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Planetary Formation and
Migration Linked to Quran
P.
Armitage
أ. د. حسين يوسف راشد عمري
Hussain Y.
Omari
rashed@mutah.edu.jo
قسم الفيزياء/ جامعة مؤتة/ الأردن
From
Scholarpedia
|
Philip
Armitage (2008), Scholarpedia, 3(3):4479. |
doi:10.4249/scholarpedia.4479
|
revision
#73183 [link to/cite this article] |
Curator: Dr. Philip Armitage, University of
Colorado, Boulder, CO
Planets form from the protoplanetary
disks of gas and dust that are observed to orbit young stars (the Nebula
Hypothesis that was advanced by Kant, Laplace, and others in the 18th
century). Once formed, planetary orbits may be modified as a result of interactions
with the gas disk, or with other planets, stars or small bodies present in the
system. Such modification can result in planetary migration.
Planetary migration is
referred to by the following verse:
(وَالأرْضَ بَعْدَ
ذَلِكَ دَحَاهَا) [النازعات 30].
إنّ الكوكب قد يغادر المكان الذي خلق فيه إلى موقعه
الحالي (Bodenheimer et al 2001) بسبب التفاعل
الجاذبي مع القرص، وهذا الانتقال هو بعض من إيحاءات الآية: (وَالأرْضَ بَعْدَ
ذَلِكَ دَحَاهَا) [النازعات 30]. فإنّ من بعض معاني دحو الأرض هو أن يرمى بها،
وهو إشارة إلى حركتها الانتقاليّة وإبعادها في مسارها عن الشّمس، فقد نقلت من
المدار الذي تخلّقت فيه ابتداءً إلى أن استقرّ لها مدارها الحالي (Dormand and Woolfson 1989 P: 141-151, 157-160). والدّحو
يشير إلى حقائق أخرى؛ فلقد أسهم إخراج ماء الأرض في تبريدها، ممّا أدّى إلى إرساء
الجبال الّذي أعقب انخفاض درجة حرارة جوف الأرض الحارّ.
(وَالأرْضَ بَعْدَ ذَلِكَ دَحَاهَا)
[النازعات 30].
"And the Ardh
(Earth), later on, Hath He Daha * He draweth out Therefrom its water and
its pasture * And the mountains Hath He firmly fixed." (Surah No. 79,
verses: 30-32).
The meanings of the Arabic word Daha (v), and dah’o (n):
Ibn al-Musaiyab was asked about dah’o by stones: He replied,
“it’s Ok”. And it means to have a competition to show the winner in throwing of
stones. In an earlier context, “The rain
daha pebbles from the surface of the earth”: (takes the pebbles away
with it). It’s also a characteristic of the rain to push away small stones and
pieces of rock. Ibn al-Manzur, pointed
that it is said to the player of nuts, who daha nuts (throws them), to move the
goal further away from him and make daho of nuts.
Moreover, abi Rafe’ said that he used to entertain al-Hassan and
al-Hussain by playing with madahi; stones like circular loaves. The Arabs used to make holes in the ground and
dahou these stones; the player throws into the hole the stones, nuts,
etc. The derivative noun, medhah means a piece of log used by a boy to
push and sweep away everything comes in its way on the ground. Moreover, Mecca
residents play medhah (small circular pebbles like loaves to be thrown
into holes particularly made for such game).
In another context, the horse daha (hops by raising its
front hooves a little bit from the ground). Not only a horse daha but
also a camel daha (making like hunters holes while laying on the
ground). The word daha also is referred to humans. A man sleeps and daha
(lie comfortably). But a man daha
a woman (marries her). The noun daho’
is used to refer to someone who has a belly. The word dahyah is also
used to mean the leader of a group of soldiers. This leader is qualified and
privileged by the boss in front of the commander who has all the privileges.
Thus the Arabic word daho can mean: Pushing, throwing, and causing to move. It means to make levelly; with smooth even surface;
like a spherical surface with large radius.
It means to enlarge, extend, to inflate.
For Earth, it also means to draw out therefrom its water and its
pasture; making it fertile and suitable for life.
The formation of planets requires
growth through at least 12 orders of magnitude in spatial scale, from
micron-sized particles of dust and ice up to bodies with radii of thousands or
tens of thousands of km. It is convenient to divide the process up into
distinct stages in which different physical processes are dominant.
The initial reservoir of solid
material for planet formation is micron-sized particles of rocky or icy dust,
which makes up about 1% of the mass of a typical protoplanetary disk. Some dust
grains travel with the gas when a portion of a molecular cloud collapses to
form a star and a protoplanetary disk, while more dust condenses from the gas
phase within the disk. The dynamics of dust within a disk is dominated by
gravity from the star and aerodynamic forces from the gas, including turbulence. In contrast, gravitational
interactions between small bodies are very weak (the escape velocity from a
Dust grains grow by colliding with
one another and sticking together by electrostatic forces. Small particles also
physically embed themselves in larger aggregates during high-speed collisions.
The motion of small dust grains is closely coupled to that of the gas, and
turbulence causes dust to diffuse over large distances leading to substantial
radial and vertical mixing of material within the disk. Particles larger than
In the absence of direct observations
or suitable laboratory experiments, much of what we know about
terrestrial-planet formation comes from computer simulations. Terrestrial
planet formation has been studied extensively using statistical models based on
the coagulation equation to study the early stages of growth, and N-body simulations to model later stages when the number of large bodies is
small. Once planetesimals have formed, their subsequent evolution is dominated
by mutual gravitational interactions and collisions as they orbit the central
star. Colliding planetesimals typically merge to form a larger body with some
mass escaping as small fragments. Planetesimals also undergo numerous close
encounters with one another, which alter their orbits but not their masses. At
an early stage, runaway growth takes place, in which large bodies
typically grow more rapidly than small ones due to differences in their orbital
eccentricities and inclinations. Typical time scales for the runaway growth
phase are of the order of 
years.
Runaway growth is followed by oligarchic
growth, in which a relatively small number of large bodies grow at similar
rates until they have swept up most of the smaller planetesimals. Collisions and
radioactive decay heat the large bodies until they melt, causing dense elements
such as iron to sink to the center to form a core overlain by a rocky mantle.
Oligarchic growth generates a population of 
lunar-to-Mars-sized
planetary embryos, probably in 1 million years or less. Subsequent
collisions between these embryos lead to the final assembly of the terrestrial
planets, on a time scale of up to 100 million years. The Moon is thought to
have formed about 40 million years after the start of the Solar System from
debris placed into orbit about the Earth when it collided with a Mars-sized
planetary embryo. A substantial fraction of the Earth's mass is thought to have
been accreted via large impacts, so requiring such a cataclysmic event to form
the Moon is in principle not a problem, though only a small fraction of giant
impacts would lead to the formation of a satellite with the properties of the
Moon. Another puzzle is why the Moon has such a similar composition to the
Earth - this is not an obvious consequence of the giant impact theory. The time
scale for lunar formation, along with other time scales such as that for
asteroids to become large enough to differentiate, is derived by applying
radionuclide chronometers to samples of rock. Such cosmochemistry
evidence is becoming increasingly important, and provides a growing number of
constraints on the formation of the early Solar System. Planets typically
acquire mass from a range of distances within a protoplanetary disk, although the
mixture is different for each object, leading to a unique chemical composition.
It is likely that Earth acquired most of its water and other volatile materials
from relatively cold regions of the Sun's protoplanetary disk such as the
asteroid belt.
Runaway growth is referred
to by the verse:
وإن صفتي الكنس (growth,
accretion) والجري
(Runaway) ذكرتهما العبارة
القرآنيّة: (الجواري الكُنّس). وفي الأثر:
(سمعت
عليا وسئل عن { لا أقسم
بالخنس
الجوار الكنس } فقال: هي النجوم تخنس بالنهار وتكنس
بالليل ) (الراوي: خالد بن
عرعرة،
إسناده جيد، المحدث: ابن كثير، المصدر: تفسير
القرآن،
الصفحة أو الرقم8/359 ).
The two characteristics: sweeping, and
runaway are mentioned by the verse:
"So verily I call to witness the receding * The runaway (hidden black holes,
planets) Konnas (sweepers)." (Surah No. 81, verses 15-16).
وإن صفة الكنس (growth,
accretion)
فيما يخصّ الأرض قد ذكرتها الآيات القرآنيّة:
-
(وَهُوَ الَّذِي مَدَّ الأرْضَ وَجَعَلَ
فِيهَا رَوَاسِيَ وَأَنْهَارًا وَمِنْ كُلِّ الثَّمَرَاتِ جَعَلَ فِيهَا
زَوْجَيْنِ اثْنَيْنِ يُغْشِي اللَّيْلَ النَّهَارَ إِنَّ فِي ذَلِكَ لآيَاتٍ لِقَوْمٍ يَتَفَكَّرُونَ) (الرعد آية 3).
أَيْ
جَعَلَهَا مُتَّسِعَة مُمْتَدَّة فِي الطُّول وَالْعَرْض (ابن كثير، جـ 2، ص 576). (مَدَّ الأرْضَ): تشير إلى تخلّق الأرض
ومدّها بمادّة تكوينها (accretion) إلى أن كبُرت وتوسّعت مساحة سطحها تدريجيّاً. كما وقد تشير إلى إمداد الأرض
بالطّاقة: كالطّاقة الشّمسيّة مثلاً، وبالتالي إمدادها بالمطر، وإمدادها بالعناصر
من خلال النيازك والشهب.
-
(وَالأرْضَ مَدَدْنَاهَا
وَأَلْقَيْنَا فِيهَا رَوَاسِيَ وَأَنْبَتْنَا فِيهَا مِنْ كُلِّ شَيْءٍ
مَوْزُونٍ) (الحجر آية 19). ثُمَّ ذَكَرَ تَعَالَى خَلْقه الأرْض وَمَدّه إِيَّاهَا وَتَوْسِيعهَا وَبَسْطهَا (ابن كثير، جـ 2، ص237 ).
(وَالأرْضَ مَدَدْنَاهَا وَأَلْقَيْنَا فِيهَا رَوَاسِيَ
وَأَنْبَتْنَا فِيهَا مِنْ كُلِّ زَوْجٍ بَهِيجٍ) (ق 7). أَيْ
وَسَّعْنَاهَا وَفَرَشْنَاهَا (ابن كثير، جـ 4، ص 428).
(وَإِذَا الأرْضُ مُدَّتْ) (الانشقاق 3): وَإِذَا الأرْض بُسِطَتْ , فَزِيدَ فِي
سَعَتهَا: " إِذَا كَانَ يَوْم الْقِيَامَة مَدَّ اللَّه الأرْض حَتَّى لا يَكُون
لِبَشَرٍ مِنْ النَّاس إِلا مَوْضِع قَدَمَيْهِ" (ابن كثير، جـ 4، ص 296؛ الطبري 1995، م 15
، ص 214) . وعَنْ مُجَاهِد , قَوْله: { مُدَّتْ }
قَالَ: يَوْم الْقِيَامَة (الطبري ، م 15 ، ص 214). وذكر القرطبي: أَيْ بُسِطَتْ وَدُكَّتْ جِبَالهَا:
(تُمَدُّ مَدَّ الأدِيم). قَالَ اِبْن عَبَّاس وَابْن
مَسْعُود : وَيُزَاد وَسِعَتهَا كَذَا وَكَذَا ; لِوُقُوفِ الْخَلائِق عَلَيْهَا لِلْحِسَابِ
حَتَّى لا يَكُون لأحَدٍ مِنْ الْبَشَر إِلا مَوْضِع
قَدَمه, لِكَثْرَةِ الْخَلائِق فِيهَا (القرطبي 1996، م 10، جـ 19، ص 177).
(وَأَلْقَتْ مَا فِيهَا وَتَخَلَّتْ) (الانشقاق 4): أَيْ أَلْقَتْ مَا فِي بَطْنهَا مِنْ الأمْوَات وَتَخَلَّتْ
مِنْهُمْ قَالَهُ مُجَاهِد وَسَعِيد وَقَتَادَة. وعَنْ قَتَادَة: أَخْرَجَتْ
أَثْقَالهَا وَمَا فِيهَا (الطبري ، م 15 ، ص 314). وَقِيلَ: أَلْقَتْ مَا فِي بَطْنهَا
كُنُوزهَا وَمَعَادِنهَا, وَتَخَلَّتْ مِنْهَا. أَيْ خَلا جَوْفهَا, فَلَيْسَ فِي
بَطْنهَا شَيْء, وَذَلِكَ يُؤْذِن بِعِظَمِ الأمْر, كَمَا تُلْقِي
الْحَامِل مَا فِي بَطْنهَا عِنْد الشِّدَّة. وَقِيلَ: تَخَلَّتْ مِمَّا عَلَى
ظَهْرهَا مِنْ جِبَالهَا وَبِحَارهَا. وَقِيلَ : أَلْقَتْ مَا اسْتُوْدِعَتْ,
وَتَخَلَّتْ مِمَّا اسْتُحْفِظَتْ (القرطبي، م 10، جـ 19، ص 177-178).
I. 2: The Madd of Earth in
Qur’anic Verses
The Arabic word
Madd means: To spread out, to inflate,
increase the surface area (Ibn
Katheer, Part II: 657). Madd can refer to the process of
accretion resulting in formation of the earth. These meanings are clearly indicated in the
verses:
1- "And it is He (Allâh) who Madd the Ardh (Earth),
and set thereon fixing mountains standing firm, and (flowing) rivers: and fruit
of every kind He made in pairs, two and two: He draweth the Night as a veil
O'er the Day. Behold, verily in these things there are Signs for those who
consider!" (Ar-Ra’d No. 13, verse 3).
2- "And the Ardh (Earth) We have Madd it; set thereon
mountains firm and immovable; and produced therein all kinds of things in due
balance." (Al-Hijr No. 15, verse 19).
Allâh mentions the
creation of Earth, and the mass accretion flow which results in Earth's
formation. Also Allâh mentions the
inflation and smoothing of Earth's surface (where it’s shape is spherical) (Ibn
Katheer, Part II: 723).
3- "And the Ardh (Earth); We have Madd it, and set
thereon fixing mountains standing firm, and produced therein every kind of
beautiful growth (in pairs)" (Qaf No. 50, verse 7). Allâh has enlarged and spread out the Earth (Ibn
Katheer, Part IV: 284).
4- "And When the Ardh (Earth) is Madd
* And casts forth what is within it and becomes -clean- empty." (Surat
Al-Inshiqaq No. 84 verse 3-4). Madd:
Spread out, inflated, have an increased surface area, earth will cast forth its
internal metals, and its interior becomes empty
(Ibn
Katheer, Part IV: 629; al-Tabri, Ibn Jareer,
1995, XV: 142; al-Qurtubi,
1996, Part XIX: 177-178). Eighteen hundred years ago, al-Razi has explained this verse. He says: “One
has to know that increasing the area of the earth is a must, whether through
inflation or accretion” (al-Razi, 1995, XVI: Part 31: 105).
Fig.1: Runaway
planetisimal
شكل 1 : تخلق الكوكب Jupiter وزيادة حجمه بالمدّ مع الزمن.
Simulations of terrestrial planet formation are
able to reproduce the basic architecture (a small number of terrestrial planets
with low eccentricity orbits) of the inner Solar System from plausible initial
conditions. The stochastic nature of planetary accretion, however, means that a
precision comparison between the Solar System and theoretical models in not
possible. The number and masses of terrestrial planets are predicted to vary
from one planetary system to another due to differences in the amount of solid
material available and the presence or absence of giant planets, as well as the
highly stochastic nature of planet formation. The presence of a giant planet
probably frustrates terrestrial-planet formation in neighboring regions of the
disk, leading to the absence of terrestrial planets in these regions or the
formation of an asteroid belt. These predictions will be tested by ongoing and
future space missions designed to search for extrasolar terrestrial planets,
such as COROT and Kepler (http://www.scholarpedia.org/article/Planetary_formation_and_migration).
|
Figure 2: Schematic illustration showing how the core
mass (blue line) and total mass (core + envelope: red line) grow in a
calculation of giant planet formation via core accretion. The formation of a
10-20 Earth mass core is followed first by slow quasi-static growth of an
envelope, before finally runaway gas accretion ensues ([1]).
The time scale of the slow phase of growth is a few million years. |
|
Accretion That Formed
Earth is Referred to by the Following Verses; Where the Arabic Word Madd (مَدَّ) means both accretion and inflation:
مَدُّ الأرض في الآيات القرآنيّة
- (وَهُوَ الَّذِي مَدَّ الأرْضَ وَجَعَلَ فِيهَا رَوَاسِيَ
وَأَنْهَارًا وَمِنْ كُلِّ الثَّمَرَاتِ جَعَلَ فِيهَا زَوْجَيْنِ اثْنَيْنِ
يُغْشِي اللَّيْلَ النَّهَارَ إِنَّ فِي ذَلِكَ لآيَاتٍ لِقَوْمٍ
يَتَفَكَّرُونَ) (الرعد آية 3). أَيْ جَعَلَهَا مُتَّسِعَة مُمْتَدَّة فِي
الطُّول وَالْعَرْض (ابن كثير، جـ 2، ص 576). (مَدَّ الأرْضَ): تشير إلى تخلّق الأرض
ومدّها بمادّة تكوينها (accretion) إلى أن كبُرت وتوسّعت مساحة سطحها تدريجيّاً. كما وقد تشير إلى إمداد الأرض
بالطّاقة: كالطّاقة الشّمسيّة مثلاً، وبالتالي إمدادها بالمطر، وإمدادها بالعناصر
من خلال النيازك والشهب.
- (وَالأرْضَ مَدَدْنَاهَا وَأَلْقَيْنَا
فِيهَا رَوَاسِيَ وَأَنْبَتْنَا فِيهَا مِنْ كُلِّ شَيْءٍ مَوْزُونٍ) (الحجر آية 19).
ثُمَّ ذَكَرَ تَعَالَى خَلْقه الأرْض وَمَدّه
إِيَّاهَا وَتَوْسِيعهَا وَبَسْطهَا (ابن
كثير، جـ 2، ص237 ).
(وَالأرْضَ مَدَدْنَاهَا وَأَلْقَيْنَا
فِيهَا رَوَاسِيَ وَأَنْبَتْنَا فِيهَا مِنْ كُلِّ زَوْجٍ بَهِيجٍ) (ق 7). أَيْ وَسَّعْنَاهَا وَفَرَشْنَاهَا (ابن كثير، جـ 4، ص 428).
ويقال: مددتَ الأرض
مَدّاً إذا زدْت فيها تراباً أو سماداً من غيرها ليكون أعمرَ لها وأكثر ريعاً
لزرعها، وكذلك الرِّمال، والسّماد مداد لها (ابن منظور، م 13 ص 50-51). ويقال وادي كذا يَمُدُّ في نَهر كذا أي يزيد فيه. ويقال منه: قلّ ماءُ ركِيَّتِنا فمدَّتها
ركيّةٌ أخرى. مدَّ النَّهرُ النهرَ إذا
جرى فيه. قال اللحياني: يقال لكلّ شيء دخل
فيه مثلُه فَكَثَّرَه : مدَّه يمُدُّه مدّاً.
(وَالْبَحْرُ يَمُدُّهُ مِنْ بَعْدِهِ سَبْعَةُ أَبْحُرٍ) أي يزيد فيه ماء من خلْفِه تجرُّه إليه وتُكثِّرُه. ومادّة الشيء: ما يمدُّه. والمادّة: كلُّ شيء يكون مدَداً لغيره. وقال الفراءُ في قوله عزّ وجل: (وَالْبَحْرُ
يَمُدُّهُ مِنْ بَعْدِهِ سَبْعَةُ أَبْحُرٍ)
قال: تكون مِداداً كالمِداد الّذي يُكتبُ به.
والشيء إذا مدّ الشّيء فكان زيادةً فيه، فهو يَمُدُّه؛ تقول: دِجلَةُ
تَمُدُّ تيَّارنا وأنهارنا، واللّهُ يمُدُّنا بها. ومَدَدْنا القومَ: صِرنا لهم أنصاراً ومَدَداً
وأمْدَدْناهم بغيرنا (ابن منظور، م 13 ص 50-51).
كلّ شيء امتَلأَ
وارتفع فقد مَدَّ. ومدَّ النهارُ إذا
ارتفع. ومدَّ الدَّواةَ وأَمَدَّها: زاد
في نِقْسِها وجعلَ فيها مِداداً، وكذلك مدَّ القلم وأمَدَّه. ... ومَدَدْنا القوم
أي صِرنا مَدَداً لهم وأَمْدَدْناهم بغيرنا. .. يقال: مددتُ الشّيءَ مَدّاً
ومِدادا:ً هو ما يكثر به ويزاد. .. ويقال: مَدَّ اللّهُ في عُمُرك أي جعل لعُمُرك
مُدة طويلة. ومُدَّ في عمره: أي نُسيءَ.
ومَدُّ النهارِ: ارتفاعُه (ابن منظور، م 13 ص 25).
The Madd of Earth
in Qur’anic Verses
Madd
means: To spread out, to inflate, increase the surface area (Ibn
Katheer, Part II: 657). Madd can refer to the process of
accretion resulting in formation of the earth. These meanings are clearly indicated in the
verses:
1- "And it is He
(Allâh)
who Madd the Ardh (Earth), and set thereon fixing mountains standing firm, and (flowing)
rivers: and fruit of every kind He made in pairs, two and two: He draweth the
Night as a veil O'er the Day. Behold, verily in these things there are Signs
for those who consider!" (Ar-Ra’d No. 13,
verse 3).
2- "And the Ardh (Earth) We have Madd it; set
thereon mountains firm and immovable; and produced therein all kinds of things
in due balance." (Al-Hijr No. 15, verse 19).
Allâh
mentions the creation of Earth, and the mass accretion flow which results in
Earth's formation. Also Allâh mentions
the inflation and smoothing of Earth's surface (where it’s shape is spherical)
(Ibn Katheer, Part II: 723).
3- "And the Ardh (Earth); We have Madd it, and
set thereon fixing mountains standing firm, and produced therein every kind of
beautiful growth (in pairs)" (Qaf No. 50, verse
7). Allâh has enlarged and spread out
the Earth (Ibn Katheer, Part IV: 284).
The Various Meanings of Madd (Ibn al-Manzur, ed. 1993,
XIII: 50-52.)
Madd: attraction; as moon-ocean force of attraction increases, Madd (tide) occurs. al-Lahyani said that the
verse: "And the Ardh
(Earth) We have Madd it." (Surah No. 50 Verse 7, Surah No. 15 Verse 19) means leveled and made it flat.
Earth will be Madd on the Day of Judgment: "And
When the Ardh (Earth) is Madd." (Surat AL-Inshiqaq No. 84, verse 3).
Also madd of the ardh (field, a piece of land) denotes
the increase of its components by addition of fertilizers and soil in order to
produce in abundance. In another
context, for example, a particular valley madd into another river means
that it adds and increases its water current.
In the same context, a river madd another river (flows and merges
into it). Generally speaking, as
al-Lahyani remarked, every thing madd another denotes addition and
increase to it. Madd also
indicates every thing that supplies others as a source for it. God’s verse says: "Say: 'If the ocean were medad (ink) wherewith to
write out the words of my Lord, Sooner would the ocean be exhausted than would
the words of my Lord, even if we added another ocean like it, for its medad'."
(Al-Kahf No. 18, verse 109). Medad means (aid, ink). Al_Farra, an Islamic scholar, interprets
Qur'anic verses: "And if all the trees
on Ardh (earth) were pens and the Ocean (were ink), with seven Oceans
behind it to Madd (add to its supply), yet would not the Words of Allâh
be exhausted (in the writing): for Allâh is exalted in power, full of Wisdom"
(Luqman No. 31, verse 27). Al_Farra says: Medad (a derivative from madd):
is like ink. Allâh madd Euphrates
with water, and Euphrates madd our water currents and rivers. In the
lexicon, the group is madd with supporters and others means assisting them
in their mission. It is mentioned that a
group madd the army (supply them with more food, water, arms and
ammunition).
According to Shammur, if something is madd, it implies that
it is full to the brim but if a river madd, its water level gets higher;
if somebody madd the bottle of ink (adds to its content). According to
Abu Zayed: People use to say Allâh madd in your life (hope you live
long). Another usage of the word madd
is to say that the day madd (the sun rises and the time is almost at
noon: it is not early morning). To madd something indicates accretion,
i.e. to add to its substance (Ibn
al-Manzur, XIII: 50-52). Also other meanings of accretion are: 1- Growing
together of separate things. 2- An
increase in size by natural growth or gradual external addition. 3- A whole that results from such growths or
additions. 4- A thing added;
addition. 5- Growth in size. 6- The increase in area of a piece of land,
beach, etc., by the washing up of soil (Barnhart, 1977, I: 15). 7- The process by which compact stars capture
ambient matter is called accretion (Shapiro, 1983, p. 403).
Madd also means inflation: 1- The act of swelling
(as with air, gas, pride, or satisfaction).
2- A swollen state; too great expansion.
3- An increase of the currency of a country by issuing much paper
money. 4- A sharp and sudden rise in
prices resulting from a too great expansion in paper money or bank credit
(Barnhart, I: 1083). Universes with
exponential expansion are nowadays called inflationary (Ross, 1994, p. 62).
Thus the Arabic word Madd can mean: Accretion, and (or) Inflation; give rope in: extends (the rope) to; plunge deeper in to; help with,
assist with; give, somebody, increase in; bestow freely on; grant resources in
abundance; aid; add to (supply): like ink for a pen; stretch out (a rope). God Madd; prolong; the shadow: Make
long-extended. God Madd the
earth: spread out; inflated; formed from small gravitating objects.
Giant planets are qualitatively
distinct from terrestrial planets in that they possess significant gaseous
envelopes. In the Solar System, the gas giants (Jupiter and Saturn) are
predominantly composed of hydrogen and helium gas, although these planets are
enriched in elements heavier than helium compared to the Sun. The ice giants
(Uranus and Neptune) have lesser, but still substantial (several Earth masses)
gas envelopes. The existence of these envelopes provides a critical constraint:
giant planets must form relatively quickly, before the gas in the
protoplanetary disk is dissipated. Observations of protoplanetary disks around
stars in young clusters pin the gas disk lifetime in the 3-10 million year
range.
The standard theory for the formation
of gas giants, core accretion, is a two-stage process whose first stage
closely resembles the formation of terrestrial planets. A core with a mass of
the order of 10 Earth masses forms in the disk by numerous collisions between
planetesimals. Typically, there is not enough solid material to form bodies
this massive in the inner region of a protoplanetary disk. At larger orbital
radii, beyond the snow line, the temperature is low enough that ices as
well as rocky materials can condense. This extra solid material, together with
the reduced gravity of the central star, allows large solid cores to form in the
outer regions of a disk. Initially a core is surrounded by a low mass
atmosphere, which grows steadily more massive as the gas cools and contracts
onto the core. Eventually the core exceeds a "critical core mass",
beyond which a hydrostatic envelope cannot be maintained. Determining an
accurate time scale for reaching the critical core mass is very difficult, in
part because the rate at which the gas cools depends upon how transparent the
envelope is. The transparency varies dramatically with the amount of dust present,
which is extremely uncertain. Once the core mass is exceeded gas begins to flow
onto the core, slowly at first but increasingly rapidly as the planet becomes
more massive. Growth ceases when the supply of gas is terminated, either
because the planet opens a gap in the disk or because the disk gas dissipates.
A second theory for gas giant
formation, gravitational disk instability,. A
gas disk is gravitationally unstable if Toomre's parameter, is less than
unity. If, additionally, the disk is able to cool on an orbital timescale, then
the instability leads to fragmentation of the disk into bound objects ([2]). In
protoplanetary disks, these objects would have masses comparable to giant
planets. A key feature of this mechanism for forming giant planets is that it
works extremely rapidly. Unlike core accretion, solids play no direct role in
the process.
Core accretion is generally
considered to be a more plausible model for giant planet formation than
gravitational instability for several reasons. First, theoretical calculations
suggest that although young protoplanetary disks may be massive enough to be
unstable, they are unlikely to cool rapidly enough to fragment (except perhaps
at very large radius). Secondly, the core accretion model naturally explains the
existence of ice giant planets like Neptune (although the time scale for
formation of the ice giants is worryingly long if they formed at their present
locations). Finally, the observed correlation between the frequency of extrasolar
planets and the metallicity of their host stars is qualitatively explicable as
a consequence of core accretion: if the disk is enriched in solids, a critical-mass
core can form more readily. It is unclear whether this correlation can be
explained by the gravitational instability model. Against this, the inferred
core mass of Jupiter (which can be estimated by comparing the measured
multipoles of the gravitational field with theoretical structure models) is
lower than simple estimates based on core accretion. More subtle observational
constraints - such as the abundance of different elements measured in Jupiter's
atmosphere by the Galileo probe - are also in conflict with at least the
simplest models of giant planet formation. These problems suggest that a full
understanding of giant planet formation has yet to be attained. Observations of
the frequency of giant planets in extrasolar planetary systems with very
different properties to the Solar System promise to provide valuable new
constraints. For example, the core accretion model predicts that giant planet
formation is very difficult at large orbital radii (even though gas disks can
be 100 AU or more in size), and that the probability of planet formation ought
to scale quite strongly with the stellar mass (generally it is believed to be
harder around lower mass stars).
The possibility that planetary orbits
might evolve subsequent to planet formation was recognized early on, notably by
Peter Goldreich and Scott Tremaine in a 1980 paper. Interest in mechanisms for planetary
migration increased dramatically with the discovery in 1995 of 51 Peg, whose orbital
period of just 4.2 days places it so close to the star that it is highly
unlikely to have formed in situ. Three main mechanisms for planetary
migration have been studied.
Gas disk migration([3]).
Figure 3 :
The surface density from a numerical simulation of the interaction between a massive
planet and the protoplanetary gas disk.
A planet orbiting within a
protoplanetary disk gravitationally perturbs the gas in its vicinity, launching
density waves at orbital radii where the gas is in resonance with the planet. Interactions with
gas in the waves adds or removes energy and angular momentum from the planet's
orbit changing the semi-major axis (planetary migration) and possibly
the orbital eccentricity.
Two main regimes of gas disk
migration have been identified. Low-mass planets undergo type-I
migration, where the surface density profile of the gas disk is only weakly
altered by the planet and the migration rate is proportional to the planet's
mass. The planet remains entirely embedded within the gas. In this situation,
the most important resonances are those located close to the planet (with a radial
displacement comparable to the thickness of the gas disk). The interaction with
the gas disk interior to the planet's orbit adds angular momentum to the
planet, while the interaction with the exterior disk removes angular
momentum. Whether the planet migrates inward or outward depends upon the
balance of the two effects. Theoretical calculations suggest that the planet
migrates inward in almost all circumstances, potentially on a short time scale
(Tanaka, Takeuchi and Ward estimate a migration time scale for
an Earth mass planet from 5 AU as only about 1 million years). In a highly
turbulent disk, type-I migration may be closer to a random walk than a smooth
inward migration. Type I migration may be a relatively minor effect for
terrestrial planets due to their low masses and because their final assembly
probably occurs after the gas disk has dispersed, but type-I migration is
likely to affect the formation of giant planets in the core accretion model.
Massive planets strongly perturb the
gas disk. The exchange of angular momentum between the planet and the disk
tends to repel gas from the vicinity of the planet's orbit, creating an
annular gap in which the surface density of gas is low. The direction and rate
of orbital migration then depends upon how quickly the gas disk, evolving under
the action of its own internal angular momentum transport processes, tries to
flow back toward the gap. In this regime, described as Type II migration, the
motion of the planet is locked to the viscous evolution of the disk. In regions
of the disk where the gas is flowing inward, the planet also moves inward, and vice
versa. Type II migration is typically slower than Type I migration. The
boundary between Type I and Type II migration is not sharp. In between these
regimes, non-linear effects become important, especially for gas moving on
horseshoe orbits in the corotation resonance close to the planet's orbit. These
effects are poorly quantified at present, but numerical models suggest
planetary migration may slow down or even change direction for
intermediate-mass planets. Planets that have formed a gap continue to accrete
some gas via narrow streams of material that cross the gap. However, the rate
of gas accretion declines as the planet grows more massive and the gap becomes
deeper.
Although there is no direct
observational evidence for gas disk migration, it is widely believed that this
mechanism explains the existence of hot Jupiters - giant planets on very
short-period orbits such as the planet orbiting 51 Pegasi. It has been
suggested that gas disk migration may also excite planetary eccentricity
(thereby providing a simultaneous explanation for the wide spread of
eccentricity observed among extrasolar planets), but this question remains open
([4]).
Planetesimal-driven migration ([5]).
Figure 4: The distribution of known
trans-Neptunian objects in semi-major axis a and eccentricity e. Note the
concentration of bodies in 3:2 resonance with Neptune - the Plutinos.
Related physics allows planets to
migrate due to interaction with smaller bodies in their vicinity. A planet that
ejects a planetesimal from the planetary system must give up energy, and
thereby moves closer toward the star (this occurs, to a negligible degree, when
spacecraft make use of gravitational slingshots from the giant planets).
Conversely a planet that scatters planetesimals into shorter period orbits
gains energy, and migrates outward. To order of magnitude, a planet will suffer
a substantial change to its orbit if it interacts with a mass of planetesimals
that is comparable to its own mass. Since the ratio of solids to gas in typical
protoplanetary disks is of the order of order of 0.01 this condition is easier
to meet for ice giants, which have accreted relatively modest gaseous
envelopes, than for very massive planets with near stellar composition.
The distribution of trans-Neptunian
objects provides strong evidence for planetesimal migration having occurred
early in Solar System history. In addition to Pluto itself, a large number of
other bodies (called Plutinos) are observed to be trapped in 3:2
resonance with Neptune. Some of these bodies have eccentricities high enough
that they cross Neptune's orbit. This unusual distribution is likely the result
of the outward migration of Neptune, driven by the scattering of a disk
of planetesimals inward into orbits that eventually led to encounters with
Jupiter and ejection from the Solar System. Simultaneously, the slow outward
motion of Neptune captured Pluto and other bodies into the 3:2 resonance (a
process known as resonant capture) and excited their eccentricity.
Although the evidence is less direct,
it is also possible that all of the giant planets in the Solar System
originated in a more compact configuration, which then evolved under the action
of planetesimal scattering to its current state. The Nice Model postulates that this evolution
included a crossing of the 2:1 resonance between Jupiter and Saturn, and links
this crossing to the Late Heavy Bombardment (a transient spike in the
crattering rate) on the Moon. The full consequences of such large-scale
rearrangements of the giant planets remain to be explored.
Interactions between planets can also
occur after both the gas and planetesimal disks have been lost (or depleted to
a dynamically negligible level). No general stability criteria is known for a planetary
system with Nplanets , so numerical N-body experiments are needed to
study the evolution of such systems. An initially unstable planetary system can
evolve via:
·
Ejection of one or more planets (typically the
lightest)
·
An increase in the orbital separation of the planets,
toward a more stable configuration
·
Physical collisions between planets, or between a
planet and the star
The relative probability of these
channels depends upon the orbital radii and masses of the planets, and so no
blanket statement about the outcome of planet-planet scattering is possible.
However, typically the survivors after scattering has ceased have migrated
modestly inward, and gained significant eccentricity. Numerical calculations
have shown that planet-planet scattering can reproduce the observed
eccentricity distribution of massive extrasolar planets, and as a result this
mechanism is the leading candidate for explaining why extrasolar planets
frequently have non-circular orbits.
·
Planet Formation, J.J. Lissauer, Annual Review of
Astronomy and Astrophysics, 31, 129 (1993)
·
Planet Formation and Migration, J.C.B. Papaloizou and C. Terquem,
Reports on Progress in Physics, 69, 119 (2006)
·
Lecture Notes on the Formation and Early Evolution of
Planetary Systems, P.J. Armitage, arXiv:astro-ph/0701485v1 (2007)
·
Growth of Dust as the Initial Step Toward Planet Formation, C. Dominik, J. Blum, J. Cuzzi, and
G. Wurm, in Protostars and Planets V (editors B. Reipurth, D. Jewitt, and K.
Keil), University of Arizona Press, Tuscon, p.783 (2007)
·
Gravitational Instabilities in Gaseous Protoplanetary Disks
and Implications for Giant Planet Formation, R. Durisen, A. Boss, L. Mayer, A.
Nelson, T. Quinn and W.K.M. Rice, in Protostars and Planets V (editors B.
Reipurth, D. Jewitt, and K. Keil), University of Arizona Press, Tuscon, p.607
(2007)
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