# What are the Mathematical Algorithms/Formulas behind hindu Sunrise and Sunset Calculations?

There are differences between Astronomical Sunrise/Sunset calculation and Hindu calendar Sunrise/Sunset calculations. The astronomical algorithms to calculate the sunrise/sunset can be found over the internet. Here is a calculation that I followed to correctly calculate the astronomical sunrise/sunset time.

Sunrise and Sunset algorithm

In the Hindu calendar, sunrise/sunset is considered when the center of the Sun disk is at the horizon, also the refraction effect must be considered.

Sunrise on the Hindu calendar = Astronomical Sunrise + Time taken by the Sun to rise half of its diameter + Time taken by the Sun to rise further to neutralize the refraction effect.

Similarly, Sunset = Astronomical Sunset - Time taken by the Sun to set half of its diameter - Time taken by the Sun to set further to neutralize the refraction effect.

I am able to derive the Astronomical Sunrise/Sunset, but how to do the calculation for the following?:

1. Time taken by the Sun to rise half of its diameter.
2. Time taken by the Sun to rise further to neutralize the refraction effect.
3. Time taken by the Sun to set half of its diameter.
4. Time taken by the Sun to set further to neutralize the refraction effect.
• There is one misconception. The effect of diffraction causes the sun to appear earlier, so you must subtract time to account for the refraction at sunrise, and add time at sunset. The calculations you link to already account for refraction. – James K Aug 2 '20 at 13:07

## 1 Answer

In the linked algorithm, the "zenith" is the position of the sun at sunrise. This is the number you need to change.

If you want to calculate the time when the top of the sun reaches the horizon you use the "official" zenith of 90⁰50' This is intended to account for refraction and should estimate the time when the sun first appears over the horizon.

Since the sun in 30' across, if you want the time when the centre of the sun is on the horizon, just subtract 15' ie use a zenith of 90⁰35' (90.583 degrees)

It isn't possible to be more accurate as the amount of refraction varies with the weather. But this should give values that are correct to the minute.

• ....Yes, that is what I meant to say! – James K Aug 2 '20 at 15:51
• "Zenith" in the linked article is a confusing shorthand for zenith angle, the angle between the Sun and the zenith. – Mike G Aug 3 '20 at 1:40
• Source Positional Astronomy: So sunrise and sunset actually occur when the Sun has altitude -0°50'. (34' for refraction, and another 16' for the semi-diameter of the disc). To get the result, I negated 0⁰50' (0⁰34' + 0⁰16') from 90⁰50'. So, I have taken the zenith = 90⁰ to consider the diameter of the sun at the horizon and to prevent the effect of refraction. – Prith Aug 14 '20 at 6:57