قبا

القبا Apsis، في الميكانيكا السماوية، هي كلّ نقطة على مسار مركزيّ يكون بعدها عن مركز القوّة أكبر أو أصغر ما يمكن. بين يوهانس كيبلر أن مدارات الكواكب تكون في شكل قطع ناقص حيث تحتل الشمس (مركز القوة) إحدى بؤرتي القطع الناقص . ينتج عن ذلك أن الكوكب في مداره يكون أحيانا قريبا من الشمس (وتزداد سرعته خلال تلك الفترة ) وأحيانا أخرى يكون فيها بعيدا عن الشمس بعد نصف دورة (بالتالي تنخفض سرعته خلال تلك الفترة) . هذان الموضعان على مدار كوكب أو أي جرم سماوي يسميان أوج عندما يكون الكوكب بعيدا عن مركز القوة ، و حضيض عندما يكون الكوكب قريبا من مركز القوة . وينطبق ذلك أيضا على أي قمر صناعي يدور حول الأرض ، أحيانا يكون قريبا منها (في الحضيض)، وأحيانا يكون بعيدا عنها (في الأوج) ،إلا إذا كان مداره دائري تماما.

الصيغة الرياضية

العلاقة بين الاختلاف المركزي ومسافتي القبا : الأوج و الحضيض هي:

E x z e n t r i z i t \ddot{a} t = \frac{Apoapsisdistanz - Periapsisdistanz}{Apoapsisdistanz + Periapsisdistanz}

حيث:

Apoapsis distance أوج (فلك)

Periapsis distance حضيض (فلك)

الاختلاف المركزي Exzentrizity

المصطلح

الجرم	Closest approach	Farthest approach
عام	Periapsis/Pericenter	Apoapsis/Apocenter
مجرة	Perigalacticon^[1]	Apogalacticon
نجم	Periastron	Apastron
ثقب أسود	Perimelasma/Peribothra/Perinigricon	Apomelasma/Apobothra/Aponigricon
الشمس	Perihelion	Aphelion
عطارد	Perihermion	Aphermion
الزهرة	Pericytherion/Pericytherean/Perikrition	Apocytherion/Apocytherean/Apokrition
الأرض	Perigee	Apogee
القمر	Periselene/Pericynthion/Perilune	Aposelene/Apocynthion/Apolune
المريخ	Periareion	Apoareion
المشترى	Perizene/Perijove	Apozene/Apojove
زحل	Perikrone/Perisaturnium	Apokrone/Aposaturnium
أورانوس	Periuranion	Apouranion
نپتون	Periposeidion	Apoposeidion

المحاور المرجعية لمدار الأرض

يسمى الخط الذي يربط بين نقطتي الأوج والحضيض "بالمحور الرئيسي"، وهو أكبر محور في قطع ناقص. وبسبب جاذبية الكواكب الأخرى فلا يبقى المحور الأساسي ثابتا وإنما يدور بطيئا في اتجاه الجرم الأم (الشمس). ويسمى ذلك دوران الأوج (أو دوران الحضيض).

أوج الأرض apoapsis حول الشمس : مسافة 152 مليون كيلومتر

حضيض الأرض periapsis حول الشمس: مسافة 147 مليون كيلومتر.

الأوج والحضيض

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^[2] 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;^[3] 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.

<timeline style="width:100%; overflow:hidden;"> ImageSize = width:1600 height:200 PlotArea = left:80 right:0 top:0 bottom:20 Period = from:0 till:14700 TimeAxis = orientation:horizontal Colors =

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bar:dwarf_planets1 text:كوكب قزم_
bar:dwarf_planets2 text:PLANETS
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bar:dwarf_planets4

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bar:planets width:48 text:Mercury color:lightpurple from:46 till:70 shift:(0,14)
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
bar:planets width:48 text:Neptune color:blue from:4460 till:4537
bar:dwarf_planets2 width:18 text:Ceres color:tan2 from:381 till:446 shift:(0,-4)
bar:dwarf_planets1 width:18 text:Pluto color:lavender from:4437 till:7376 shift:(0,-4)
bar:dwarf_planets2 width:18 text:Haumea color:tan1 from:5158 till:7706 shift:(0,-4)
bar:dwarf_planets3 width:18 text:Makemake color:pink from:5672 till:7895 shift:(0,-4)
bar:dwarf_planets4 width:18 text:Eris color:lightorange from:5766 till:14595 shift:(-250,-4)
bar:dwarf_planets4 text:SUN color:yellow from:0 till:0.696 shift:(2,-20)
bar:comet width:12 text:Halley's_Comet color:yellowgreen from:88 till:5251 shift:(0,-4)
bar:au shift:(1,-12) text:0AU at:0
bar:au shift:(1,-12) text:10_AU at:1326
bar:au shift:(1,-12) text:20_AU at:2822
bar:au shift:(1,-12) text:30_AU at:4318
bar:au shift:(1,-12) text:40_AU at:5814
bar:au shift:(1,-12) text:50_AU at:7310
bar:au shift:(1,-12) text:60_AU at:8806
bar:au shift:(1,-12) text:70_AU at:10302
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bar:au shift:(1,-12) text:90_AU at:13294

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يوضح الرسم البياني مسافات الأجسام المختارة للنظام الشمسي من الشمس. تتوافق الحواف اليسرى واليمنى لكل شريط مع الحضيض والأوج للجسم، على التوالي، وبالتالي فإن القضبان الطويلة تشير إلى انحراف مداري كبير. يبلغ قطر الشمس 0.7 مليون كيلومتر، ويبلغ قطر المشتري (أكبر كوكب) 0.07 مليون كيلومتر، وكلاهما صغير جداً بحيث لا يمكن حلهما في هذه الصورة.

حضيض وأوج الأرض

سنة	الحضيض		الأوج
سنة	تاريخ	ساعة	تاريخ	ساعة
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

الكواكب الأخرى

The following table shows the distances of the planets and dwarf planets from the Sun at their perihelion and aphelion.^[4]

Type of body	Body	Distance from Sun at perihelion	Distance from Sun at aphelion	difference (%)	insolation difference (%)
الكوكب	1 !Mercury	46،001،009 km (28،583،702 mi)	69،817،445 km (43،382،549 mi)	34%	57%
	2 !Venus	107،476،170 km (66،782،600 mi)	108،942،780 km (67،693،910 mi)	1.3%	2.8%
	3 !Earth	147،098،291 km (91،402،640 mi)	152،098،233 km (94،509،460 mi)	3.3%	6.5%
	4 !Mars	206،655،215 km (128،409،597 mi)	249،232،432 km (154،865،853 mi)	17%	31%
	5 !Jupiter	740،679،835 km (460،237،112 mi)	816،001،807 km (507،040،016 mi)	9.2%	18%
	6 !Saturn	1،349،823،615 km (838،741،509 mi)	1،503،509،229 km (934،237،322 mi)	10%	19%
	7 !Uranus	2،734،998،229 km (1.699449110×10⁹ mi)	3،006،318،143 km (1.868039489×10⁹ mi)	9.0%	17%
	8 !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	9 !Ceres	380،951،528 km (236،712،305 mi)	446،428،973 km (277،398،103 mi)	15%	27%
	10 !Pluto	4،436،756،954 km (2.756872958×10⁹ mi)	7،376،124،302 km (4.583311152×10⁹ mi)	40%	64%
	11 !Haumea	5،157،623،774 km (3.204798834×10⁹ mi)	7،706،399،149 km (4.788534427×10⁹ mi)	33%	55%
	12 !Makemake	5،671،928،586 km (3.524373028×10⁹ mi)	7،894،762،625 km (4.905578065×10⁹ mi)	28%	48%
	13 !Eris	5،765،732،799 km (3.582660263×10⁹ mi)	14،594،512،904 km (9.068609883×10⁹ mi)	60%	84%

الصيغ الرياضية

These formulae characterize the pericenter and apocenter of an orbit:

Pericenter: Maximum speed, $v_{per} = \sqrt{\frac{(1 + e) μ}{(1 - e) a}}$ , at minimum (pericenter) distance, $r_{per} = (1 - e) a$ .
Apocenter: Minimum speed, $v_{ap} = \sqrt{\frac{(1 - e) μ}{(1 + e) a}}$ , at maximum (apocenter) distance, $r_{ap} = (1 + e) a$ .

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: $h = \sqrt{(1 - e^{2}) μ a}$
Specific orbital energy: $ε = - \frac{μ}{2 a}$

where:

$r_{ap}$ is the distance from the apocenter to the primary focus
$r_{per}$ is the distance from the pericenter to the primary focus
a is the semi-major axis:
$a = \frac{r_{per} + r_{ap}}{2}$
μ is the standard gravitational parameter
e is the eccentricity, defined as
$e = \frac{r_{ap} - r_{per}}{r_{ap} + r_{per}} = 1 - \frac{2}{\frac{r_{ap}}{r_{per}} + 1}$

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

\sqrt{- 2 ε} = \sqrt{\frac{μ}{a}}

which is the speed of a body in a circular orbit whose radius is $a$ .

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.^[5] Using an epoch of 2008 shows a less accurate perihelion date of 30 March 1997.^[6] 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,^[7] but using an epoch of 2012 produces a less accurate unperturbed perihelion date of 20 January 2006.^[8]

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^[9]	2024-Apr-21.139
2018	2024-Apr-23.069

Numerical integration shows dwarf planet Eris will come to perihelion around December 2257.^[10] Using an epoch of 2021, which is 236 years early, less accurately shows Eris coming to perihelion in 2260.^[11]

4 Vesta came to perihelion on 26 December 2021,^[12] but using a two-body solution at an epoch of July 2021 less accurately shows Vesta came to perihelion on 25 December 2021.^[13]

الأقواس القصيرة

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 سنة (28،220 يوم) in the perihelion date.^[14]

انظر أيضاً

المصادر

^ Croswell, Ken (1995). The Alchemy of the Heavens. Anchor Books. ISBN 0-385-47214-5.
^ "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.
^ "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 2023-02-12. Retrieved 2023-02-11. (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 13 September 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 2021-09-26. (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.{{cite web}}: CS1 maint: bot: original URL status unknown (link)

وصلات خارجية

Apogee - Perigee Photographic Size Comparison, perseus.gr
Aphelion - Perihelion Photographic Size Comparison, perseus.gr
Earth's Seasons: Equinoxes, Solstices, Perihelion, and Aphelion, 2000-2020, usno.navy.mil

الكلمات الدالة:

[alchemy-1] Croswell, Ken (1995). The Alchemy of the Heavens. Anchor Books. ISBN 0-385-47214-5.

[:0-2] "the definition of apsis". Dictionary.com. Archived from the original on December 8, 2015. Retrieved November 28, 2015.

[darlinglon-3] Darling, David. "line of nodes". The Encyclopedia of Astrobiology, Astronomy, and Spaceflight. Archived from the original on August 23, 2019. Retrieved May 17, 2007.

[4] "NASA planetary comparison chart". Archived from the original on August 4, 2016. Retrieved August 4, 2016.

[5] "JPL SBDB: Hale-Bopp (Epoch 1996)". Archived from the original on July 16, 2020. Retrieved July 16, 2020.

[6] "JPL SBDB: Hale-Bopp". Archived from the original on July 17, 2020. Retrieved July 16, 2020.

[7] "101P/Chernykh – A (NK 1293) by Syuichi Nakano". Archived from the original on October 3, 2020. Retrieved July 17, 2020.

[8] JPL SBDB: 101P/Chernykh (Epoch 2012)

[Horizons2024-9] "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 2023-02-12. Retrieved 2023-02-11. (JPL#K242/3 Soln.date: 2022-Oct-24)

[Eris-10] "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 13 September 2021.

[11] "JPL SBDB: Eris (Epoch 2021)". Archived from the original on January 31, 2018. Retrieved January 5, 2021.

[Horizons2021-12] "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 2021-09-26. (Epoch 2021-Jul-01/Soln.date: 2021-Apr-13)

[13] JPL SBDB: 4 Vesta (Epoch 2021)

[14] "JPL SBDB: 2015 TH367". Archived from the original on March 14, 2018. Retrieved September 23, 2021.{{cite web}}: CS1 maint: bot: original URL status unknown (link)

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