Astronomy:Apsis

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Short description: Either of two extreme points in a celestial object's orbit


The apsides refer to the farthest (2) and nearest (3) points reached by an orbiting planetary body (2 and 3) with respect to a primary, or host, body (1)

An apsis (from grc ἁψίς (hapsís) 'arch, vault'; pl. apsides /ˈæpsɪˌdiːz/ AP-sih-deez)[1][2] is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides is the line connecting the two extreme values.

For example, for orbits about the Sun the apsides are called aphelion (farthest) and perihelion (nearest). 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.

Part of a series on
Astrodynamics
Angular parameters of an elliptical orbit
Orbital parameters
Types of two-body orbits, by
eccentricity
Equations
Gravitational influences
N-body orbits
Preflight engineering
Efficiency measures

General description

The two-body system of interacting elliptic orbits: The smaller, satellite body (blue) orbits the primary body (yellow); both are in elliptic orbits around their common center of mass (or barycenter), (red +).
∗Periapsis and apoapsis as distances: the smallest and largest distances between the orbiter and its host body.

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. 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 orbital mechanics, the apsides technically refer to the distance measured between the center of mass of the central body and the center of mass of the orbiting body. However, in the case of a spacecraft, the terms are commonly used to refer to the orbital altitude of the spacecraft above the surface of the central body (assuming a constant, standard reference radius).

Keplerian orbital elements: point F, the nearest point of approach of an orbiting body, is the pericenter (also periapsis) of an orbit; point H, the farthest point of the orbiting body, is the apocenter (also apoapsis) of the orbit; and the red line between them is the line of apsides.

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/);[3] 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").[4]
  • For objects in lunar orbit, the point of least distance are called the pericynthion (Lua error: Internal error: The interpreter exited with status 1.) and the greatest distance the apocynthion (Lua error: Internal error: The interpreter exited with status 1.). The terms perilune and apolune, as well as periselene and aposelene are also used.[5] 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[6] 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).[3]

Various related terms are used for other celestial objects. The suffixes -gee, -helion, -astron and -galacticon are frequently used in the astronomical literature when referring to the Earth, Sun, stars, and the galactic center respectively. The suffix -jove is occasionally used for Jupiter, but -saturnium has very rarely been used in the last 50 years for Saturn. The -gee form is also used as a generic closest-approach-to "any planet" term—instead of applying it only to Earth.

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.[7] More recently, during the Artemis program, the terms perilune and apolune have been used.[8]

Regarding black holes, the term peribothron was first used in a 1976 paper by J. Frank and M. J. Rees,[9] 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,[10] thus appearing before perinigricon and aponigricon (from Latin) in the scientific literature in 2002.[11]

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/(primary) system. However, only for the Earth, Moon and Sun systems are the unique suffixes commonly used. Exoplanet studies commonly use -astron, but typically, for other host systems the generic suffix, -apsis, is used instead.[12]Lua error: Internal error: The interpreter exited with status 1.

Host objects in the Solar System with named/nameable apsides
Astronomical
host object 		Suffix Origin
of the name
Sun -helion Helios
Mercury -hermion Hermes
Venus -cythe Cytherean
Earth -gee Gaia
Moon -lune[5]
-cynthion
-selene[5] 		Luna
Cynthia
Selene
Mars -areion Ares
Ceres -demeter[13] Demeter
Jupiter -jove Zeus
Jupiter
Saturn -chron[5]
-kronos
-saturnium
-krone[14] 		Cronos
Saturn
Other host objects with named/nameable apsides
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: Lua error: Internal error: The interpreter exited with status 1.; black

Perihelion and aphelion

Diagram of a body's direct orbit around the Sun with its nearest (perihelion) and farthest (aphelion) points

The perihelion (q) and aphelion (Q) are the nearest and farthest points respectively of a body's direct orbit around the Sun.

Comparing osculating elements at a specific epoch to effectively those at a different epoch will generate differences. The time-of-perihelion-passage as one of six osculating elements is not an exact prediction (other than for a generic two-body model) of the actual minimum distance to the Sun using the full dynamical model. Precise predictions of perihelion passage require numerical integration.

Inner planets and outer planets

The two images below show the orbits, orbital nodes, and positions of perihelion (q) and aphelion (Q) for the planets of the Solar System[15] as seen from above the northern pole of Earth's ecliptic plane, which is coplanar with Earth's orbital plane. The planets travel counterclockwise around the Sun and for each planet, the blue part of their orbit travels north of the ecliptic plane, the pink part travels south, and dots mark perihelion (green) and aphelion (orange).

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 orbital plane of reference. At the time of vernal equinox, the Earth is at the bottom of the figure. The second image (below-right) shows the outer planets, being Jupiter, Saturn, Uranus, and Neptune.

The orbital nodes are the two end points of the "line of nodes" where a planet's tilted orbit intersects the plane of reference;[16] 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 the inner planets of the Solar System

  • The perihelion (green) and aphelion (orange) points of the outer planets of the Solar System

Lines of apsides

The chart shows the extreme range—from the closest approach (perihelion) to farthest point (aphelion)—of several orbiting celestial bodies of the Solar System: the planets, the known dwarf planets, including Ceres, and Halley's Comet. The length of the horizontal bars correspond to the extreme range of the orbit of the indicated body around the Sun. These extreme distances (between perihelion and aphelion) are the lines of apsides of the orbits of various objects around a host body.

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bar:planets width:48 text:Venus color:redorange from:107 till:109 shift:(0,1)
bar:planets width:48 text:Earth color:oceanblue from:147 till:152 shift:(0,-12)
bar:planets width:48 text:Mars color:coral from:207 till:249 shift:(0,-25)
bar:planets width:48 text:Jupiter color:orange from:741 till:816
bar:planets width:48 text:Saturn color:yellow from:1350 till:1504
bar:planets width:48 text:Uranus color:skyblue from:2735 till:3006
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bar:dwarf_planets4 width:18 text:Eris color:lightorange from:5766 till:14595 shift:(-250,-4)
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Distances of selected bodies of the Solar System from the Sun. The left and right edges of each bar correspond to the perihelion and aphelion of the body, respectively, hence long bars denote high orbital eccentricity. The radius of the Sun is 0.7 million km, and the radius of Jupiter (the largest planet) is 0.07 million km, both too small to resolve on this image.

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 Lua error: Internal error: The interpreter exited with status 1. astronomical units (AU) or Lua error: Internal error: The interpreter exited with status 1. 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 Lua error: Internal error: The interpreter exited with status 1. or Lua error: Internal error: The interpreter exited with status 1..

The dates of perihelion and aphelion change over time due to precession and other orbital factors, which follow cyclical patterns known as Milankovitch cycles. In the short term, such dates can vary up to 2 days from one year to another.[17] This significant variation is due to the presence of the Moon: while the Earth–Moon barycenter is moving on a stable orbit around the Sun, the position of the Earth's center which is on average about Lua error: Internal error: The interpreter exited with status 1. from the barycenter, could be shifted in any direction from it—and this affects the timing of the actual closest approach between the Sun's and the Earth's centers (which in turn defines the timing of perihelion in a given year).[18]

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.[19] 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 Lua error: Internal error: The interpreter exited with status 1. warmer than in the southern hemisphere, because the northern hemisphere contains larger land masses, which are easier to heat than the seas.[20]

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).[21]

Astronomers commonly express the timing of perihelion relative to the First Point of Aries not in terms of days and hours, but rather as an angle of orbital displacement, the so-called longitude of the periapsis (also called longitude of the pericenter). For the orbit of the Earth, this is called the longitude of perihelion, and in 2000 it was about 282.895°; by 2010, this had advanced by a small fraction of a degree to about 283.067°.[22]

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 plane of the ecliptic. The Earth's eccentricity and other orbital elements are not constant, but vary slowly due to the perturbing effects of the planets and other objects in the solar system (Milankovitch cycles).

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 apsidal precession. (This is closely related to the precession of the axes.) The dates and times of the perihelions and aphelions for several past and future years are listed in the following table:[23]

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.[24]

Type of body Body Distance from Sun at perihelion Distance from Sun at aphelion difference (%) insolation
difference (%)
Planet 1 Mercury Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 34% 57%
2 Venus Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 1.3% 2.8%
3 Earth Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 3.3% 6.5%
4 Mars Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 17% 31%
5 Jupiter Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 9.2% 18%
6 Saturn Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 10% 19%
7 Uranus Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 9.0% 17%
8 Neptune Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 1.7% 3.4%
Dwarf planet 9 Ceres Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 15% 27%
10 Pluto Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 40% 64%
11 Haumea Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 33% 55%
12 Makemake Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 28% 48%
13 Eris Lua error: Internal error: The interpreter exited with status 1. Lua error: Internal error: The interpreter exited with status 1. 60% 84%

Mathematical formulae

These formulae characterize the pericenter and apocenter of an orbit:

Pericenter
Maximum speed, [math]\displaystyle{ v_\text{per} = \sqrt{ \frac{(1 + e)\mu}{(1 - e)a} } \, }[/math], at minimum (pericenter) distance, [math]\displaystyle{ r_\text{per} = (1 - e)a }[/math].
Apocenter
Minimum speed, [math]\displaystyle{ v_\text{ap} = \sqrt{\frac{(1 - e)\mu}{(1 + e)a} } \, }[/math], at maximum (apocenter) distance, [math]\displaystyle{ r_\text{ap} = (1 + e)a }[/math].

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
[math]\displaystyle{ h = \sqrt{\left(1 - e^2\right)\mu a} }[/math]
Specific orbital energy
[math]\displaystyle{ \varepsilon = -\frac{\mu}{2a} }[/math]

where:

  • a is the semi-major axis:
    [math]\displaystyle{ a = \frac{r_\text{per} + r_\text{ap}}{2} }[/math]
  • μ is the standard gravitational parameter
  • e is the eccentricity, defined as
    [math]\displaystyle{ e = \frac{r_\text{ap} - r_\text{per}}{r_\text{ap} + r_\text{per}} = 1 - \frac{2}{\frac{r_\text{ap}}{r_\text{per}} + 1} }[/math]

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 arithmetic mean of the two limiting distances is the length of the semi-major axis a. The geometric mean of the two distances is the length of the semi-minor axis b.

The geometric mean of the two limiting speeds is

[math]\displaystyle{ \sqrt{-2\varepsilon} = \sqrt{\frac{\mu}{a}} }[/math]

which is the speed of a body in a circular orbit whose radius is [math]\displaystyle{ a }[/math].

Time of perihelion

Orbital elements such as the time of perihelion passage are defined at the epoch chosen using an unperturbed two-body solution that does not account for the n-body problem. To get an accurate time of perihelion passage you need to use an epoch close to the perihelion passage. For example, using an epoch of 1996, Comet Hale–Bopp shows perihelion on 1 April 1997.[25] Using an epoch of 2008 shows a less accurate perihelion date of 30 March 1997.[26] Short-period comets can be even more sensitive to the epoch selected. Using an epoch of 2005 shows 101P/Chernykh coming to perihelion on 25 December 2005,[27] but using an epoch of 2012 produces a less accurate unperturbed perihelion date of 20 January 2006.[28]

Two body solution vs n-body solution for 12P/Pons–Brooks time of perihelion passage
Epoch Date of perihelion (tp)
2010 2024-Apr-19.892
n-body[29] 2024-Apr-21.139
2018 2024-Apr-23.069

Numerical integration shows dwarf planet Eris will come to perihelion around December 2257.[30] Using an epoch of 2021, which is 236 years early, less accurately shows Eris coming to perihelion in 2260.[31]

4 Vesta came to perihelion on 26 December 2021,[32] but using a two-body solution at an epoch of July 2021 less accurately shows Vesta came to perihelion on 25 December 2021.[33]

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 Lua error: Internal error: The interpreter exited with status 1. in the perihelion date.[34]

See also

References

  1. ↑ Lua error: Internal error: The interpreter exited with status 1. "apsis". Dictionary.com Unabridged. Random House. https://www.dictionary.com/browse/Lua error: Internal error: The interpreter exited with status 1.. 
  2. ↑ "apsis". Boston: Houghton Mifflin Harcourt. 2014. https://www.ahdictionary.com/word/search.html?q=apsis. 
  3. ↑ 3.0 3.1 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] , pronouncing the "p" and "h" in separate syllables. However, the pronunciation Lua error: Internal error: The interpreter exited with status 1. [2] 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] , page 26.) Many [4] dictionaries give both pronunciations
  4. ↑ Lua error: Internal error: The interpreter exited with status 1.
  5. ↑ 5.0 5.1 5.2 5.3 "Basics of Space Flight". NASA. https://solarsystem.nasa.gov/basics/glossary. 
  6. ↑ Klein, Ernest, A Comprehensive Etymological Dictionary of the English Language, Elsevier, Amsterdam, 1965. (Archived version)
  7. ↑ "Apollo 15 Mission Report". Glossary. https://history.nasa.gov/alsj/a15/a15mr-f.htm. 
  8. ↑ 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. https://ntrs.nasa.gov/citations/20210019019. Retrieved July 18, 2022. 
  9. ↑ Frank, J.; Rees, M.J. (September 1, 1976). "Effects of massive black holes on dense stellar systems.". MNRAS 176 (6908): 633–646. doi:10.1093/mnras/176.3.633. Bibcode: 1976MNRAS.176..633F. 
  10. ↑ Perimelasma , by Geoffrey Landis, first published in Asimov's Science Fiction, January 1998, republished at Infinity Plus
  11. ↑ R. Schödel; T. Ott; R. Genzel; R. Hofmann; M. Lehnert; A. Eckart; N. Mouawad; T. Alexander et al. (October 17, 2002). "A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way". Nature 419 (6908): 694–696. doi:10.1038/nature01121. PMID 12384690. Bibcode: 2002Natur.419..694S. 
  12. ↑ "MAVEN » Science Orbit". http://lasp.colorado.edu/home/maven/science/science-orbit/. 
  13. ↑ "Dawn Journal: 11 Years in Space". http://www.planetary.org/blogs/guest-blogs/marc-rayman/20181019-dawn-journal-11-years-in-space.html. 
  14. ↑ Cecconi, B.; Lamy, L.; Zarka, P.; Prangé, R.; Kurth, W. S.; Louarn, P. (March 4, 2009). "Goniopolarimetric study of the revolution 29 perikrone using the Cassini Radio and Plasma Wave Science instrument high-frequency radio receiver". Journal of Geophysical Research: Space Physics 114 (A3): A03215. doi:10.1029/2008JA013830. Bibcode: 2009JGRA..114.3215C. https://ui.adsabs.harvard.edu/abs/2009JGRA..114.3215C/abstract. Retrieved December 9, 2019. 
  15. ↑ "the definition of apsis". http://dictionary.reference.com/browse/apsis. 
  16. ↑ Darling, David. "line of nodes". The Encyclopedia of Astrobiology, Astronomy, and Spaceflight. http://www.daviddarling.info/encyclopedia/L/line_of_nodes.html. Retrieved May 17, 2007. 
  17. ↑ "Perihelion, Aphelion and the Solstices". timeanddate.com. https://www.timeanddate.com/astronomy/perihelion-aphelion-solstice.html. 
  18. ↑ "Variation in Times of Perihelion and Aphelion". Astronomical Applications Department of the U.S. Naval Observatory. August 11, 2011. http://aa.usno.navy.mil/faq/docs/apsides.php. 
  19. ↑ "Solar System Exploration: Science & Technology: Science Features: Weather, Weather, Everywhere?". NASA. http://www.nasa.gov/audience/foreducators/postsecondary/features/F_Planet_Seasons.html. 
  20. ↑ "Earth at Aphelion". Space Weather. July 2008. http://spaceweather.com/glossary/aphelion.html. 
  21. ↑ 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?". University of Southern Maine. https://usm.maine.edu/planet/how-much-does-aphelion-affect-our-weather-were-aphelion-summer-would-our-summers-be-warmer-if. 
  22. ↑ "Data.GISS: Earth's Orbital Parameters". http://data.giss.nasa.gov/ar5/srorbpar.html. 
  23. ↑ Espenak, Fred. "Earth at Perihelion and Aphelion: 2001 to 2100". http://astropixels.com/ephemeris/perap2001.html. 
  24. ↑ "NASA planetary comparison chart". http://solarsystem.nasa.gov/planets/compare. 
  25. ↑ "JPL SBDB: Hale-Bopp (Epoch 1996)". https://ssd.jpl.nasa.gov/sbdb.cgi?soln=J971A%2F1&sstr=Hale-Bopp&cad=1. 
  26. ↑ "JPL SBDB: Hale-Bopp". https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1995O1. 
  27. ↑ "101P/Chernykh – A (NK 1293) by Syuichi Nakano". http://www.oaa.gr.jp/~oaacs/nk/nk1293.htm. 
  28. ↑ JPL SBDB: 101P/Chernykh (Epoch 2012)
  29. ↑ "Horizons Batch for 12P/Pons-Brooks (90000223) at 2024-Apr-21 03:20". JPL Horizons. https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%2790000223%27&START_TIME=%272024-Apr-21%2003:00%27&STOP_TIME=%272024-Apr-21%2003:40%27&STEP_SIZE=%27120%27&QUANTITIES=%2719%27.  (JPL#K242/3 Soln.date: 2022-Oct-24)
  30. ↑ "Horizons Batch for Eris at perihelion around 7 December 2257 ±2 weeks". JPL Horizons. Jet Propulsion Laboratory. https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%27Eris%27&START_TIME=%272257-11-28%27&STOP_TIME=%272257-12-17%27&STEP_SIZE=%273%20hours%27&QUANTITIES=%2719%27. 
  31. ↑ "JPL SBDB: Eris (Epoch 2021)". https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=Eris. 
  32. ↑ "Horizons Batch for 4 Vesta on 2021-Dec-26". JPL Horizons. https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%27Vesta%27&START_TIME=%272021-Dec-25%2023:00%27&STOP_TIME=%272021-Dec-26%2004:00%27&STEP_SIZE=%2715%20minutes%27&QUANTITIES=%2719%27.  (Epoch 2021-Jul-01/Soln.date: 2021-Apr-13)
  33. ↑ JPL SBDB: 4 Vesta (Epoch 2021)
  34. ↑ "JPL SBDB: 2015 TH367". https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2015TH367. 

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