Apsis
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An apsis (from
Apsides pertaining to orbits around the Sun have distinct names to differentiate themselves from other apsides; these names are aphelion for the farthest and perihelion for the nearest point in the solar orbit.[3] The Moon's two apsides are the farthest point, apogee, and the nearest point, perigee, of its orbit around the host Earth. Earth's two apsides are the farthest point, aphelion, and the nearest point, perihelion, of its orbit around the host Sun. The terms aphelion and perihelion apply in the same way to the orbits of Jupiter and the other planets, the comets, and the asteroids of the Solar System.
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General description
There are two apsides in any elliptic orbit. The name for each apsis is created from the prefixes ap-, apo- (from ἀπ(ό), (ap(o)-) 'away from') for the farthest or peri- (from περί (peri-) 'near') for the closest point to the primary body, with a suffix that describes the primary body. The suffix for Earth is -gee, so the apsides' names are apogee and perigee. For the Sun, the suffix is -helion, so the names are aphelion and perihelion.
According to Newton's laws of motion, all periodic orbits are ellipses. The barycenter of the two bodies may lie well within the bigger body—e.g., the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface.[4] If, compared to the larger mass, the smaller mass is negligible (e.g., for satellites), then the orbital parameters are independent of the smaller mass.
When used as a suffix—that is, -apsis—the term can refer to the two distances from the primary body to the orbiting body when the latter is located: 1) at the periapsis point, or 2) at the apoapsis point (compare both graphics, second figure). The line of apsides denotes the distance of the line that joins the nearest and farthest points across an orbit; it also refers simply to the extreme range of an object orbiting a host body (see top figure; see third figure).
In
Terminology
The words "pericenter" and "apocenter" are often seen, although periapsis/apoapsis are preferred in technical usage.
- For generic situations where the primary is not specified, the terms pericenter and apocenter are used for naming the extreme points of orbits (see table, top figure); periapsis and apoapsis (or apapsis) are equivalent alternatives, but these terms also frequently refer to distances—that is, the smallest and largest distances between the orbiter and its host body (see second figure).
- For a body orbiting the Sun, the point of least distance is the perihelion (/ˌpɛrɪˈhiːliən/), and the point of greatest distance is the aphelion (/æpˈhiːliən/);[5] when discussing orbits around other stars the terms become periastron and apastron.
- When discussing a satellite of Earth, including the Moon, the point of least distance is the perigee (/ˈpɛrɪdʒiː/), and of greatest distance, the apogee (from Ancient Greek: Γῆ (Gē), "land" or "earth").[6]
- For objects in lunar orbit, the point of least distance are called the pericynthion (/ˌpɛrɪˈsɪnθiən/) and the greatest distance the apocynthion (/ˌæpəˈsɪnθiən/). The terms perilune and apolune, as well as periselene and aposelene are also used.[7] Since the Moon has no natural satellites this only applies to man-made objects.
Etymology
The words perihelion and aphelion were coined by Johannes Kepler[8] to describe the orbital motions of the planets around the Sun. The words are formed from the prefixes peri- (Greek: περί, near) and apo- (Greek: ἀπό, away from), affixed to the Greek word for the Sun, (ἥλιος, or hēlíos).[5]
Various related terms are used for other
During the Apollo program, the terms pericynthion and apocynthion were used when referring to orbiting the Moon; they reference Cynthia, an alternative name for the Greek Moon goddess Artemis.[9] More recently, during the Artemis program, the terms perilune and apolune have been used.[10]
Regarding black holes, the term peribothron was first used in a 1976 paper by J. Frank and M. J. Rees,[11] who credit W. R. Stoeger for suggesting creating a term using the greek word for pit: "bothron".
The terms perimelasma and apomelasma (from a Greek root) were used by physicist and science-fiction author Geoffrey A. Landis in a story published in 1998,[12] thus appearing before perinigricon and aponigricon (from Latin) in the scientific literature in 2002.[13]
Terminology summary
The suffixes shown below may be added to prefixes peri- or apo- to form unique names of apsides for the orbiting bodies of the indicated host/
Astronomical host object |
Suffix | Origin of the name |
---|---|---|
Sun | -helion | Helios |
Mercury | -hermion | Hermes |
Venus | -cythe | Cytherean |
Earth | -gee | Gaia
|
Moon | -lune[7] -cynthion -selene[7] |
Luna Cynthia Selene |
Mars | -areion | Ares |
Ceres | -demeter[15] | Demeter |
Jupiter | -jove | Zeus Jupiter |
Saturn | -chron[7] -kronos -saturnium -krone[16] |
Cronos Saturn |
Uranus | -uranion | Uranus |
Neptune | -poseideum[17] -poseidion |
Poseidon |
Astronomical host object |
Suffix | Origin of the name |
---|---|---|
Star | -astron | Lat: astra ; stars
|
Galaxy | -galacticon | Gr: galaxias; galaxy |
Barycenter
|
-center -focus -apsis |
|
Black hole | -melasma -bothron -nigricon |
Gr: melos; black Gr: bothros; hole Lat: niger; black |
Perihelion and aphelion
The perihelion (q) and aphelion (Q) are the nearest and farthest points respectively of a body's direct orbit around the Sun.
Comparing
Inner planets and outer planets
The two images below show the orbits,
The first image (below-left) features the inner planets, situated outward from the Sun as Mercury, Venus, Earth, and Mars. The reference Earth-orbit is colored yellow and represents the
The orbital nodes are the two end points of the "line of nodes" where a planet's tilted orbit intersects the plane of reference;[19] here they may be 'seen' as the points where the blue section of an orbit meets the pink.
-
The perihelion (green) and aphelion (orange) points of theinner planetsof the Solar System
-
The perihelion (green) and aphelion (orange) points of theouter planetsof the Solar System
Lines of apsides
The chart shows the extreme range—from the closest approach (perihelion) to farthest point (aphelion)—of several orbiting
Earth perihelion and aphelion
Currently, the Earth reaches perihelion in early January, approximately 14 days after the December solstice. At perihelion, the Earth's center is about 0.98329 astronomical units (AU) or 147,098,070 km (91,402,500 mi) from the Sun's center. In contrast, the Earth reaches aphelion currently in early July, approximately 14 days after the June solstice. The aphelion distance between the Earth's and Sun's centers is currently about 1.01671 AU or 152,097,700 km (94,509,100 mi).
The dates of perihelion and aphelion change over time due to precession and other orbital factors, which follow cyclical patterns known as
Because of the increased distance at aphelion, only 93.55% of the radiation from the Sun falls on a given area of Earth's surface as does at perihelion, but this does not account for the seasons, which result instead from the tilt of Earth's axis of 23.4° away from perpendicular to the plane of Earth's orbit.[22] Indeed, at both perihelion and aphelion it is summer in one hemisphere while it is winter in the other one. Winter falls on the hemisphere where sunlight strikes least directly, and summer falls where sunlight strikes most directly, regardless of the Earth's distance from the Sun.
In the northern hemisphere, summer occurs at the same time as aphelion, when solar radiation is lowest. Despite this, summers in the northern hemisphere are on average 2.3 °C (4 °F) warmer than in the southern hemisphere, because the northern hemisphere contains larger land masses, which are easier to heat than the seas.[23]
Perihelion and aphelion do however have an indirect effect on the seasons: because Earth's orbital speed is minimum at aphelion and maximum at perihelion, the planet takes longer to orbit from June solstice to September equinox than it does from December solstice to March equinox. Therefore, summer in the northern hemisphere lasts slightly longer (93 days) than summer in the southern hemisphere (89 days).[24]
Astronomers commonly express the timing of perihelion relative to the
For the orbit of the Earth around the Sun, the time of apsis is often expressed in terms of a time relative to seasons, since this determines the contribution of the elliptical orbit to seasonal variations. The variation of the seasons is primarily controlled by the annual cycle of the elevation angle of the Sun, which is a result of the tilt of the axis of the Earth measured from the
On a very long time scale, the dates of the perihelion and of the aphelion progress through the seasons, and they make one complete cycle in 22,000 to 26,000 years. There is a corresponding movement of the position of the stars as seen from Earth, called the
Year | Perihelion | Aphelion | ||
---|---|---|---|---|
Date | Time (UT) | Date | Time (UT) | |
2010 | January 3 | 00:09 | July 6 | 11:30 |
2011 | January 3 | 18:32 | July 4 | 14:54 |
2012 | January 5 | 00:32 | July 5 | 03:32 |
2013 | January 2 | 04:38 | July 5 | 14:44 |
2014 | January 4 | 11:59 | July 4 | 00:13 |
2015 | January 4 | 06:36 | July 6 | 19:40 |
2016 | January 2 | 22:49 | July 4 | 16:24 |
2017 | January 4 | 14:18 | July 3 | 20:11 |
2018 | January 3 | 05:35 | July 6 | 16:47 |
2019 | January 3 | 05:20 | July 4 | 22:11 |
2020 | January 5 | 07:48 | July 4 | 11:35 |
2021 | January 2 | 13:51 | July 5 | 22:27 |
2022 | January 4 | 06:55 | July 4 | 07:11 |
2023 | January 4 | 16:17 | July 6 | 20:07 |
2024 | January 3 | 00:39 | July 5 | 05:06 |
2025 | January 4 | 13:28 | July 3 | 19:55 |
2026 | January 3 | 17:16 | July 6 | 17:31 |
2027 | January 3 | 02:33 | July 5 | 05:06 |
2028 | January 5 | 12:28 | July 3 | 22:18 |
2029 | January 2 | 18:13 | July 6 | 05:12 |
Other planets
The following table shows the distances of the planets and dwarf planets from the Sun at their perihelion and aphelion.[27]
Type of body | Body | Distance from Sun at perihelion | Distance from Sun at aphelion | difference (%) | insolation difference (%) |
---|---|---|---|---|---|
Planet | Mercury | 46,001,009 km (28,583,702 mi) | 69,817,445 km (43,382,549 mi) | 34% | 57% |
Venus | 107,476,170 km (66,782,600 mi) | 108,942,780 km (67,693,910 mi) | 1.3% | 2.8% | |
Earth | 147,098,291 km (91,402,640 mi) | 152,098,233 km (94,509,460 mi) | 3.3% | 6.5% | |
Mars | 206,655,215 km (128,409,597 mi) | 249,232,432 km (154,865,853 mi) | 17% | 31% | |
Jupiter | 740,679,835 km (460,237,112 mi) | 816,001,807 km (507,040,016 mi) | 9.2% | 18% | |
Saturn | 1,349,823,615 km (838,741,509 mi) | 1,503,509,229 km (934,237,322 mi) | 10% | 19% | |
Uranus | 2,734,998,229 km (1.699449110×109 mi) | 3,006,318,143 km (1.868039489×109 mi) | 9.0% | 17% | |
Neptune | 4,459,753,056 km (2.771162073×109 mi) | 4,537,039,826 km (2.819185846×109 mi) | 1.7% | 3.4% | |
Dwarf planet | Ceres | 380,951,528 km (236,712,305 mi) | 446,428,973 km (277,398,103 mi) | 15% | 27% |
Pluto | 4,436,756,954 km (2.756872958×109 mi) | 7,376,124,302 km (4.583311152×109 mi) | 40% | 64% | |
Haumea |
5,157,623,774 km (3.204798834×109 mi) | 7,706,399,149 km (4.788534427×109 mi) | 33% | 55% | |
Makemake |
5,671,928,586 km (3.524373028×109 mi) | 7,894,762,625 km (4.905578065×109 mi) | 28% | 48% | |
Eris | 5,765,732,799 km (3.582660263×109 mi) | 14,594,512,904 km (9.068609883×109 mi) | 60% | 84% |
Mathematical formulae
These formulae characterize the pericenter and apocenter of an orbit:
- Pericenter
- Maximum speed, , at minimum (pericenter) distance, .
- Apocenter
- Minimum speed, , at maximum (apocenter) distance, .
While, in accordance with Kepler's laws of planetary motion (based on the conservation of angular momentum) and the conservation of energy, these two quantities are constant for a given orbit:
- Specific relative angular momentum
- Specific orbital energy
where:
- a is the semi-major axis:
- μ is the standard gravitational parameter
- e is the eccentricity, defined as
Note that for conversion from heights above the surface to distances between an orbit and its primary, the radius of the central body has to be added, and conversely.
The
The geometric mean of the two limiting speeds is
which is the speed of a body in a circular orbit whose radius is .
Time of perihelion
Epoch | Date of perihelion (tp) |
---|---|
2010 | 2024-Apr-19.892 |
n-body[32] | 2024-Apr-21.139 |
2018 | 2024-Apr-23.069 |
Numerical integration shows dwarf planet Eris will come to perihelion around December 2257.[33] Using an epoch of 2021, which is 236 years early, less accurately shows Eris coming to perihelion in 2260.[34]
4 Vesta came to perihelion on 26 December 2021,[35] but using a two-body solution at an epoch of July 2021 less accurately shows Vesta came to perihelion on 25 December 2021.[36]
Short arcs
Trans-Neptunian objects discovered when 80+ AU from the Sun need dozens of observations over multiple years to well constrain their orbits because they move very slowly against the background stars. Due to statistics of small numbers, trans-Neptunian objects such as 2015 TH367 when it had only 8 observations over an observation arc of 1 year that have not or will not come to perihelion for roughly 100 years can have a 1-sigma uncertainty of 77.3 years (28,220 days) in the perihelion date.[37]
See also
- Distance of closest approach
- Eccentric anomaly
- Flyby (spaceflight)
- Hyperbolic trajectory § Closest approach
- Mean anomaly
- Perifocal coordinate system
- True anomaly
References
- ^ "apsis". Dictionary.com Unabridged (Online). n.d.
- ^ "apsis". The American Heritage Dictionary of the English Language (5th ed.). HarperCollins.
- ^ Joe Rao (July 6, 2023). "Happy Aphelion Day! Earth is at its farthest from the sun for 2023 today". Space.com. Retrieved April 22, 2024.
- ^ "Earth-Moon Barycenter - SkyMarvels.com". www.skymarvels.com. Retrieved April 23, 2024.
- ^ a b Since the Sun, Ἥλιος in Greek, begins with a vowel (H is the long ē vowel in Greek), the final o in "apo" is omitted from the prefix. =The pronunciation "Ap-helion" is given in many dictionaries [1] Archived December 22, 2015, at the Wayback Machine, pronouncing the "p" and "h" in separate syllables. However, the pronunciation /əˈfiːliən/ [2] Archived July 29, 2017, at the Wayback Machine is also common (e.g., McGraw Hill Dictionary of Scientific and Technical Terms, 5th edition, 1994, p. 114), since in late Greek, 'p' from ἀπό followed by the 'h' from ἥλιος becomes phi; thus, the Greek word is αφήλιον. (see, for example, Walker, John, A Key to the Classical Pronunciation of Greek, Latin, and Scripture Proper Names, Townsend Young 1859 [3] Archived September 21, 2019, at the Wayback Machine, page 26.) Many [4] dictionaries give both pronunciations
- ^ Chisholm, Hugh, ed. (1911). . Encyclopædia Britannica. Vol. 21 (11th ed.). Cambridge University Press. p. 149.
- ^ a b c d "Basics of Space Flight". NASA. Archived from the original on September 30, 2019. Retrieved May 30, 2017.
- ^ Klein, Ernest, A Comprehensive Etymological Dictionary of the English Language, Elsevier, Amsterdam, 1965. (Archived version)
- ^ "Apollo 15 Mission Report". Glossary. Archived from the original on March 19, 2010. Retrieved October 16, 2009.
- ^ R. Dendy; D. Zeleznikar; M. Zemba (September 27, 2021). NASA Lunar Exploration – Gateway's Power and Propulsion Element Communications Links. 38th International Communications Satellite Systems Conference (ICSSC). Arlington, VA. Archived from the original on March 29, 2022. Retrieved July 18, 2022.
- .
- ^ Perimelasma Archived February 25, 2019, at the Wayback Machine, by Geoffrey Landis, first published in Asimov's Science Fiction, January 1998, republished at Infinity Plus
- S2CID 4302128.
- ^ "MAVEN » Science Orbit". Archived from the original on November 8, 2018. Retrieved November 7, 2018.
- ^ "Dawn Journal: 11 Years in Space". www.planetary.org. Archived from the original on October 24, 2018. Retrieved October 24, 2018.
- from the original on December 9, 2019. Retrieved December 9, 2019 – via ui.adsabs.harvard.edu.
- arXiv:2106.09409.
- ^ "the definition of apsis". Dictionary.com. Archived from the original on December 8, 2015. Retrieved November 28, 2015.
- ^ Darling, David. "line of nodes". The Encyclopedia of Astrobiology, Astronomy, and Spaceflight. Archived from the original on August 23, 2019. Retrieved May 17, 2007.
- ^ "Perihelion, Aphelion and the Solstices". timeanddate.com. Archived from the original on January 3, 2018. Retrieved January 10, 2018.
- ^ "Variation in Times of Perihelion and Aphelion". Astronomical Applications Department of the U.S. Naval Observatory. August 11, 2011. Archived from the original on January 11, 2018. Retrieved January 10, 2018.
- ^ "Solar System Exploration: Science & Technology: Science Features: Weather, Weather, Everywhere?". NASA. Archived from the original on September 29, 2015. Retrieved September 19, 2015.
- ^ "Earth at Aphelion". Space Weather. July 2008. Archived from the original on July 17, 2015. Retrieved July 7, 2015.
- ^ Rockport, Steve C. "How much does aphelion affect our weather? We're at aphelion in the summer. Would our summers be warmer if we were at perihelion, instead?". Planetarium. University of Southern Maine. Archived from the original on July 6, 2020. Retrieved July 4, 2020.
- ^ "Data.GISS: Earth's Orbital Parameters". data.giss.nasa.gov. Archived from the original on October 2, 2015.
- ^ Espenak, Fred. "Earth at Perihelion and Aphelion: 2001 to 2100". astropixels. Archived from the original on July 13, 2021. Retrieved June 24, 2021.
- ^ "NASA planetary comparison chart". Archived from the original on August 4, 2016. Retrieved August 4, 2016.
- ^ "JPL SBDB: Hale-Bopp (Epoch 1996)". Archived from the original on July 16, 2020. Retrieved July 16, 2020.
- ^ "JPL SBDB: Hale-Bopp". Archived from the original on July 17, 2020. Retrieved July 16, 2020.
- ^ "101P/Chernykh – A (NK 1293) by Syuichi Nakano". Archived from the original on October 3, 2020. Retrieved July 17, 2020.
- ^ JPL SBDB: 101P/Chernykh (Epoch 2012)
- ^ "Horizons Batch for 12P/Pons-Brooks (90000223) at 2024-Apr-21 03:20" (Perihelion occurs when rdot flips from negative to positive). JPL Horizons. Archived from the original on February 12, 2023. Retrieved February 11, 2023. (JPL#K242/3 Soln.date: 2022-Oct-24)
- ^ "Horizons Batch for Eris at perihelion around 7 December 2257 ±2 weeks". JPL Horizons (Perihelion occurs when rdot flips from negative to positive. The JPL SBDB generically (incorrectly) lists an unperturbed two-body perihelion date in 2260). Jet Propulsion Laboratory. Archived from the original on September 13, 2021. Retrieved September 13, 2021.
- ^ "JPL SBDB: Eris (Epoch 2021)". Archived from the original on January 31, 2018. Retrieved January 5, 2021.
- ^ "Horizons Batch for 4 Vesta on 2021-Dec-26" (Perihelion occurs when rdot flips from negative to positive). JPL Horizons. Archived from the original on September 26, 2021. Retrieved September 26, 2021. (Epoch 2021-Jul-01/Soln.date: 2021-Apr-13)
- ^ JPL SBDB: 4 Vesta (Epoch 2021)
- ^ "JPL SBDB: 2015 TH367". Archived from the original on March 14, 2018. Retrieved September 23, 2021.
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External links
- Apogee – Perigee Photographic Size Comparison, perseus.gr
- Aphelion – Perihelion Photographic Size Comparison, perseus.gr
- Earth's Seasons: Equinoxes, Solstices, Perihelion, and Aphelion, 2000–2020 Archived October 13, 2007, at the Wayback Machine, usno.navy.mil
- Dates and times of Earth's perihelion and aphelion, 2000–2025 Archived October 13, 2007, at the Wayback Machine from the United States Naval Observatory
- List of asteroids currently closer to the Sun than Mercury (These objects will be close to perihelion)
- JPL SBDB list of Main-Belt Asteroids (H<8) sorted by perihelion date