Upagrahas (shadow sub-planets)
Gulika, Dhuma, Vyatipata, Parivesha, Indrachapa and Upaketu - the sensitive shadow points, with sign, degree and nakshatra.
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Beyond the nine grahas, classical astrology tracks the Upagrahas - shadow sub-planets that mark sensitive points in the chart. Gulika (Mandi) is the most used, a powerful malefic point; the five Sun-derived chaya grahas (Dhuma, Vyatipata, Parivesha, Indrachapa, Upaketu) refine the reading of affliction and fortune.
Sivayan computes Gulika from the rising sign during Saturn's portion of the day, and the chaya grahas from the Sun's longitude - each with sign, degree and nakshatra.
What you get
Gulika (Mandi)
The strongest malefic upagraha - the ascendant rising in Saturn's portion.
Dhuma
The “smoke” point - discontent and separation.
Vyatipata
The calamity point - sudden reversals.
Parivesha
The “halo” - confusion and illusion.
Indrachapa
The “rainbow” - fluctuating fortune.
Upaketu
The comet point - upheaval, endings and fresh starts.
Common questions
A shadow sub-planet (also called Mandi) - the ascendant rising during Saturn's eighth-portion of the day. It is treated as a strong malefic sensitive point.
By fixed offsets from the Sun's longitude: Dhuma = Sun + 133°20′, Vyatipata = 360° − Dhuma, Parivesha = Vyatipata + 180°, Indrachapa = 360° − Parivesha, Upaketu = Indrachapa + 16°40′.
Gulika needs the birth time (it depends on the ascendant); the chaya grahas only need the Sun, but exact time is recommended.
Mainly to refine affliction analysis - a benefic or house conjunct Gulika is studied carefully, for example.