycho Brahe, Julius Scaliger.

In the 16th century, Ahargana was taken to Europe and Christianized as the Julian day number. This was so named by Julius Scaliger in 1583 a contemporary of Clavius after his father’s name, Julius Caesar Scaliger.

Julian day number is a Christianized ahargana

The only difference from Ahargana is the choice of the start day or epoch which was selected as 1 Jan 4713 BC. The day that the universe began as per Christian belief.

The only difference between the Kali Ahargana number (KAN) and the Julian day number(JDN) is a constant due to different starting epochs,

KAN = JDN – 588465.54The (tropical) year, summer and winter

Sun rarely rises from the exact east. Only in two days of the year it will rise exactly in the east. The sun moves north 23.44° then moves south 23.44° east. The end of the movement, the exact two instants when the sun just stops moving and reverses direction of movement are called solstices (end of movement).

There are two solstices, in the northern hemisphere the summer solstice or longest day and the winter solstice or shortest day.

Daylight duration varies with the latitude. Aryabhat had commented that Gods (assigned to the north pole) and Asuras (assigned to the south pole) see the sun after it rises for half a year. Divine day is one year of mortals. 1 Divine year is 360 years.

In summer, when the north pole is pointing towards the sun, the day in the northern hemisphere are longer and nights are shorter. In winter the situation is reversed, days are short and nights are long. In the southern hemisphere the situation is the opposite, because summer and winter are the opposite of those in the northern hemisphere.

Equinoxes

At sunrise the position of the sun keeps moving from east to 23.44° north and  22.44° south throughout the year. The two instants exactly midway between the two solstices are called equinoxes. Nox means Night. Equinox indicates that the day and night are the same length (at the equator). The vernal equinox marks the beginning of warmer season in the northern hemisphere, while the autumn equinox marks the beginning of the cool season, in the northern hemisphere.

The earth (while revolving around the sun) is also rotating around its axis, which axis points to the north celestial pole, a point in the sky near the pole star, currently polaris.

Summer and winter in the southern hemisphere are the opposite of those in the northern hemisphere. Hot and cold seasons are not due to distance from the sun, but the tilt of the earth.