Kepler’s Laws and Sri Rama’s Jataka Chakram

What I am trying to do : is see whether if we use elliptical orbits instead of circular orbits, the velocity variations can explain how the sun could be in Mesha, on a Chaitra Suklapaksha Navami with the moon in  the last pada of Punarvasu. (For a discussion of the problem, please see : A Jatakam almost like Sri Rama’s in 1956 and Casting Sri Rama’s Jataka Chakram!.. If you like astrology, you can also see : Vimsottara Dasas for Sri Rama, but it is not connected to the discussion below.)

ie I am trying to see whether on that day it is possible for the sun and the moon to be separated by less than 93 degrees.

The earth’s velocity of orbit varies, with its position in the orbit. When it is nearer the sun it goes faster. That means to someone on the earth, it looks as if the sun is moving past the background stars faster at this time.

We normally take an average value of 360degrees/365.25days = 0.9856deg/day as the relative angular velocity of the sun with respect to the earth.

But you can see from the Kepler’s Second Law that the sun  appears to move faster when the earth is closer. Similarly, the moon moves slower, in its orbit when it is farther from the earth.

Will this give us a sufficient correction is the question?

Also does it impact ‘tithi’ calculations in anyway?

If a tithi is defined by the degrees of separation between the sun and the moon, then it is the duration of the tithi that will change with orbital velocities, but  not the degree of separation. All modern Hindu Calendars, give us variable tithi lengths. Was this also the same case in Valmiki‘s time? This needs to be ascertained from ancient texts.

Source and Reference for Material Below :

  1. Tithi: The moment of new Moon, or that point of time when the longitudes of Sun and Moon are equal is called ‘amavasya’. The tithi is the time taken by the Moon inincreasing its distance from the Sun by 12 degrees. The complete revolution of the Moon(29.5 days) occupies 30 tithis for 360 degrees. Since the motions of the Sun and Moon are always varying in speed the length of a tithi constantly alters.
  2. One Tithi ends at the moment of time when the angular distance between the Sun and Moon becomes an integral multiple of 12°. In other words, a tithi ends at the same instant of time for all places on Earth and a tithi is not sensitive to the longitude (or latitude) of the region. The moment of Sunrise of course varies with longitude and therefore local time of Moon’s entry into any tithi will differ at different places. For the same reason expunction and repetition of tithis may differ by a day in different longitudes.
  3. Lunation is the time taken by the Moon to complete one revolution around the Earth. The 360o angular path of the Moon in the sky is divided into 10,000 parts and 1 part, the finest possible resolution amounts 2.16 arc min.
  4. When the angular difference between the Sun and Moon is less than +2.16 arc min (measured eastward angle), the Sun and Moon are said to be in conjunction. This moment of time is said to be the amavasya moment or new Moon.
  5. To travel 21,600 min of arc, (360 deg) Moon takes 29.53 (solar) days or 42,480 minutes. So, to travel 2.16 min of arc it takes 4.25 minutes. The Moon remains in this position for approximately 4.25 minutes. This interval defines the accuracy of all astronomical observations in ancient Indian calendar. Since Amavasya (new Moon) lasts for the movement of the Moon from -2.16 to + 2.16 arc min around the Sun, it last for 8.50 minutes only, according to this formulation.

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