But a more convenient method of obtaining the approximate longitudes of the planets geocentrically is by means of the Planetary Geocentric periods. Thus Uranus has a period of 84 years, after which it returns to the same longitude on the same day of the year and will be further advanced in its orbit by 1° 5′. Saturn has a period of 59 years, after which it comes to the same place in the zodiac and will be further advanced by 1° 53′. Jupiter has a period of 83 years, when it is found to be only 4′ advanced upon its former longitude. Mars’ period is 79 years plus an advance of 2° 4′. Mercury’s period is also 79 years, and its advance is 5° 32′. Venus has a period of 8 years, when it is further advanced in the zodiac by 1° 32′.
For the calculation of the approximate geocentric longitude of the major planets these periods are very useful, but are of less value in regard to the minor planets Venus and Mercury.
Suppose I want the longitude of Uranus in the year A. D. 827. I have its longitude on the first of January, 1912, in Capricorn 28° 17′. Then 1912-827 gives 1,085 years, which being divided by the period of Uranus (84 years), yields 12 periods and 77 years. The increment for 1 period being 1° 5′, that for 12 will be 13°, and 77-84ths of 1° 5′ will be another degree, making 14 degrees. As the date is anterior, this amount must be subtracted from its longitude on the first of January, A. D. 827, and in effect we obtain Capricorn 14 degs. 17 mins. as the longitude of Uranus on the first of January, 827, as seen from the Earth.
For the purpose of determining the effects, if any, due to the presence of a planet in its Aphelion, Perihelion, or Node, the following values are given for the year 1800 A. D.:
| Planet. | Aphelion. | Perihelion. | Node. | ||||||
| S. | ° | ′ | S. | ° | ′ | S. | ° | ′ | |
| Mercury | 8 | 14 | 21 | 2 | 14 | 21 | 1 | 15 | 57 |
| Venus | 10 | 8 | 36 | 4 | 8 | 36 | 2 | 14 | 52 |
| Mars | 5 | 2 | 23 | 11 | 2 | 23 | 1 | 18 | 1 |
| Jupiter | 6 | 11 | 8 | 0 | 11 | 8 | 3 | 8 | 24 |
| Saturn | 8 | 29 | 4 | 2 | 29 | 4 | 3 | 21 | 57 |
| Uranus | 11 | 17 | 21 | 5 | 17 | 21 | 2 | 12 | 51 |
| Neptune | 7 | 12 | 22 | 2 | 12 | 22 | 4 | 9 | 35 |
The longitudes of the Aphelia are increased in 100 years by the following quantities: Neptune, 1° 25′; Uranus, 1° 28′; Saturn, 1° 50′; Jupiter, 1° 35′; Mars, 1° 52′; Venus, 1° 43′; Mercury, 1° 34′. These quantities are additive for years after 1800, and subtractive for years before that epoch.
In the present state of astronomical science it is not certain that these values are absolutely correct. Calculated from the Tables of Kepler, the differences are only slight, but still sufficient to make considerable error in testing for exact conjunctions or ingresses.
Lilly, who predicted the Great Plague and Fire of London some years previous to the event from the ingress of the Aphelion of Mars to the sign Virgo, evidently made use of the Rudolphine Tables constructed by Tycho and Kepler, and according to these the ingress took place in 1654, while according to more modern Tables it did not take place until 1672. It is probable, however, that the positions of the Aphelia here given will be sufficiently close for all practical purposes.
A word or two may now be said regarding the periodic conjunctions of the planets.
As will be seen from the periods given, five periods of Jupiter are nearly equal to two of Saturn. It is found that the two planets form their conjunctions every 20 years. Thus there was a conjunction in Virgo in 1861, another in Taurus in 1881, and another in Capricornus in 1901. The next will be in Virgo in 1921. The two planets are thus now forming their successive conjunctions in the Earthly Tripicity; but in 1981 will make their mutation conjunction by falling together in the Airy sign Libra.