Synodic period
The synodic period or synodic period of rotation (from ancient Greek σύνοδος synodos ' meeting ') is the time span between the points in time of successive identical positions of a celestial body with respect to earth and sun . Seen from the earth, the celestial body after its synodic period is again at the same angle to the sun ( elongation ), for example again in opposition (180 °) opposite or again in conjunction (0 °).
In astronomy, the mean synodic period is the average time span, calculated from opposition to opposition or from one conjunction to the next, e.g. from new moon to new moon for the moon.
Basics
How long it takes for a celestial body observed from the earth to assume the same position relative to the sun again is called the duration of its synodic period . It depends on its period and direction. With the same direction of rotation of the celestial body and the earth around the sun, one of the two must complete exactly one more orbit until an angle that is the same in terms of elongation is reached again, for example conjunction or opposition (see adjacent figure).
The time that elapses until then can be calculated from the speed of the circulation. The planets of the solar system all orbit the sun in the same direction ( prograd ), and the further away, the longer their orbit lasts. If a celestial body moves three times faster than the earth around the sun, it makes one and a half orbits during half a year on earth. If the earth is three times faster than a celestial body, it will have covered half a revolution after a year and a half. The synodic period is half a year in one case and one and a half years in the other.
If, on the other hand, a celestial body moves in the opposite direction (retrograde), this results in a shorter duration for its synodic period: If it rotates three times faster than the earth, it covers three quarters of its orbit during one quarter of the earth's annual cycle; if it is three times slower, it takes nine months until the same constellation is reached again relative to the sun. The synodic period is therefore a quarter or a three-quarter year.
For the observation of celestial phenomenology, astronomical phenomenology , it is not only the knowledge of synodic periods that is of interest. Sidereal periods are also important for celestial mechanical tasks : the orbital times of celestial bodies, determined for a fixed star (infinitely distant) as a reference point. On the other hand, tropical periods refer to the vernal equinox , while anomalistic periods refer to the apses of the orbit .
Current and Middle Synodic Period
The current synodic period fluctuates around a mean value. This is what is meant when the synodic period is mentioned without further details . Due to the elliptical orbits of the celestial bodies, the dwell times in the individual sectors of the orbit are different. The earth - to which a synodic period is commonly referred as a place of observation - moves on its orbit around the sun with different orbital and angular velocities. In the northern winter half year it is closer to the sun (the passage of perihelion , at the point closest to the sun, falls on a date between January 2nd and 5th) and its orbital speed is therefore higher than in the northern summer half year ( aphelion passage between July 3rd and 6th). The same applies to the other celestial bodies, which is why the time span of a current synodic period also depends on where the earth and the other object are located on their orbit. Irregularities also arise from orbital disturbances by the remaining masses in the solar system. For more complex orbits like the moon and other objects orbiting the earth (satellites), or other less massive celestial bodies, the calculations are even more complex.
Dimensioning and modification
Different values also result for a mean synodic period depending on which reference value is used for the elongation. Common is the geocentric conjunction with the sun, with the planets near the earth or with the earth moon at the new moon. The mean values also depend on the period over which the mean is taken. Because the movements of the celestial bodies are subject to long-term periodic changes on the one hand, and to non-periodic changes on the other hand, which become clear in the long term (secular change): The moon moves further and further away from the earth, its mean synodic period increases continuously.
The values of the synodic period given in the literature are generally - although a typical observer- related quantity - related to a heliocentric ecliptical length difference of the planetary centers and to the center of the earth ( geocentric ), more precisely to the earth-moon center of gravity . Then the synodic period is independent of whether and where the observer is on planet A or B, or on the sun.
For the location earth, the synodic period of the observed celestial bodies depends on their mean distance from the sun, set in relation to the distance between the earth and the sun (1 AU ). With a prograde orbit at a shorter distance - like the inner planets - the period increases the closer the distance from the sun approaches that of the earth. With a prograde orbit at a greater distance - like the outer planets - the period decreases with increasing distance from the sun. The illustration on the right shows these relationships for simplified conditions assuming circular paths.
Of course, synodic periods could also be determined for all celestial bodies in the solar system, for example in relation to Mars. They would tell an astronaut on a mission to Mars at what time intervals the respective celestial bodies shine particularly brightly when one is on the neighboring planet. Viewed from there, the “synodic period” of the space station ISS would be different from that seen from Earth; a spaceman on board experiences this as the time span from sunrise to sunrise, around 1½ hours. The synodic period of an exoplanet , measured in relation to its central star, is of particular scientific importance : it is used to determine its sidereal period, around which the synodic period fluctuates in relation to the annual parallax of the distant “sun”. The Kepler orbit period is then determined from modeling of the masses of the exoplanet and its sun.
Synodic periods in the solar system
earth
A synodic period cannot be given for the earth , since its definition relates to the positions of celestial bodies with respect to earth and sun.
The periodically repetitive movements of the earth the sun come regarding by daily rotation ( rotation and annual circulation () Revolution ) together about. A sunny day is the period of time until the same meridian points to the sun again and the sun culminates again at the places facing the sun on this longitude . A solar year as a tropical year is the period of time until the inclined axis of the earth takes up the same position to the sun again and a date that is the same seasonally is reached again; it takes less than a complete orbit of the earth around the sun based on the fixed star background, a sidereal year .
moon
In the case of moons , the synodic period is the time between two identical moon phases . It is also called the lunation for the earth's moon . Deviating from the planetary definition, the synodic period of the moon is based on the geocentric length difference. Today it is customary to measure the lunations from new moon to new moon (or from conjunction to conjunction) - in historical astronomy, the full moon was the reference of choice for reasons of observability .
The mean value is called the synodic month and is 29.5306 d or 29 days, 12 hours, 44 minutes; it represents the basic quantity for the month of the calculation of time. The individual lunations, however, fluctuate and deviate from this mean duration by up to around 7 hours; with the fluctuation range observed so far (up to 6 h 12 min shorter and up to 7 h 15 min longer than the average value), a lunation as the true synodic period is between 29.27 d and 29.83 d.
Planets
For planets that orbit the sun at a mean distance less than 2 2/3 ≈ 1.59 times as far as the earth (1.00 AU ) - i.e. Mercury , Venus and Mars - their sidereal orbital period is shorter than that respective synodic period . The period of time until the return of the same phase with the same elongation angle earth-sun-planet therefore lasts longer than the sidereal orbit of these celestial bodies around the sun.
For example, Venus orbits the sun in the same direction as the earth, but with an average distance of about 0.72 AU as the inner planet , it runs away much faster (see third Kepler's law ) and takes it back after almost 2.6 sidereal orbits a. During this time, the earth covered just under 1.6 orbits, the synodic period of Venus thus lasts just under 1.6 years, about 584 days. A similarly long synodic period would also result for a fictitious celestial body that covered just under 0.6 orbits in just under 1.6 years, i.e. would have a sidereal orbit period of almost 1000 days. Mars orbits the sun in around 687 days with an average solar distance of 1.52 AU as an outer planet, significantly slower than the earth. This circles the sun 2.135 times in 780 days, Mars 1.135 times during this time, until a constellation with the same elongation angle is reached again. The synodic period of Mars is also larger than its sidereal period.
A fictitious inner planet or solar satellite whose prograde orbit around the sun lasted 9/10 of a year would have a considerably higher synodic period. Its angular velocity of 10/9 revolutions per year compared to the earth with exactly one revolution per year would result in a relative angular velocity of 1/9 revolutions per year. Ergo it would take 9 years until it would have caught up with the earth again after 10 of its sun orbits. The same applies to a fictitious outer planet with a 10/9 year orbital period, which the earth would catch up with after 10 orbits, while it would have orbited the sun nine times. In both cases the synodic cycle lasts longer than the sidereal one.
Only with more distant celestial bodies with an average distance of more than 1.59 AU from the sun, such as the large outer planets, is the synodic period smaller than the sidereal period, which is now more than two years. During this time the earth makes more than two orbits and overtakes the celestial body. Because of its low orbital speed, the orbital period of the earth increasingly determines the synodic period as the distance increases. The more distant a planet is, the slower it shifts towards the starry sky; the synodic period approaches 1 year with increasing distance, since the planet is almost stationary when viewed from the earth .
For celestial bodies that orbit the sun in less than 0.5 2/3 ≈ 0.63 AU, the synodic period is shorter than 1 year, since they require less than half a year of orbit and so after two orbits in less than a year have already lapped the earth. Seen from the earth, these celestial bodies can be in lower conjunction more than once within a year. For bodies in orbit with a semi-major axis of more than 0.63 AU, however, the synodic period lasts over a year. The less the mean solar distance differs from that of the earth, the greater it is (see example above with 9 or 10 years). With a large semi-axis of approximately 1 AU, the synodic period of rotation is very long. For outer planets, the synodic period decreases again with increasing distance and finally approaches a year.
table
The following table contains time information for the duration of the mean synodic periods observed from Earth for the planets of the solar system , a body in the asteroid belt and Trans-Neptunes , as well as the Earth's moon (given in days and calendar years ); for comparison, the respective mean sidereal period in days is entered in the second column from the left :
| object | middle sidereal period |
middle synodic period |
true synodic period |
fluctuation | |
|---|---|---|---|---|---|
| moon | 27.32 days | 29.53 days | 0.081 years | 29.27 to 29.83 days | ± 0.9% |
| Mercury | 87.97 days | 115.88 days | 0.317 years | 106 to 130 days | |
| Venus | 224.7 days | 583.92 days | 1,599 years = 1 year 218.7 days |
579 to 589 days | ± 1% |
| Mars | 687.0 days | 779.94 days | 2.135 years = 2 years 49.5 days |
764 to 811 days | ± 3% |
| Ceres | 1682 days | 466.72 days | 1.278 years = 1 year 101.5 days |
||
| Jupiter | 4333 days | 398.88 days | 1.092 years = 1 year 33.6 days |
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| Saturn | 10750 days | 378.09 days | 1.035 years = 1 year 12.8 days |
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| Uranus | 30690 days | 369.66 days | 1.012 years = 1 year 4.4 days |
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| Neptune | 60190 days | 367.49 days | 1.006 years = 1 year 2.2 days |
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| Pluto | 90500 days | 366.73 days | 1.004 years = 1 year 1.5 days |
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| Quaoar | 1.05 x 10 5 days | 366.54 days | 1.0036 years = 1 year 1.3 days |
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| Sedna | 4.0 × 10 6 days | 365.29 days | 1,0001 years = 1 year 0.05 days |
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Cultural meaning
The daily high of the sun is easy to observe, that of the moon is not that easy. What is more noticeable here is the change in the phases of the moon , which depends on the angle at which the sunlit half of the moon appears. Seen from the earth, the sun and moon stand opposite each other when the moon is full, in opposition , the moon then culminates at midnight. This is the case again after a synodic period of the moon, a month later.
In the lunar calendars of different cultures, this time span becomes fundamental for a time frame of reference for different socially organized processes. The current term of the month is also derived from this period, as a period of time that divides the course of the year into sections with seasonal repetitions. Even religious festivals such as Easter or Passover addressed yet by the moon or the full moon in spring (see date of Easter ). The calendar of the Mayans considered additionally, the synods of the planet Venus . The achievement of the early Indian astronomers is reflected in the calendar system of the Vedic tradition, where one gets a detailed breakdown of the month by observing the daily sidereal movement of the moon.
But neither the sidereal nor the synodic periods of the moon are of constant duration. Average values are therefore used for orientation.