Upagraha
In Jyotiṣa or Indian astrology, the term Upagrāha (Sanskrit: उपग्रह) refers to the so-called "shadow planets" (Sanskrit: छायाग्राह, "chāyāgrāha") that are actually mathematical points, that are used for astrological evaluation. Upagrāha is a generic term used for two distinct and different calculations. One type of Upagrāha called Aprakāśa (अप्रकाश) is calculated from the degree of the Sun. Another type is more generally called Upagrāha or Kālavelā (कालवेला) is calculated by dividing duration of diurnal sky (from sunrise to sunset) or the duration of the nocturnal sky (from sunset to sunrise) into eight parts. The classic writers like Parāśara , Varāhamihira and later writers like Vankatesa Śarma, author of Sarvartha Chintamani, all classify the Upagrāhas in various ways. Overview. The Vedic astrology is primarily based on the calculation of mathematical points. For instance, the "Yoga", also referred to as the fifth part of Panchangam, is the sum of the combined longitudes of the Sun and Moon. Specifically, Upagraha is based on the longitude of the Sun so that astrological insights involving it needs the calculation of the sun's path in relation to other planets. For example, "Rāhu" and "Ketu" are determined according to the intersection of the sun and  moon's paths in the sky. This serves a number of purposes and one of the most important of these is the determination of the power wielded by the "upagraha" to provide benefit or harm. For example, an "upagrāha"'s interaction with "Dhūma" will result in excessive heat, risks of fire, and mental anguish. Mantreśvara in the 25th chapter of his Phaladīpika deals with the nine traditional "upagrāhas"; the nine "upagrāhas" are – "Māndi" (मान्दि), "Yamakaṇṭaka" (यमकण्टक), "Ardhaprahāra" (अर्द्धप्रहार), "Kāla" (काल), "Dhūma" (धूम), "Vyatipāta" (व्यतीपात), "Paridhi" (परिधि), "Indradhanu" (इन्द्रधनु) and "Upaketu" (उपकेतु). Gopsh Kumar Ojha clarifies that "Māndi" is "Gulika" (गुलिक ). With the exception of "Yamakantaka" the rest eight "upagrahas" are malefics and produce bad results. "Yamakantaka" is powerful in conferring benefits same as Jupiter but the other eight have evil influences in the "bhavas" (houses) they are found to occupy. Aprakāśa Upagrāha calculation. The resulting calculations will always leave Dhūma in opposition (180°) to Indracāpa and Vyatīpāta in opposition to Pariveṣa. All the Aprakāśa Upagrāhas are always in a fixed distance from the Sun. Kālavelā Upagrāha calculation. Mapping the Kālavelā Upagrāha by Graha. The table below shows how the five Kālavelās correlate to five of the Grahas ("Su" for  Sun, "Ma" for Mars, "Me" for Mercury, "Ju" for Jupiter, "Sa" for Saturn). Use this abbreviation of the Grahas to find the index of the 1/8th part of each Kālavelā in the daytime and nighttime tables above. If the intention is to calculate Kāla, use "Su" (Sun) in the tables above, if Gulika, use "Sa" (Saturn) to identify the index of the part sought. The calculation steps below involve calculating units of time. In the Indian classics Ancient Indian units of time (kāla vyavahāra) were used, but modern units (24-hour day) can be used as well. Rising time of  Upagrahas. "Māndi’s" rising is got by firstly finding out the duration of day and night; if the duration is equal i.e. of thirty "ghatis" each (one ghati=24 minutes), "Māndi" would rise at the end of "ghatis" 26 on Sunday, at the end of "ghatis" 22 on Monday, at the end of "ghatis" 18 on Tuesday, at the end of "ghatis" 14 on Wednesday, at the end of "ghatis" 10 on Thursday, at the end of 6 "ghatis" on Friday, and at the end of 2 "ghatis" on Saturday. In the case of "night-births" the 5th of that particular  weekday will have to be considered, and if the day and night durations vary then the rising of "Māndi" will have to be altered proportionately. The rising times of "Kala" during day-time on weekdays are in order at the end of "ghatis" 2, 26, 22, 18, 14, 10 and 6; those of "Yamakantaka" are at the end of "ghatis" 18, 14, 10, 6, 2, 26 and 22, and those of "Ardhaprahar" are at the end of "ghatis" 14, 10, 6, 2, 26, 22, 18. "Dhooma" is got by adding 4 signs 13 degrees and 20 minutes to the Sun ’s latitude; "Vyatipata" is got by subtracting the figures for "Dhooma" from 12 signs; "Paridhi" is obtained by adding six signs to the figures for "Vyatipata"; "Indradhanu" or "Kodanda" is got by subtracting "Paridhi" from 12 signs; and "Upaketu" is got by adding 16 degrees 40 minutes to "Indradhanu". The simpler method for determining "Māndi’s" rising sign is - For day born, the duration of the day ("Dinamāna") divided by 8 gives eight parts each part governed by a planet; the first part is ruled by the day-lord. For night born, the first part is ruled by the 5th  planet in the given order; the sign rising in the east in the part ruled by Saturn is "Māndi’s" rising sign. General effects. Mantresvara tells us:- He further clarifies that "Gulika", which is Saturn in effect, is more powerful in giving bad results, the rest produce half of the evil it produces. If "Gulika" ("Mandi") is found situated in the "Janma Lagna" then the person will be a thief, hot-tempered, cruel, disrespectful, unintelligent, uneducated, heavy eater, not stoutly built, not long-lived, have defective eyesight and no sons. Situated in the 2nd house, "Gulika" makes one harsh in  speech, misbehaved, quarrelsome, unreliable, unreasonable and illogical in thought and deeds, and suffer from want of wealth. If "Gulika" is in the 3rd house the person will be arrogant, hot-tempered, greedy, a loner, fearless, impervious, a show-off who derives no happiness through brothers. The 4th house "Gulika" makes one devoid of relatives and friends, devoid of wealth and conveyance. If "Gulika" is in the 5th house the person will be evil-minded and evil-tempered, unsteady and short-lived; if it is in the 6th house then one will be fond of the occult and the mysterious, brave , victorious and blessed with a very able son. If "Gulika" is in the 7th house the person will be quarrelsome, unfriendly towards all, envious, possess little knowledge and understanding and much married. "Gulika" situated in the 8th house makes one short-statured with a defective face, appearance, eyesight and speech. The 9th house "Gulika" does not give an able father, guide or teacher or son; if it is in the 10th house then the person engages in evil and unworthy deeds and is not generous. The 11th house "Gulika" gives happiness, a commanding over-bearing personality and good sons. "Gulika  occupying the 12th house makes one spend recklessly, lose wealth and suffer poverty. The rising sign in the Janam lagna" will be a trikonasthana counted from the sign occupied by "Gulika" or the navamsa occupied by "Gulika". "Gulika" in conjunction with the Sun indicates that the father will be short-lived, in conjunction with the Moon proves harmful for mother, in conjunction with Mars makes brothers unfortunate and unhelpful and separation from brothers, in conjunction with Mercury it makes one a fool or mentally ill, in conjunction with Jupiter, unscrupulous, in conjunction with Venus it makes one seek women of  ill-repute, in conjunction with Saturn it makes one suffer many calamities, ailments, leprosy and be short-loved, and in conjunction with Rahu or Ketu gives infections and diseases and imbalance. If a person is born with "Gulika" situated in "Tyajyakaala" i.e. in "Vishaghati" or "Vyatipata", "Vaidhrti", "Kulika", "Ardhyaama", "Paatayoga", "Vishkumbha yogas" or "Bhadrakarana", "Kshya-tithi" or "Vrddhi-tithi", the person even though born in a royal family will remain a daridra and a beggar. The planet in conjunction with "Yamakantaka" and the "bhava" occupied by it flourish, they give good results. "Ardhaprahār" situated in benefic vargas in the "bhava  that has gained more benefic bindus" in the "Ashtakavarga" gives very good results. The rest produce evil results. The good or bad indicated by these "Upagrahas" is experienced during the course of the dashas of the lords of the "bhavas" they happen to be in and according to the status of their dispositors. If the dispositor of "Gulika" is in a "kendra" or a "trikona" vested with requisite strength in own or exaltation or friendly sign then one possesses a pleasing personality, is popular and famous and enjoys the benefits of Raja yoga, he becomes a powerful ruler. The "kendras  and the trikonas" not occupied by "taragrahas" are indicative of a turbulent life; the "chayagrahas" tenanting the "kendras" in particular cause immense pain. Rectification of rising sign in lagna. Kalidasa in his Uttara Kalamrita recommends the use of "Mandi" for the purpose of Lagna-shuddhi. He states – find out the "rasis" and the "navamsas" occupied by "Mandi" and the Moon, the rising lagna at the time of birth will be in the sign occupied by "Mandi" or the Moon or in the 7th sign or in the 5th or in the 9th from these two or from the "navamsa" occupied , whichever is stronger.