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Day and Year Measurements
Sidereal Day = 23.9344699
One sidereal day is the time it takes for a given star in the sky to return to the same coordinates in the sky.
A sidereal day is when the earth rotates exactly 360 degrees. A sidereal day is 23 hours 56 minutes and 4.0916 seconds long.
It is not to be confused with the Synodic Day. When the Earth begins a sidereal day at NOON, and ends once it rotates a full 360 degrees,
the time the rotation is completed is actually almost four minutes short, ending at 11:56:04 AM.
The Synodic Day below explains more.
Synodic Day = 24 hours
This is what days are measured by in the solar calendar. This is also called the mean solar day, which is the basis of a calendar day.
The Earth rotates a little bit over 360 degrees so that the Sun's point in the sky at NOON when it begins the synodic day is on average the same latitude
the next day when a new synodic day begins. It's motion is relative to the noontime point of the Sun.
A synodic day is the time it takes the sun to successively pass the meridian (astronomical noon).
In a given synodic year, there is one more sidereal day than a synodic day due to the difference of four minutes a day multiplied by 365.24218967.
Julian Year = 365.25 days
The original Julius Caesar based calendar. It's length runs close to the length of the Sothic Year below.
Sothic year = 365.25 days approximately
The Sothic year is the interval between heliacal risings of the star Sirius. It is currently less than the sidereal year and its duration is very close to the mean Julian year of 365.25 days.
Gregorian Year = 365.2425 days
A refinement of the Julian calendar that adjusts the frequency of adding leap year days to help align the calendar to the traditional seasonal dates since the first century Easter Day was celebrated.
Tropical Year = 365.24218967 synodic days (or 366.242186698 sidereal days)
Also called Synodic, Solar, or Equinoxial Year. It's used for most seasonal based calendars and based on longtitude.
The mean tropical year is defined as the period of time for the mean ecliptic longitude of the Sun to increase by 360 degrees.
It's simply the period between two returns of the sun to the same equinox.
The Sun's ecliptic longitude is measured with connection to the equinox, the tropical year is a complete cycle of the seasons.
The tropical year is defined as the points in time at which seasons predictably repeat each year.
It is the time it takes the Sun to return to the same exact point on the ecliptic (equinox to equinox).
It is just over 20 minutes shorter than a sidereal year.
Earth's Axis Rotation
Earth's axis rotates clockwise by 1/25,800 of a degree per year.
This explains why the Tropical Year beats the Sidereal Year on Earth by just over 20 minutes a year.
The Earth rotates around the Sun counterclockwise, as does the direction of the Earth's rotation.
If a Calendar based on the Sidereal Year was created, the calendar would still line up with the distant stars each year
when the Earth rotates 360 degrees, but the seasons would be about one hour early on the calendar every three years,
or one day early on the calendar for every 180 years. A calendar on for another planet that is based on the sidereal
year of Earth would be of much more use there for whatever purposes the inhabitants of that planet would employ (religious,
Which brings up explaing the Sidereal Year below.
Sidereal Year = 365.256363004 synodic days (or 366.256363004 sidereal days)
Its orbit around the sun based on position of the stars.
The sidereal year is the amount of time taken for the Earth to complete one revolution of its orbit, as measured against a fixed frame of reference (such as the fixed stars or other points in the sky), as it returns to the same position where it started.
It is 20 minutes and 23 seconds longer than the tropical year because of the precession of the equinoxes; for this reason, the sidereal year does not stay in step with the seasons and no practical calendars based on the sidereal year would be of any use.
Gaussian year = 365.2568983
The Gaussian year is the sidereal year for a planet of negligible mass (relative to the Sun) and unperturbed by other planets that is governed by the Gaussian gravitational constant.
Such a planet would be slightly closer to the Sun than Earth's mean distance. Its length is: 365.2568983 days (365 days 6 hours 9 minutes 56 seconds).
Anomalistic Year = 365.259636
This is where the Earth completes one revolution with respect to its apsides.
The anomalistic year is the time taken for the Earth to complete one revolution with respect to its apsides (starting from the farthest point from the Sun and ending at the same point after completing one orbit, while passing the Sun from the closest point of its
orbit in the middle.
The orbit of the Earth is elliptical; the extreme points, called apsides, are the perihelion, where the Earth is closest to the Sun (around January 3), and the aphelion, where the Earth is farthest from the Sun (around July 4).
The anomalistic year is usually defined as the time between perihelion passages.
Lunar month = 29.53059 days approximately
This is the mean time the Moon rotates around the Earth each cycle, varying in length by up to six hours either way.
Draconic year = 346.620075883 days
The draconic year, draconitic year, eclipse year, or ecliptic year is the time taken for the Sun (as seen from the Earth) to complete one revolution with respect
to the same lunar node (a point where the Moon's orbit intersects the ecliptic).
This period is associated with eclipses: these occur only when both the Sun and the Moon are near these nodes; so eclipses occur within
about a month of every half eclipse year. Hence there are parts of two or three (with the middle one a whole one) eclipse years every synodic year.
The average duration of the eclipse year is 346.620075883 days (346 days 14 hours 52 minutes 54 seconds).
Lunar year = 354.36708 days approximately
The lunar year comprises twelve full cycles of the phases of the Moon as seen from Earth.
Like the Draconic year, the Lunar Year can have parts of two or three (with the middle one a whole one) Lunar years every synodic year.
Muslims use this as the basis for their Hijri calendars. A Muslim calendar year is based on the lunar cycle.
Due to the length of days difference, there are approximately 33 Lunar Years for each group of 32 Sunodic years. Seasons tend to drift 11 days later each year on the Hijri calendar
while the start of the Islam calendar drifts 11 days earlier each year on the Gregorian calendar.
Vague year = 365 days
The vague year is an approximation to the year equaling 365 days.
The vague year consists of 12 months of 30 days, plus five extra days that are epagomenal.
The vague year was used in the calendars of Ancient Egypt, Iran, Armenia and in Mesoamerica among the Aztecs and Maya.
Many Zoroastrian communities still use it. Due to the lack of leap year days, the Vague year falls short of 97 days every 400 Gregorian calendar years,
resulting in the start of seasons drifting over three months late on the Vague calendar in that amount of time.
Leap Year = 366 days
A leap year is used in Julian, Gregorian and many solar calendars at certain intervals to help keep the solar calendars aligned with the starts of the seasons in their expected traditional time frames.
For example, the first day of Spring would begin between March 19 and 21 depending on year, with the eariest start day of Spring less than three weeks after a leap year day passed.
Full moon cycle = 411.78443029 days
The full moon cycle is the time for the Sun (as seen from the Earth) to complete one revolution with respect to the perigee of the Moon's orbit.
This period is associated with the apparent size of the full moon, and also with the varying duration of the synodic month. The duration of one full moon cycle is:
411.78443029 days (411 days 18 hours 49 minutes 34 seconds).