Calculating Sunrise and Sunset using Surya Siddhantha principles - by Yogesh Tiwari

🌅 Calculating Sunrise and Sunset Using Surya Siddhanta — Ancient Wisdom, Modern Tech

by Yogesh Tiwari

Have you ever wondered how our ancestors, thousands of years ago, calculated the exact time of sunrise and sunset — without satellites, atomic clocks, or weather apps?

The answer lies in an extraordinary astronomical text: Surya Siddhanta. It’s one of the oldest known treatises on astronomy, combining precision with poetic elegance — and yes, it still works!

Today, let’s explore how sunrise and sunset times can be calculated using the logic of Surya Siddhanta — and how modern technology like Python and AI can help simulate it.

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🕉️ What Is Surya Siddhanta?

The Surya Siddhanta is an ancient Indian text on astronomy and mathematics, dating back over 1,500 years. It presents:

• Planetary positions

• Sunrise and sunset timings

• Solar and lunar eclipses

• Time calculation based on celestial motion

Its calculations are geocentric (Earth-based), and it measures time based on the apparent motion of the Sun and Moon, using concepts like desantara, ayanamsa, and declination.

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🌍 How Sunrise and Sunset Are Calculated

The time of sunrise or sunset depends on the following factors:

Factor	Meaning
Latitude	Position north/south of the equator
Declination	Angle between Sun’s rays and equatorial plane
Hour Angle (H₀)	Angular distance the Sun must travel before rising or after setting
Altitude (h₀)	Apparent position of Sun on the horizon (typically –0.833° for sunrise/sunset)

In Surya Siddhanta, calculations are made using spherical trigonometry, usually with tables or mean motions.

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🔢 The Core Formula

Let’s simplify the key formula used for calculating sunrise/sunset hour angle (H₀):

$$\cos H₀ = \frac{\sin h₀ - \sin \phi \cdot \sin \delta}{\cos \phi \cdot \cos \delta}$$

Where:

• $\phi$ = Observer’s latitude

• $\delta$ = Solar declination on that day

• $h₀$ = Apparent altitude of the Sun at sunrise/sunset (~–0.833°)

Once you get the hour angle, convert it into time by dividing by 15 (since Earth rotates 15° per hour).

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🧪 Example: Ujjain on August 4

Let’s calculate sunrise and sunset for Ujjain (23.18°N, 75.78°E) using a Python script.

📌 Inputs:

• Latitude: 23.18°

• Solar declination on August 4: ~17.7°

• Timezone: IST (+5:30)

• Standard meridian: 82.5°E

🖥️ Output:

📍 Location: Ujjain
📅 Date: August 4
🌅 Sunrise (IST): 06:44 AM
🌇 Sunset  (IST): 18:10 PM

This matches closely with actual Panchang and NASA calculations — confirming the ancient accuracy!