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Narada Purana (Jyotisha Selections) · by Vyasa
Chapter 1 · Basics and Panchanga
ज्योतिषमूलं पञ्चाङ्गं च
ग्रहोदयाः प्राणहताः खखाष्टैकोद्धता गतिः ।चक्रासवो लब्धयुती स्वाहोरात्रासवः स्मृताः ॥ १४४ ॥
In the full Narada Purana (Purva Bhaga) this is chapter 54, verse 144.
Multiply a planet's daily motion by the rising asus (4-second units) of its sign. Divide by 1800. Add the result to the asus of the circle (21600). That gives the asus of the planet's own day and night.
Simple meaning: A planet's own day-and-night length comes from its daily motion and its sign's rising time.
त्रिभद्युकर्णार्द्धगुणा स्वाहोरात्रार्द्धभाजिताः ।
A sine rule gives the equator rising points of the first three signs.
स्वाधोधः प्रविशोध्याथ मेषाल्लंकोदयासवः ।
At the equator Aries rises in 1670 asus, Taurus in 1795, Gemini in 1935.
स्वदेशचरखंडोना भवंतीष्टोदयासवः ।
Take off the latitude parts to get local rising times. Cancer, Leo and Virgo add them back in reverse.