Basics of Jyotish: sidereal vs tropical
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Short answer: Vedic astrology measures planets against the fixed stars (sidereal zodiac). Western astrology measures them against the equinox (tropical zodiac). The two zodiacs have drifted apart by about 24 degrees today, which is why your Western sign and your Vedic rashi are often different.
Two zodiacs
The tropical zodiac starts at the spring equinox point. The sidereal zodiac starts at a point fixed against the stars. The two starting points are separated by the ayanamsa, which grows slowly over time because of the precession of the equinoxes.
What the ayanamsa is
The ayanamsa is the angle between the tropical and sidereal zero points on the ecliptic. To get a sidereal longitude, subtract the ayanamsa from the tropical longitude. Different schools use different values; the calculator must state which one it uses.
Which ayanamsa joshiastro uses
All calculations use the Lahiri (Chitrapaksha) ayanamsa, the standard used by the Indian government's national calendar. The exact value and formula are on the method page.
Where to go next
Try the daily panchang to see the sidereal Moon's nakshatra for today, then read about the 27 nakshatras (coming soon).
[Source to be added before publishing: exact text, chapter and edition.]