The below is only for information. Parts of it should not be construed as any kind of prognostication on our part.
The great Hindu naturalist Varāhamihira describes various kinds of planetary conjunctions or grahayuddha-s in his Brihatsaṃhitā (chapter 17) thus:
yuddhaṃ yathā yadā vā bhaviṣyam ādiśyate trikālajñaiḥ |
tad vijñānaṃ karaṇe mayā kṛtaṃ sūrya-siddhānte ||
The time and nature of planetary conjunctions (graha-yuddha) can be predicted by astronomers. That science has been [taught] in astronomical work composed by me [based on] the Sūrya Siddhānta. [Here he is referring to his Pañcasiddhānta]
viyati caratāṃ grahāṇām uparyupary ātma-mārga-saṃsthānām |
ati-dūrād dṛg-viṣaye samatām iva samprayātānām ||
The planets revolve in space in their respective orbits that are positioned one above the other. [However,] due to their great distance, when observed they appear as if revolving on the same surface (i.e. the sky). [Here, Varāhamihira clarifies that even though it is called a yuddha how it must be understood in the scientific sense.]
āsanna-krama-yogād bheda+ullekha+aṃśu+mardana+asavyaiḥ |
yuddhaṃ catuṣprakāraṃ parāśara ādyair munibhir uktam ||
In the order of the proximity of the conjunct planets: 1. bheda (occultation); 2. ullekha (near tangential contact); 3. aṃśumardana (the grazing of rays); 4. asavya (apart) are the four types of conjunctions described by Parāśara and other sages.
bhede vṛṣṭi-vināśo bhedaḥ suhṛdāṃ mahākulānāṃ ca |
ullekhe śastra-bhayaṃ mantrivirodhaḥ priyānnatvam ||
In the bheda conjunction, there is drought and friends and persons of great families become enemies; in the ullekha conjunction there is fear of weapons, a rebellion of ministers, but there is [abundance of] good food.
amśu-virodhe yuddhāni bhūbhṛtāṃ śastra-ruk-kṣud-avamardāḥ |
yuddhe ca+apy apasavye bhavanti yuddhāni bhūpānām ||
In the aṃśumardana conjunction, kings go to war and people are afflicted by weapons, disease or famine. In apasavya (asavya) conjunction, rulers go to war.
ravir ākrando madhye pauraḥ pūrve +apare sthito yāyī |
paurā budha-guru-ravijā nityaṃ śītāṃśur ākrandaḥ ||
The Sun in mid-heaven is [called] ākranda; paura in the east and when stationed in the west a yāyin. Mercury, Jupiter, and Saturn are always paura. The Moon is always ākranda.
ketu-kuja-rāhu-śukrā yāyina ete hatā ghnanti |
ākranda-yāyi-paurān-jayino jayadāḥ sva-vargasya ||
Ketu, Mars, Rāhu and Venus are always yāyin-s. These are either struck (defeated) or strike (win). Depending on whether the ākranda, yāyin or paura losses or wins the objects associated with of their respective categories [suffer or prosper].
paure paureṇa hate paurāḥ paurān nṛpān vinighnanti |
evaṃ yāyy ākrandā nāgara-yāyi-grahāś ca+eva ||
A paura defeated by another paura, results in city-dwellers and kings being smitten. Similarly, if a yāyin or an ākranda is defeated by another or respectively by a paura or yāyin [the objects associated with them are affected accordingly].
dakṣiṇa-diksthaḥ paruṣo vepathur aprāpya sannivṛtto +aṇuḥ |
adhirūḍho vikṛto niṣprabho vivarṇaś ca yaḥ sa jitaḥ ||
That [planet] which is positioned to the south, at a cusp, showing rapid variability of brightness, goes retrograde immediately after conjunction, with the smaller disc, occulted, gets dimmer or changes color is said to be defeated.
ukta-viparīta-lakṣaṇa-sampanno jayagato vinirdeśyaḥ |
vipulaḥ snigdho dyutimān dakṣiṇadikstho +api jayayuktaḥ ||
If the planet appears endowed with the appearance opposite of the above-described it is deemed the victor. So also that which appears bigger, smooth in the motion or brighter is considered the winner even if stationed to the south.
dvāv api mayūkha-yuktau vipulau snigdhau samāgame bhavataḥ |
tatra +anyonyaṃ prītir viparītāv ātmapakṣaghnau ||
If both are endowed with bright rays, growing larger and smooth moving it becomes a samāgama conjunction. There is [consequentially] a conciliation between the objects associated with the two planets; if it is the opposite (i.e. both are small, growing dim, etc) both the associated objects will be destroyed.
yuddhaṃ samāgamo vā yady avyaktau svalakṣaṇair bhavataḥ |
bhuvi bhūbhṛtām api tathā phalam avyaktaṃ vinirdeśyam ||
In cases where it the characteristics are not clear as to whether the conjunction of two planets is in a yuddha or a samāgama conjunction, it is likewise unclear as to what the fruits will be for the rulers.
Thus, Varāhamihira describes the general omenology of planetary conjunctions as per hoary Hindu tradition. This year is marked by a remarkable conjunction of Jupiter and Saturn that will peak as per geocentric coordinates on the day of the winter solstice (December 21, 2020; Figure 1).
This has caused tremendous fear and excitement among those with a belief in such omenology. Even as we were examining the conjunction for purely astronomical reasons, we received one such call from a believer. Hence, we looked up Varāhamihira to see what he has to say. Notably, this conjunction on Dec 21 is the closest since the famous Keplerian conjunction of 1623 CE. Thus, it is definitely an aṃśumardana and nearly an ullekha. From the above, we can see that, as per tradition, it is a grahayuddha of the aṃśumardana type between two paura planets, which prognosticates death from weapons, disease, or famine. Further, it is evident that Jupiter is to the south and it reduces in magnitude as it emerges from the conjunction. So as per the Hindu typology of conjunctions, it is defeated by Saturn (Figure 2).
Varāhamihira further provides specific omenology for the defeat of Jupiter by Saturn (BS 17.19):
bhaumena hate jīve madhyo deśo nareśvarā gāvaḥ |
saureṇa ca+arjunāyana-vasāti-yaudheya-śibi-viprāḥ ||
If Jupiter is beaten by Mars, Madhyadeśa region, kings and cows suffer. [When beaten by] Saturn, the Arjunāyana, Vasāti, Yaudheya, Śibi [peoples] and the Brāhmaṇa-s suffer. [It is noteworthy that one of the used words for Jupiter in the last 2000 years is Jiva. This word is not encountered in the earlier layers of the Sanskrit tradition. It is a loan from Greek, the vocative declension of Zeus, and is one of the marks of the influence of Greek astrology (e.g. the Paulīśa-siddhānta and Yavana-jātakam) on its Indian counterpart.]
It was that latter prognostication that caused the fear in our interlocutor. These conjunctions of Jupiter and Saturn have an interesting geometric feature: the great trigon. For superior planets one can approximately calculate the frequency of conjunctions thus: Let be the periods of revolution of the two planets and . Then will be the mean angular speeds of the two planets respectively. The difference in their speeds would be:
Hence, the time the faster planet will take relative to the slower planet to complete one revolution (i.e. catch up with it again) will be:
This will be the duration between successive conjunctions. The period of Jupiter is 4331 days of Saturn is 10747 days. Hence, . Thus, the Jupiter-Saturn conjunctions will repeat approximately every 20 years. One can see that the next two conjunctions will occur with respect to the original one at:
Thus, the three successive conjunctions will trace out an approximate equilateral triangle on the ecliptic circle — the great trigon. This trigon caught the attention of the great German astrologer Johannes Kepler, the father of the modern planetary theory in the Occident. He described this in his work the “De Stella Nova in Pede Serpentarii” that announced the discovery of his famous supernova. Since the successive trigons are not exactly aligned, they will progress along the ecliptic (Figure 3). We see that after 40 successive conjunctions it occurs very close to the original conjunction (Figure 3). This amounts to about 290182.4 days (794.4979 years). This is the roughly 800 cycle that Kepler was excited about and thought that he was in the 8th such cycle since the creation of the world (being conditioned by one of the West Asian diseases of the mind).
Figure 3. Progression of the trigons in the cycle of 40
The above formula can also be used to calculate the successive oppositions (when the configuration is Sun–Earth–superior planet) or inferior conjunctions (Earth–inferior planet–Sun) or superior conjunctions (Earth-Sun-inferior planet). We those obtain other interesting patterns. One such is successive oppositions of Jupiter which happen every 398.878 days. Thus, they nearly inscribe a hendecagon on the ecliptic circle (Figure 4).
Now the successive inferior or superior conjunctions of Venus happen every 583.9578 days. Thus, these successive events trace out a near pentagonal star (Figure 5). This comes from the fact the ratio of the orbital periods of Earth to Venus is nearly which is a convergent of the Golden Ratio.
Beyond this, we may also note that the successive oppositions of Saturn nearly inscribe a 28-sided polygon (roughly corresponding to one per nakṣatra) whereas those of Mars nearly inscribe a polygon of half that number (14 sides). The minor planet Ceres nearly inscribes an 18-sided star in the ecliptic circle (Figure 6).