Summary of Previous session.F
- An angle is not about two straight lines meeting at a common point.
- Latitude and longitude are angles on the surface of the earth which cannot be measured using that definition or a protractor placed at the center of the earth.
- Angle is the relative length of the arc. Hence a protractor is shaped like a semi-circle.
- Angle(arc) measured relative to the circumference in degrees.
- Angle(arc) measured relative to the radius in radians.
- Indian prime meridian is meridian through Uijaini, Rohtak, Kurukshetra, Lanka (!= Sri Lanka, Its a point on the equator)
- Both angles and time are measured using the Sexgesimal system and can be used interchangeably.
- With respect to a time in the day the sun moves from west to east approximately 1° each day and the moon moves from west to east approximately 13.3° each day.
- The Indian system of time measured is Fully Sexgesimal.
1 day = 60 (ghati = nadi of 24 mins), 1 ghati = 60 pala (a pala 24 seconds), 1 pala = 60 vipala(= 0.4s)
Homework: What is the proof of Thomas Macauly’s “immeasurable superiority” of the west?
(Sorry, no weapons of mass destruction found)
Proof 1 – Crosus conveyed to King Solon that the year was 375 days long
Proof 2 – Roman calendar needed to be corrected and for correction 448 days needed to added that year
Proof 3 – Cesar conquered Egypt and asked them to help correct the calendar.
Proof 4 –
- Egyptians had a fraction (“Eye of Horus” fraction) but Romans didn’t. The Romans could only accept 365 ¼ days which was wrong. Even for this the Egyptians then had 7 months of 30 days alternating with 5 months of 31 days (210+155 = 365 days) plus a leap year system adding an extra day every 4th year.
The above are the symbols for the fractions made to look like an eye.
Proof 5 – Inspite of being given instructions the Roman took 20 years after the Julian calendar reform to understand that system and in these 20 years they did a leap year every 3 years. They counted the first year as year 1 and did the leap year when they reached 4.
One day was removed from February and given to August (Augustus) for this feat.
Proof 6 –
- Roman calendar was adopted as the official christian calendar in the 4th c.(1st council of Nicea)
- Changes to the year-of-the-lord(AD-BC) calendar in the 6th c.
- As a result the date of the equinox slipped by 10 days by the 15th c.
Proof 7 –
- It is necessary to correct it for navigation.
- By this time, the west has learnt a fraction from India via Fibonacci.
- And Introduced in the Jesuit curriculum by Calvius ca in 1572.
- Gregorian calendar reform still use
leap year(hence equinox still does not come on fixed day)
- Leap year every 4 years
- But, not every 100 years
- But, every 1000 years
- Phew! Now the equinox will be correct on an average every 1000 years, but incorrect every year.
What about the smartness of colonized Indians?
- On Maculay’s advice and colonial education we learn to trust the west and distrust anything from India
- We trust Wikipedia
- We trust those who came here for wealth and reduced Indian from one of the richest countries in the world to one of the poorest
- We trust those who killed 50 million Indians through their systematic policies e.g. during the Bengal Famine.
Sidereal day and year.
Indian tradition used sidereal days and the sidereal year. The sidereal day is the time for the earth to make one full rotation about its axis (with reference to a distant star). The sidereal year is the period in which the earth makes one revolution around the sun (with reference to a distant star).
Why is a sidereal day shorter by about 4 minutes than the tropical or civil day?
First, the earth rotates in the same direction as it revolves around the sun. After one full rotation that star is seen again in the same place, say directly overhead. This creates a parallax error due to the closeness of the sun and the star being much further.
Parallax
When you move, a distant object seems to move with you, nearby objects seem to move past you. As you drive the trees will look like they are going to pass you, but the moon looks like it is moving with you.
He gave an example with the experiment to perform with two pens, one at 1 meter and other at 5 meters distance from the eye. Children did the experiment and found there is a relative motion between two objects.
The sun is nearby compared to the star. In time the earth rotated once about its axis. It has also moved around the sun. So, the sun is seen in a different position due to parallax. A little more rotation is needed to bring a point on the earth back to the same position directly nearest to the sun.
How much extra rotation?
The earth is moving around the Sun in approximately 360 days i.e. approximately 1°. When the sun is seen from the earth at the same time every day it will look like it is moving 1° from west to east. As the star is far and does not move as seen from earth in one day the sun moves by approx 1° relative to the star as seen from earth. From earth’s perspective, it also takes 24 hours for the sun to rotate 360 degrees round the earth or 15 degrees in 1 hour. So, it takes approximately 4 min for the earth to rotate to its axis that extra 1°.
That is the approximate difference between the sidereal day and the tropical or civil day.
Venus spins in the other direction as it rotates around the Sun so the Sidereal day there is longer than the tropical day.
Inter day vs Intra day
We watched a demo in which we picked a time of day and moved the dates to see how the moon moves every day at the same time. This helps understand the Inter day vs Intra day movement.
A constellation is a group of stars near the ecliptic (observed path of the Sun). For our scientific purposes these are 30’ apart. In India we had Nakshatras initially; these constellations of Rashi’s came later. There are 12 of these corresponding to the ‘Sun signs’ and are used to see the movement of the Sun (during sunrise).
These are Masha – Aries, Vishuv Taurus, etc. Sankranti (every month) is when the Sun enters a new constellation. The Indian calendar follows a luni-solar system.
Summary
Rashi’s mark a region of 30’ in the sky
Sum moves approximately 1’ in each day
Sun takes on an average 30 days to move from one to the other
Sankranti is when the Sun enters a new Rashi
Nakshatra – are used to measure the movement of the Moon (west to east 13.17’)
Hence they divide the sky in 27 regions in the sky which are 13.33’ apart close to the time it takes the moon to go around the Earth. Covers 1 Nakshatra in 1 day and is considered the sidereal month (actually 27.321582’) hence spends more time in one Nakshatra (Rohini)
Horoscope
Not that you should believe in one, but understand what it has. Has the other circle corresponding to the Nakshatra and Inner circle corresponding to the Rashis.
The Laghu Bhaskara evaluates the angle of the Nakshatras by dividing by 800 minutes. Why 800 minutes? 13’20’ = 13*60’+20’ = 800’
