A. Day

Earth's sidereal day 23 Hours 56 minutes 4.091 seconds

This interval is responsible for the stars rising about four minutes earlier each day. However for the sun who's distance from the earth changes throughout the year, the shape of the analemma (figure eight on globes and sundials) embodies what is known as the equation of time for an example how this rate varies with time. Because of the Earth's orbital eccentricity and obliquity, the sun transits the sky (due south in northern hemisphere) by - 16.25 to + 14.25 minutes of local noontime during this present era.

B. 1 Day to 1 Week

Lunar retardaton 24 Hours + 50 minutes

The average time-difference between one moonrise and the next. For the northern hemisphere, this value is reduced to as little as 15 minutes later the next day when the full Moon occurs nearest the time of the autumnal equinox (the Harvest Moon is the first full moon after the equinox). The greatest time delay between adjacent moonrise occurs during the vernal equinox. The reverse situation happenings in the southern hemisphere. The following charts represent the moonrise delay from Fairbanks, Alaska for the period 2000-2018 AD. Because Fairbanks is situated near 65N, there is a period of 210 days out of 6050 days when the moon is circumpolar (never sets) or never rises for several days. The first chart shows the cumulative days when the moonrises in bins of 10 minute increments. The second chart shows a histogram by percent of occurrence. The third chart shows the sequential order of moonrise delay. The last chart shows a blow-up of the region centered around 24 hours. It should be noted that for latitudes south of 60 degrees, the charts would appear similiar except for the events lasting more than 27 hours.

C. 1 Week to 1 Month

Moon's nodical month 27.21222 Days

This is the time it takes for the Moon to cross its orbit's nodes (e.g., ascending-descending-ascending) above-below-above the ecliptic plane. This factor explains why there are eclipse-seasons and whether an eclipse is total, annular-partial, or penumbral (for the Moon). (See Nutation Period, 18.61 Years)

Moon's Tropical month 27.32158 Days

This is the time it takes for the Moon to return to the same celestrial longtiude (about 7 seconds shorter than the sidereal month).

Moon's sidereal month 27.32166 Days

This is the mean time it takes for the Moon to complete one revolution measured against the background of fixed stars.

Moon's anomalistic month. 27.55455 Days

This is the mean time (standard deviation (SD) = 1.136 days based on period 1900-2078) it takes for the Moon to reach its next perigee. Moon:Perigee; (closest approach to Earth). The interval between apogee is the same as perigee but the SD = 0.267 day. This factor is responsible for whether a solar eclipse is annular or total and why tide tables show repeated monthly cycles.

Moon's synodic month 29.53059 Days

This is the time it takes for the Moon to complete all its phases (e.g., 1st quarter to 1st quarter). From 1600 to 2400 A.D., the shortest month is 29.27152 days, the longest 29.83263 days.

D. Month to 1 Year

Eclipse-Season 31 to 38 Days

The duration of an eclipse-season results from the fact that the sun's eclipse zone is 37 degrees or within 18.5 degrees of the node (point on orbital plane where moon crosses). However, because the moon's eclipse zone is 12.25 degree from the node (or 24.5 degrees wide) and it takes 30.616 degrees for the moon to travel to its nodal position a synodic month later, the moon cannot have more than one partial or total eclipse during a three eclipse-season. Up to three eclipses (Sun Moon-Sun or Moon-Sun-Moon) can occur during this period. Since the Sun's eclipse zone is larger than the moon's, there are more partial and total eclipses of the sun than the moon (3:2 ratio). Between 1900-2078, the shortest period between two adjacent eclipses is 13 days 21 hours 35 minutes and for three eclipses is 29 days 6 hours 40 minutes. If three eclipses occur (about 1 in 7 eclipse-seasons), only the middle one will be significant (total or annular) while the flanking eclipses will be penumbral or minor partials. If the season has only two eclipses, both will be prominent (total, annular, or major partials). In most calendar years (about 63% of them), there are just two eclipse-seasons (four eclipses; two solar and two lunar).

Mercury's greatest elongation 39-48 Days to 70-73 Days

For northern mid-latitude regions, best viewing occurs after sunset in late winter and before sunrise in late summer based on the greatest inclination of the ecliptic plane with the horizon (Mercury at aphelion and +/- 90 degrees in longitude away). The reverse periods apply to the southern hemisphere. The time between East to West elongation's is 44 days (passing through inferior conjunction) and from West to East elongation's is 72 days (passing through superior conjunction). The series of elongation's alternate between the two periods noted above. Less than two weeks after inferior conjunction, Mercury becomes observable; viewed 10 to 17 days before greatest evening (Eastern) elongation but vanishes six to seven days afterwards. Extremes in elongation's is approx.: 27 deg 50' to 17 deg 52'. The first events in the 21st century occur on 28 Jan 2001 and 11 Mar 2001.

Mercury's Sidereal year 88.025 Days

The inner most planet revolves: 2.55 times faster than Venus, 4.15 times Earth, 7.81 times Mars, 49.22 times Jupiter, 122.23 times Saturn, 348.63 times Uranus, and 683.76 times Neptune.

Mercury's Synodic year 105 to 129 Days

The interval (116 Days) between succeeding circumstances. At inferior conjunctions, Mercury is only visible during transits of the Sun. At superior conjunctions, it can be only visible during a total eclipse. It retrogrades for a period of 22 days centered on inferior conjunction.

Venus' greatest elongation 134-142 Days to 439-443 Days

The time between East to West elongation's is (303 days) shorter (passing through inferior conjunction) than West to East elongation's (passing through superior conjunctions). Best visible in evening in spring and morning in autumn (northern hemisphere). It retrogrades for a period of 40 days centered on inferior conjunction. Extremes in elongation is approximately: 47 deg 19' to 45 deg 23'. First event in 21st century occurs on 17 Jan 2001 followed by 8 Jun 2001.

Eclipse-seasons 173.31 Days

The interval (6 months - 9.31 days) between the center of eclipse-seasons (half an Eclipse-year). This explains why the Earth experiences an eclipse (solar or lunar) 18.6 days earlier following most calendar years.

Venus' sidereal year 224.7 Days

The 2nd planet from the sun revolves: 0.39 times that of Mercury, 1.625 time faster than Earth, 3.06 times Mars, 19.29 times Jupiter, 47.90 times Saturn, 136.64 times Uranus, and 267.98 times Neptune.

Eclipse Year 346.62 Days

Interval required for the Sun to move from the moon's ascending node to ascending node or descending node to descending node. There are several eclipse series based on nearly even whole or half multiples of Eclipse-years and the moon's synodic months (e.g., 4, 9.5, 11.5, 19, 20, 23, 30.5, 42, 57, 61, 91.5, 324, and 385, 549 eclipse-years). The amount and types of lunar and solar eclipses occurring in a calendar year range from four to seven events. Solar eclipse frequency include: 26.9% total, 33.2% annular, 4.8% total/annular, and 35.2% partial.

Earth's Tropical year 365.24219 Days

Interval for Earth to return to same equinox. This explains why leap years exist. Leap years also occur only in years when centuries are evenly divisible by four (e.g., 1600, 2000, 2400, etc.). The Gregorian calendar therefore is equal to 365 days 5 hours 49 minutes 12 seconds.

Earth's Sidereal year 365.25636 Days

Interval for Earth to return to same fixed star.

Earth's Anomalistic year 365.25964 Days

Interval for Earth to orbit the Sun as measured from its closest point (perihelion) to its return back. This period is slightly less than five minutes longer than the sidereal year because the position of the perihelion point moves along the Earth's orbit by about 1.1 minutes of arc yearly. During this current epoch, the Earth is closest the Sun just after the new year. It will take about 12,500 years for this date to advance six months.

E. 1 Year to 1 Decade

Neptune's Synodic year 1 Year + 1.8 days

Interval (367 days) between Neptune's oppositions. Planet is observed in retrograde motion five months centered on opposition. Planet's maximum size is 2.4".

Uranus' Synodic year 1 Year + 4.5 days

Interval (369.7 days) between Uranus' oppositions.i.Oppositions:Uranus;. Planet is observed in retrograde motion five months centered on opposition. Planet's maximum size is 4".

Saturn's Synodic year 1 Year + 12 to 14 days

Interval (378 days) between Saturn's oppositions.i.Oppositions:Saturn;. Planet is observed in retrograde motion 138 days centered on opposition. Extreme brightness range at opposition: +0.9 to -0.6 which correlates to the planet's ring orientation and distance.

Jupiter's Synodic year 1 Year + 30 to 38 days

Interval (398.88 days) between Jupiter's oppositions. Extreme brightness range at opposition is -2.5 to -2.9 which correlates to the planet's apparent size. Planet is in retrograde motion 121 days centered on opposition. At superior conjunction, Jupiter can be as small as 31".

Venus' Synodic year 1 Year 6 months + 5 to 41 days

Interval (584 days) between Venus' inferior conjunctions. Only specialized techniques allow for daylight observations. Also visible as silhouette on Sun during transits and during solar totality. When Venus passes well north or south of the Sun, it can become a morning and evening object for a few days. Planet is in retrograde motion 42 days centered on inferior conjunction. At superior conjunction, Venus can be as small as 10". From this position, it reaches greatest elongation in about 220 days, but back to inferior conjunction in only 72 days.

Mars' Sidereal year 1.881 Years

The 4th planet from the sun revolves: 0.128 times that of Mercury, 0.327 times Venus, 0.532 times Earth, 6.31 times faster than Jupiter, 15.66 times Saturn, 44.67 times Uranus, and 87.61 times Neptune.

Moon's phases 2 Years + 0 to 1 Day

Interval when preceding lunar phases (same elongation from the Sun) occurs. Useful method for determining optimal meteor shower observing.

Mars' Synodic year 2 Years + 1 to 2.5 Months

Interval (779.7 days) when Mars reaches opposition. The synodic period (opposition to opposition) occurs 764 days near perihelion and about 811 days near aphelion. On average, Mars is in retrograde 73 days centered on opposition. During this period, Mars' movement forms a loop near 9 hours and 21 hours R.A. and a zigzag paths near 3 hours and 15 hours R.A. Next oppositions will occur: 13 Jun 2001 (20.8") and 28 Aug 2003 (25.1"). Oppositions occurring in August (during this epoch) are the most favorable; with Mars' brightness exceeding Jupiter's. Extreme brightness range at oppositions is -1.2 to nearly -3.0 which correlates to the planet's apparent size. At aphelion oppositions, the planet's size can be as small as 14".

Mercury's Transit 3.5 to 13 Years

Interval between Mercury's transit of the Sun. The cycle generally intervals at 3.5 years, 9.5 years (6, 3.5 years), 3.5 years, 13 years (6, 7 or 9.5, 3.5 years), 7 years (3.5, 3.5 years), 9.5 years, then back to 3.5 years. Because transits occur within a day or two of May 7th and November 9th (at a 3:7 ratio) the cycle interval varies as noted by the parenthesis. May transits parallel one another as does November events; both moving east to west (retrograde) across the sun's disk. May transits are fewer because the Earth is further from the sun and Mercury is closer to Earth. Mercury's size during May transits approximate 13" while November's approach 9.8". First transits in the 21st century occur on 7 May 2003 and 8 Nov 2006.

Spica's Occultation season 5 Years + 3 to 6 months to 10 Years + 3 to 6 months

Alternating interval between Spica's two occultation-seasons. Seasons' duration are 1 Year 5 to 6 months. Last series ended 9 Jun 1995. Next season begins 7 Sep 2005 - 11 Jan 2007 then begins again 25 Jul 2012 - 27 Dec 2013 followed by 16 Jun 2024 - 17 Nov 2025.

Regulus' Occultation season 7 Years 3 months to 8 Years 7 months

Interval between Regulus' occultation-seasons. Season's duration is between 1 Year 4 months and 1 Year 7 months. First season in 21st Century begins 7 Jan 2007 and ends 12 May 2008. Seasons alternate between >7 years to >8 years intervals.

Venus' Elongation 7 Years 11 months 30 days 7 hours 2 min 39 sec

Interval when Venus returns to approximately the same elongation (within 20') in the sky. This situation partially explains why the pair of transits with the Sun occur at this relatively short interval. Next transits will occur on 8 Jun 2004 and 6 Jun 2012.

Venus' Transits 8 Years - 2 to 3 days to 121 Years 6 months + 2 to 3 days

The Venus transit cycle interval occurs at 121.5 years, 8 years, abouit 105 years, then repeats with 121.5 years. No events occurred in 20th century. Transit pair events occur in the alternating months of June and December. After the last single transit event in 1396, the next single events will occur in 3089, 3332, 3575, 3818, 3956, and 4061. If Venus in transit passes more than 12' from the sun's center, it must pass over the sun's disc again 8 years earlier or later.

Moon's Phases 8 Years + 1 to 2 days

Interval when the same lunar phase repeats.

Moon's Perigee 8.85 Years

Time it takes the moon's perigee to advance (in the same direction as the Earth rotates) one revolution. This is analogous to Earth's Precession of the Equinoxes.

Half SAROS Cycle 9 Years + 5.5 days

A total solar eclipse is followed by a total lunar eclipse at nearly the same longitude although widely apart in latitude. This period is equal to 9.5 eclipse-years.

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