Chapter 2: PREDICTABLE NON-PERIODIC EVENTS-PART I Chapter 2: PREDICTABLE NON-PERIODIC EVENTS-PART I
INTRODUCTION
As inferred in chapter one, long term planetary orbital stability helps explain why predictable periodic astronomical events occur. One body's interaction with another is some even (or nearly so) period multiple of the other; another words some degree of commersurability exist. If for example, Jupiter returns to the same part of the sky in thirteen years and Saturn in twenty nine, they meet up again on average every twentieth year. Another shared characteristic is that these events are generally observable over several days or weeks and are visible over large regions at the same instant of time. However, predictable but non-periodic planet-moon, planet-star, planet-planet, and moon-star alignments and configurations do not follow this regularity. Planets may occult the same star only a few times because of the star's rapid proper motion. Over the long haul, even gravitational perturbations will affect planetary orbital stability. When considering lunar occultation of planets, although more than 200 events occur on average per century per planet, many are not visible. Some occur during daylight while others are visible over small geographical area since the events may not be central to the moon's equatorial axis. Still other types of events, such as certain planet-on-planet occultations will occur several times over a relatively short period only to return after gaps of several millennia.
Moon-on-Star Occultations
The large apparent size of the moon and it's ability to complete one revolution in under a month (moves its own diameter in about one hour), enables it to occult many stars. Using the 19 year Metonic Cycle as a convenient interval since the moon nearly repeats its position and phase in the sky, semi-regular patterns emerge. Table 2.1 shows the 19 year average occurrences of worldwide occultations verses star magnitude. Considering the effects of daylight, the star's low altitude, and cloud cover, the frequency of viewing an occultation is significantly less; more than 50 percent less at a given locale. The magnitude limit for a confident sighting of a star to be occulted depends strongly on the telescope diameter, lunar phase and less on the magnification. These factors should not be confused with general visibility through binoculars which improves by multiplying the aperture by the power. One should also remember that the number of stars that are naked-eye at the zenith depends on time of year, local hour and one's latitude. On the other hand, the moon can only occult stars that lie within an average of five degrees nine minutes of the ecliptic plane.Table 2.1: Moon-Star Occultation Frequency by Magnitude Star Mag. Frequency Star Mag. Frequency >=1 43.6 days >=5 16.6 hours >=2 23.0 days >=6 5.52 hours >=3 6.38 days >=7 1.92 hours >=4 2.26 days >=8 0.72 hour
The average worldwide frequency of lunar-stellar occultations based on a 19 year average. Bright star occultations occur during occultation-seasons; when several years may elapse without an event. LOCAL
In the United States, during the period 2000-2079, 6.2% to 7.2% of stars brighter than 1st magnitude which are occulted will be observable with the Sun below the horizon (-1 to -14 degrees). The percentage drops 0.5% if considering when the Sun is 15 degrees or more below the horizon. However, if stars brighter than 2nd magnitude are considered, the average frequency of favorable occultations drops to 4.3% overall. The reason this happens is because during this period, several star occulted between 1st and 2nd magnitude occur more often but under less favorably conditions than the brightest three stars; Antares, Aldebaran, and Spica. In general, over the long term, one could safely assume that a higher percentage of stars are favorably occulted as fainter stars are considered.
Moon-on-Planet Occultations
LOCAL
During the period 2000-2099, the United States will experience about 39 favorable moon-planet occultation or 3.7% of all events (excluding Mercury, Neptune and Pluto). However, 20 events will occur when the moon is greater than 80% luminated. Not all locales will be able to view both the disappearance and reappearance of the planet. No visible occultations occur in the US during these long gaps: 2005-2019, 2049-2057, and 2061-2069. Based on the period 2000-2499 A.D., the worldwide number of viewable occultations per century include: MERCURY: 0 to 3 events; VENUS: 0 to 5 events; MARS: 3 to 12 events; JUPITER: 2 to 15 events; and SATURN: 5 to 15. Only Mercury occultations are readily visible from the tropical latitudes in dark skies. Most bright planets daylight occultations can be visible with some aid, thus increasing observable events by several factors. Bright planet lunar occultations (Venus-Saturn) occurring worldwide in daylight and in dark for the next 500 years and a histogram showing the number of annual events.Moon-Mercury Occultations 153 to 171 Days
Interval when the Moon occults Mercury based on the period (2000-2499). Average worldwide interval between occultations is 162 days. Best visible from the tropics a few times per century.Moon-Saturn Occultations 159 to 176 Days
Interval when the Moon occults Saturn. Average worldwide interval (based on 500 years) between occultations is 168 days. Per calendar year, zero to 13 occultations can occur. Annual gaps between occultations can range from two to five years. For events occurring for the next +100 years. For a histogram of events per year . Moon-Venus Occultations 165 to 192 Days
Interval when the Moon occults Venus. Average worldwide interval (based on 500 years) between occultations is 177 days. Per calendar year, zero to six occultations can occur. For events occurring for the next +300 years. For a histogram of events per year. Moon-Jupiter Occultations 162 to 193 Days
Interval when the Moon occults Jupiter. Average worldwide interval (based on 500 years) between occultations is 180 days. Per calendar year, zero to 12 occultations can occur (a total of 13 consecutive moon encounters are possible). Annual gaps between occultations can range from one to three years. This happens because during its 11.86 years traversing the ecliptic, Jupiter intersects the rotation of the line of possible lunar nodes for a period of 7.24 years; allowing for two periods of occultations. The time interval between the occultation periods averages 3.62 years. For events occurring for the next +300 years. For a histogram of events per year. Compare these charts with Uranus'. and for a histogram of events per year here.Moon-Mars Occultations 174 to 188 Days
Interval when the Moon occults Mars. Average worldwide interval (based on 500 years) between occultations is 180 days. Per calendar year, zero to five occultations can occur. No annual occultation occur on average about once in 15 years.
Planet-on-Star Occultations
For more detailed list of events with stars as faint as 12th magnitude from 1950-2050 AD. LOCAL
During the next 500 years, favorable planet-brighter star occultations (Sun is below the horizon) for parts of the North America will include about 36 events or 13 percent of the total as noted in Table 2.2, page 8 and Chart 2-15. The frequency nearly triples if daylight events are included (although nearly impossible to view). Events usually last less than 10 minutes.Table 2.2: Planet-Star Occultations Frequency by MagnitudeWorldwide (AVERAGE) years per event >=8th >=7th >=6th >=5th >=4thMercury: 41.6 YearsVenus: 21.7 YearsMars: 8.47 Years 29.4 Years 167 Years Jupiter: 4.62 Years 14.3 Years 62.5 YearsSaturn: 18.5 Years 50.0 Years 250 YearsUranus: 71.4 Years 167 Years 250 Years 250 YearsNeptune: 167 Years 500 Years
The average frequency of planet-star occultations by magnitude. Missing data indicates the event is either very rare or not readily visible.
Mercury:
During the period (2000-2499 A.D.), 12 occultations to 4th magnitude. All events invisible or very difficult worldwide due to the proximity of the Sun.
Venus:
During the period (2000-2499 A.D.), 23 occultations to 4th magnitude, of which 5 are to 2nd, and 3 are to 1st. For parts of North America, two occultations will be readily visible in 500 years and occur on 12 Aug 2420 (3.5) and 19 Nov 2445 (3.9). For up coming events from the year 2000 AD.
Mars:
During the period (2000-2499 A.D.), 59 occultations to 6th magnitude, of which 17 are to 5th, 3 are to 4th, and 2 are to 3rd. For parts of North America, only two events will be easily visible during the next 500 years and occurs on 5 Feb 2113 (6.1 magnitude) and 24 Mar 2129 (5.8). For up coming events from the year 2000 AD.
Jupiter:
During the period (2000-2499 A.D.), 30 occultations to 8th magnitude (2000-2069 only), 108 to 7th magnitude, of which 35 are to 6th, 8 are to 5th. For parts of North America, about 20 events to 7th magnitude will be visible under dark skies in 500 years. During the 21st century, the only event >7 magnitude visible will occur on 2 Feb 2074 (6.7).
Saturn:
During the period (2000-2499 A.D.), 71 occultations to 8th magnitude, of which 27 are to 7th, 10 are to 6th, and 2 are to 5th. For parts of North America, about ten occultations will be visible in 500 years. During the 21st century, the only event visible will occur on 7 Apr 2032 (5.9).
Uranus:
During the period (2000-2499 A.D.), 7 occultations to 8th magnitude, of which 3 are to 7th, 2 are to 6th, and 2 are to 5th. For parts of the North America., two occultations will be visible in 500 years and occurs on 9 Sep 2169 (7.1) and 15 Jan 2480 (4.5).
Neptune:
During the period (2000-2499 A.D.), 3 occultations to 8th magnitude, of which 1 is to 7th. No events will be visible over North America.LOCAL
During the next 500 years, favorable planet-bright star occultations (sun is below the horizon) for parts of North America will include about 36 events or 13 percent of the total. The frequency nearly triples if daylight events are included (although nearly impossible to view). Events usually last less than 10 minutes. Frequency of worldwide planet-bright star occultations during the next 500 years apply to stars brighter than 4th magnitude for Mercury (12 events) & Venus (23), to 6th magnitude for Mars (59), to 7th magnitude for Jupiter (108) and 8th magnitude for Saturn (71), Uranus (7) & Neptune (3).
Planet-Star Conjunctions
The following tables show the interval of years required to complete 100 worldwide events as a function of planet-star separation and stellar magnitude.Table 2.3: Superior Planet-Bright Star (>=3rd Magnitude Conjunctions <= 60' for 100 YearsWorldwide (AVERAGE) days or years per event LOCAL (AVG.) SEP <=60' SEP <=30' SEP <=10' Min. Sep Obs (%)Mars: 205 Days 351 Days 5.26 Years 43 Jupiter: 1.92 Years 2.78 Years 25.0 Years 50Saturn 4.76 Years 12.5 Years 25.0 Years 19Uranus: 11.1 Years 16.7 Years 33.3 Years 55Neptune: 9.09 Years 12.5 Years 33.3 Years 45
The average worldwide average frequency of planet-star conjunctions with stars of 3rd magnitude or brighter as a function of separation. Percentages (observable conjunctions) are based on solar elongation of 15 or greater. Nearly all events will be visible to some extent although separation will be greater. Only Neptune will yield more events during the 21st century than on average over the next 600 years for separation <=10.Table 2.4: Planet-Bright Star Conjunctions <=10' for 600 Years (2000-2599)Worldwide (AVERAGE) years per event LOCAL:(AVG.) SEP <=10' SEP <=5' SEP <=99" Min. Sep Obs (%)Mars: 4.80 Years 8.33 Years 30.0 Years 29Jupiter: 21.4 Years 33.3 Years 120 Years 68Saturn: 25.0 Years 46.2 Years 200 Years 50Uranus: 28.6 Years 28.6 Years 85.7 Years 19Neptune: 50.0 Years 100 Years >600 Years 42
Table 2.5: Planet-Star Conjunctions <= 90 arc seconds for 100 Years (2000-2099)Worldwide (AVERAGE) days or years per event LOCAL (AVG.) SEP <=90" SEP <=50" SEP <=10" Min. Sep Obs (%)Mars: 30.9 Days 54.8 Days 208 DaysJupiter: 156 Days 285 Days 5.00 Years 19Saturn: 295 Days 1.72 Years 9.09 Years 23Uranus: 2.00 Years 3.13 Years 20.0 Years 30Neptune: 2.63 Years 4.55 Years 100 Years 60
The average frequency of planet-star conjunctions of stars of 8th magnitude or brighter as a function of separation. Percentages (observable conjunctions) are based on solar elongation of 10 degrees (except 15 degrees for Uranus and Neptune). Mars data applies for the years 2000-2024.Table 2.6: Planet-Star Conjunctions <=99 arc seconds vs. MagnitudeWorldwide (AVERAGE) days or years per eventSeparation: <=90" <=99" <=99" <=99" <=99"Stellar Mag.: >= 8th >=6th >=5th >=4th >=3rdVenus: Mars: 30.9 days 233 days 2.41 years 11.4 years 35.7 years Jupiter: 156 days 2.77 years 5.49 years 167 years 167 yearsSaturn: 295 days 4.72 years 17.9 years 33.3 years 250 yearsUranus: 2.00 years 6.10 years 14.7 years 41.7 years 83.3 yearsNeptune: 2.63 years 17.8 years 21.7 years 55.6 years >500 years
The average frequency of planet-star very close conjunctions as a function of stellar magnitude. For stars 6th magnitude or brighter, data are based on 500 years; 100 years or less for 8th magnitude events, except 25 years for Mars.
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