Elliptic orbit

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Animation of Orbit by eccentricity
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Two bodies with similar mass orbiting around a common barycenter with elliptic orbits.

Two bodies with unequal mass orbiting around a common barycenter with circular orbits.

Two bodies with highly unequal mass orbiting a common barycenter with circular orbits.

An elliptical orbit is depicted in the top-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the orbital speed is shown in red. The height of the kinetic energy decreases as the orbiting body's speed decreases and distance increases according to Kepler's laws.

In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1 (thus excluding the circular orbit). In a wider sense, it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1.

In a gravitational two-body problem with negative energy, both bodies follow similar elliptic orbits with the same orbital period around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit.

Examples of elliptic orbits include Hohmann transfer orbits, Molniya orbits, and tundra orbits.

Velocity

Under standard assumptions, no other forces acting except two spherically symmetrical bodies m₁ and m₂, the orbital speed (${\displaystyle v}$) of one body traveling along an elliptic orbit can be computed from the vis-viva equation as:

${\displaystyle v=\sqrt{\mu \left(\frac{2}{r}-\frac{1}{a}\right)}}$

where:

• ${\displaystyle \mu }$ is the standard gravitational parameter, G(m₁+m₂), often expressed as GM when one body is much larger than the other.
• ${\displaystyle r}$ is the distance between the orbiting body and center of mass.
• ${\displaystyle a}$ is the length of the semi-major axis.

The velocity equation for a hyperbolic trajectory has either + ${\displaystyle \frac{1}{a}}$, or it is the same with the convention that in that case a is negative.

Orbital period

Under standard assumptions the orbital period (${\displaystyle T}$) of a body travelling along an elliptic orbit can be computed as:

${\displaystyle T=2\pi \sqrt{\frac{a^3}{\mu }}}$

where:

• ${\displaystyle \mu }$ is the standard gravitational parameter.
• ${\displaystyle a}$ is the length of the semi-major axis.

Conclusions:

• The orbital period is equal to that for a circular orbit with the orbital radius equal to the semi-major axis (${\displaystyle a}$),
• For a given semi-major axis the orbital period does not depend on the eccentricity (See also: Kepler's third law).

Energy

Under standard assumptions, the specific orbital energy (${\displaystyle ϵ}$) of an elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form:

${\displaystyle \frac{v^2}{2}-\frac{\mu }{r}=-\frac{\mu }{2a}=ϵ<0}$

where:

• ${\displaystyle v}$ is the orbital speed of the orbiting body,
• ${\displaystyle r}$ is the distance of the orbiting body from the central body,
• ${\displaystyle a}$ is the length of the semi-major axis,
• ${\displaystyle \mu }$ is the standard gravitational parameter.

Conclusions:

• For a given semi-major axis the specific orbital energy is independent of the eccentricity.

Using the virial theorem to find:

• the time-average of the specific potential energy is equal to −2ε
  • the time-average of r⁻¹ is a⁻¹
• the time-average of the specific kinetic energy is equal to ε

Energy in terms of semi major axis

It can be helpful to know the energy in terms of the semi major axis (and the involved masses). The total energy of the orbit is given by

${\displaystyle E=-G\frac{Mm}{2a}}$,

where a is the semi major axis.

Derivation

Since gravity is a central force, the angular momentum is constant:

${\displaystyle \dot{\mathbf{L}}=\mathbf{r}\times \mathbf{F}=\mathbf{r}\times F(r)\hat{\mathbf{r}}=0}$

At the closest and furthest approaches, the angular momentum is perpendicular to the distance from the mass orbited, therefore:

${\displaystyle L=rp=rmv}$.

The total energy of the orbit is given by

${\displaystyle E=\frac{1}{2}m{v}^2-G\frac{Mm}{r}}$.

Substituting for v, the equation becomes

${\displaystyle E=\frac{1}{2}\frac{L^2}{m{r}^2}-G\frac{Mm}{r}}$.

This is true for r being the closest / furthest distance so two simultaneous equations are made, which when solved for E:

${\displaystyle E=-G\frac{Mm}{r_1+r_2}}$

Since $r_1=a+aϵ$ and ${\displaystyle r_2=a-aϵ}$, where epsilon is the eccentricity of the orbit, the stated result is reached.

Flight path angle

The flight path angle is the angle between the orbiting body's velocity vector (equal to the vector tangent to the instantaneous orbit) and the local horizontal. Under standard assumptions of the conservation of angular momentum the flight path angle ${\displaystyle \varphi }$ satisfies the equation:

${\displaystyle h=rv\cos \varphi }$

where:

• ${\displaystyle h}$ is the specific relative angular momentum of the orbit,
• ${\displaystyle v}$ is the orbital speed of the orbiting body,
• ${\displaystyle r}$ is the radial distance of the orbiting body from the central body,
• ${\displaystyle \varphi }$ is the flight path angle

${\displaystyle \psi }$ is the angle between the orbital velocity vector and the semi-major axis. ${\displaystyle \nu }$ is the local true anomaly. ${\displaystyle \varphi =\nu +\frac{\pi }{2}-\psi }$, therefore,

${\displaystyle \cos \varphi =\sin (\psi -\nu )=\sin \psi \cos \nu -\cos \psi \sin \nu =\frac{1+e\cos \nu }{\sqrt{1+e^2+2e\cos \nu }}}$

${\displaystyle \tan \varphi =\frac{e\sin \nu }{1+e\cos \nu }}$

where ${\displaystyle e}$ is the eccentricity.

The angular momentum is related to the vector cross product of position and velocity, which is proportional to the sine of the angle between these two vectors. Here ${\displaystyle \varphi }$ is defined as the angle which differs by 90 degrees from this, so the cosine appears in place of the sine.

Equation of motion

Main article: orbit equation

From initial position and velocity

An orbit equation defines the path of an orbiting body ${\displaystyle m_2}$ around central body ${\displaystyle m_1}$ relative to ${\displaystyle m_1}$, without specifying position as a function of time. If the eccentricity is less than 1 then the equation of motion describes an elliptical orbit. Because Kepler's equation ${\displaystyle M=E-e\sin E}$ has no general closed-form solution for the Eccentric anomaly (E) in terms of the Mean anomaly (M), equations of motion as a function of time also have no closed-form solution (although numerical solutions exist for both).

However, closed-form time-independent path equations of an elliptic orbit with respect to a central body can be determined from just an initial position (${\displaystyle \mathbf{r}}$) and velocity (${\displaystyle \mathbf{v}}$).

For this case it is convenient to use the following assumptions which differ somewhat from the standard assumptions above:

1. The central body's position is at the origin and is the primary focus (${\displaystyle \mathbf{F}\mathbf{1}}$) of the ellipse (alternatively, the center of mass may be used instead if the orbiting body has a significant mass)
2. The central body's mass (m1) is known
3. The orbiting body's initial position(${\displaystyle \mathbf{r}}$) and velocity(${\displaystyle \mathbf{v}}$) are known
4. The ellipse lies within the XY-plane

The fourth assumption can be made without loss of generality because any three points (or vectors) must lie within a common plane. Under these assumptions the second focus (sometimes called the "empty" focus) must also lie within the XY-plane: ${\displaystyle \mathbf{F}\mathbf{2}=\left(f_x,f_y\right)}$ .

Using vectors

The general equation of an ellipse under these assumptions using vectors is:

${\displaystyle |\mathbf{F}\mathbf{2}-\mathbf{p}|+|\mathbf{p}|=2a\mid z=0}$

where:

• ${\displaystyle a}$ is the length of the semi-major axis.
• ${\displaystyle \mathbf{F}\mathbf{2}=\left(f_x,f_y\right)}$ is the second ("empty") focus.
• ${\displaystyle \mathbf{p}=\left(x,y\right)}$ is any (x,y) value satisfying the equation.

The semi-major axis length (a) can be calculated as:

${\displaystyle a=\frac{\mu |\mathbf{r}|}{2\mu -|\mathbf{r}|{\mathbf{v}}^2}}$

where ${\displaystyle \mu =G{m}_1}$ is the standard gravitational parameter.

The empty focus (${\displaystyle \mathbf{F}\mathbf{2}=\left(f_x,f_y\right)}$) can be found by first determining the Eccentricity vector:

${\displaystyle \mathbf{e}=\frac{\mathbf{r}}{|\mathbf{r}|}-\frac{\mathbf{v}\times \mathbf{h}}{\mu }}$

Where ${\displaystyle \mathbf{h}}$ is the specific angular momentum of the orbiting body:

${\displaystyle \mathbf{h}=\mathbf{r}\times \mathbf{v}}$

Then

${\displaystyle \mathbf{F}\mathbf{2}=-2a\mathbf{e}}$

Using XY Coordinates

This can be done in cartesian coordinates using the following procedure:

The general equation of an ellipse under the assumptions above is:

${\displaystyle \sqrt{{\left(f_x-x\right)}^2+{\left(f_y-y\right)}^2}+\sqrt{x^2+y^2}=2a\mid z=0}$

Given:

${\displaystyle r_x,r_y}$ the initial position coordinates

${\displaystyle v_x,v_y}$ the initial velocity coordinates

and

${\displaystyle \mu =G{m}_1}$ the gravitational parameter

Then:

${\displaystyle h=r_x{v}_y-r_y{v}_x}$ specific angular momentum

${\displaystyle r=\sqrt{r_x^2+r_y^2}}$ initial distance from F1 (at the origin)

${\displaystyle a=\frac{\mu r}{2\mu -r\left(v_x^2+v_y^2\right)}}$ the semi-major axis length

${\displaystyle e_x=\frac{r_x}{r}-\frac{h{v}_y}{\mu }}$ the Eccentricity vector coordinates

${\displaystyle e_y=\frac{r_y}{r}+\frac{h{v}_x}{\mu }}$

Finally, the empty focus coordinates

${\displaystyle f_x=-2a{e}_x}$

${\displaystyle f_y=-2a{e}_y}$

Now the result values fx, fy and a can be applied to the general ellipse equation above.

Orbital parameters

The state of an orbiting body at any given time is defined by the orbiting body's position and velocity with respect to the central body, which can be represented by the three-dimensional Cartesian coordinates (position of the orbiting body represented by x, y, and z) and the similar Cartesian components of the orbiting body's velocity. This set of six variables, together with time, are called the orbital state vectors. Given the masses of the two bodies they determine the full orbit. The two most general cases with these 6 degrees of freedom are the elliptic and the hyperbolic orbit. Special cases with fewer degrees of freedom are the circular and parabolic orbit.

Because at least six variables are absolutely required to completely represent an elliptic orbit with this set of parameters, then six variables are required to represent an orbit with any set of parameters. Another set of six parameters that are commonly used are the orbital elements.

Solar System

In the Solar System, planets, asteroids, most comets, and some pieces of space debris have approximately elliptical orbits around the Sun. Strictly speaking, both bodies revolve around the same focus of the ellipse, the one closer to the more massive body, but when one body is significantly more massive, such as the sun in relation to the earth, the focus may be contained within the larger massing body, and thus the smaller is said to revolve around it. The following chart of the perihelion and aphelion of the planets, dwarf planets, and Halley's Comet demonstrates the variation of the eccentricity of their elliptical orbits. For similar distances from the sun, wider bars denote greater eccentricity. Note the almost-zero eccentricity of Earth and Venus compared to the enormous eccentricity of Halley's Comet and Eris.

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.

Radial elliptic trajectory

A radial trajectory can be a double line segment, which is a degenerate ellipse with semi-minor axis = 0 and eccentricity = 1. Although the eccentricity is 1, this is not a parabolic orbit. Most properties and formulas of elliptic orbits apply. However, the orbit cannot be closed. It is an open orbit corresponding to the part of the degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again. In the case of point masses one full orbit is possible, starting and ending with a singularity. The velocities at the start and end are infinite in opposite directions and the potential energy is equal to minus infinity.

The radial elliptic trajectory is the solution of a two-body problem with at some instant zero speed, as in the case of dropping an object (neglecting air resistance).

See also: Free fall § Inverse-square law gravitational field

History

The Babylonians were the first to realize that the Sun's motion along the ecliptic was not uniform, though they were unaware of why this was; it is today known that this is due to the Earth moving in an elliptic orbit around the Sun, with the Earth moving faster when it is nearer to the Sun at perihelion and moving slower when it is farther away at aphelion.

In the 17th century, Johannes Kepler discovered that the orbits along which the planets travel around the Sun are ellipses with the Sun at one focus, and described this in his first law of planetary motion. Later, Isaac Newton explained this as a corollary of his law of universal gravitation.

Generations of Noah

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Generations_of_Noah

This T and O map, from the first printed version of Isidore's Etymologiae (Augsburg 1472), identifies the three known continents (Asia, Europe, and Africa) as respectively populated by descendants of Sem (Shem), Iafeth (Japheth), and Cham (Ham).

The world as known to the Hebrews according to the Mosaic account (1854 map), from the Historical Textbook and Atlas of Biblical Geography by Lyman Coleman.

The Generations of Noah, also called the Table of Nations or Origines Gentium, is a genealogy of the sons of Noah, according to the Hebrew Bible (Genesis 10:9), and their dispersion into many lands after the Flood, focusing on the major known societies. The term 'nations' to describe the descendants is a standard English translation of the Hebrew word "goyim", following the c. 400 CE Latin Vulgate's "nationes", and does not have the same political connotations that the word entails today.

The list of 70 names introduces for the first time several well-known ethnonyms and toponyms important to biblical geography, such as Noah's three sons Shem, Ham, and Japheth, from which 18th-century German scholars at the Göttingen school of history derived the race terminology Semites, Hamites, and Japhetites. Certain of Noah's grandsons were also used for names of peoples: from Elam, Ashur, Aram, Cush, and Canaan were derived respectively the Elamites, Assyrians, Arameans, Cushites, and Canaanites. Likewise, from the sons of Canaan: Heth, Jebus, and Amorus were derived Hittites, Jebusites, and Amorites. Further descendants of Noah include Eber (from Shem), the hunter-king Nimrod (from Cush), and the Philistines (from Misrayim).

As Christianity spread across the Roman Empire, it carried the idea that all people were descended from Noah. Not all Near Eastern people were covered in the biblical genealogy, as well as the Northern European peoples important to the Late Roman and Medieval world, such as the Celtic, Slavic, Germanic, and Nordic peoples; nor were others of the world's peoples, such as sub-Saharan Africans, Native Americans, and peoples of Central Asia, the Indian subcontinent, the Far East, and Australasia. Scholars derived a variety of arrangements to make the table fit, with for example the Scythians, which do feature in the tradition, being claimed as the ancestors of much of Northern Europe.

According to the biblical scholar Joseph Blenkinsopp, the 70 names in the list express symbolically the unity of humanity, corresponding to the 70 descendants of Israel who go down into Egypt with Jacob at Genesis 46:27 and the 70 elders of Israel who visit God with Moses at the covenant ceremony in Exodus 24:1–9.

Table of Nations

On the family pedigrees contained in the biblical pericope of Noah, Saadia Gaon (882‒942) wrote:

The Scriptures have traced the patronymic lineage of the seventy nations to the three sons of Noah, as also the lineage of Abraham and Ishmael, and of Jacob and Esau. The blessed Creator knew that men would find solace at knowing these family pedigrees, since our soul demands of us to know them, so that [all of] mankind will be held in fondness by us, as a tree that has been planted by God in the earth, whose branches have spread out and dispersed eastward and westward, northward and southward, in the habitable part of the earth. It also has the dual function of allowing us to see the multitude as a single individual, and the single individual as a multitude. Along with this, man ought to contemplate also on the names of the countries and of the cities [wherein they settled]."

Maimonides, echoing the same sentiments, wrote that the genealogy of the nations contained in the Law has the unique function of establishing a principle of faith, how that, although from Adam to Moses there was no more than a span of two-thousand five hundred years, and the human race was already spread over all parts of the earth in different families and with different languages, they were still people having a common ancestor and place of beginning.

Other Bible commentators observe that the Table of Nations is unique compared to other genealogies since it depicts a "broad network of cousins", with a "shallow chain of brotherly relationships". Meanwhile, the other genealogies focus on "narrow chains of father-son relationships".

Book of Genesis

Noah dividing the world between his sons. Anonymous painter; Russian Empire, 18th century

Chapters 1–11 of the Book of Genesis are structured around five toledot statements ("these are the generations of..."), of which the "generations of the sons of Noah, Shem, Ham, and Japheth" is the fourth. Events before the Genesis flood narrative, the central toledot, correspond to those after: the post-Flood world is a new creation corresponding to the Genesis creation narrative, and Noah had three sons who populated the world. The correspondences extend forward as well: there are 70 names in the Table, corresponding to the 70 Israelites who go down into Egypt at the end of Genesis and to the 70 elders of Israel who go up the mountain at Sinai to meet with God in Exodus. The symbolic force of these numbers is underscored by the way the names are frequently arranged in groups of seven, suggesting that the Table is a symbolic means of implying universal moral obligation. The number 70 also parallels Canaanite mythology, where 70 represents the number of gods in the divine clan who are each assigned a subject people, and where the supreme god El and his consort, Asherah, has the title "Mother/Father of 70 gods", which, due to the coming of monotheism, had to be changed, but its symbolism lived on in the new religion.

The overall structure of the Table is:

• 1. Introductory formula, v.1
• 2. Japheth, vv.2–5
• 3. Ham, vv.6–20
• 4. Shem, vv.21–31
• 5. Concluding formula, v.32.

The overall principle governing the assignment of various peoples within the Table is difficult to discern: it purports to describe all humankind, but in reality restricts itself to the Egyptian lands of the south, the Mesopotamian lands, and Anatolia/Asia Minor and the Ionian Greeks, and in addition, the "sons of Noah" are not organized by geography, language family or ethnic groups within these regions. The Table contains several difficulties: for example, the names Sheba and Havilah are listed twice, first as descendants of Cush the son of Ham (verse 7), and then as sons of Joktan, the great-grandsons of Shem, and while the Cushites are North African in verses 6–7 they are unrelated Mesopotamians in verses 10–14.

The date of composition of Genesis 1–11 cannot be fixed with any precision, although it seems likely that an early brief nucleus was later expanded with extra data. Portions of the Table itself 'may' derive from the 10th century BCE, while others reflect the 7th century BCE and priestly revisions in the 5th century BCE. Its combination of world review, myth and genealogy corresponds to the work of the Greek historian Hecataeus of Miletus, active c. 520 BCE.

Book of Chronicles

I Chronicles 1 includes a version of the Table of Nations from Genesis, but edited to make clearer that the intention is to establish the background for Israel. This is done by condensing various branches to focus on the story of Abraham and his offspring. Most notably, it omits Genesis 10:9–14, in which Nimrod, a son of Cush, is linked to various cities in Mesopotamia, thus removing from Cush any Mesopotamian connection. In addition, Nimrod does not appear in any of the numerous Mesopotamian King Lists.

Book of Jubilees

Ionian world map

The Table of Nations is expanded upon in detail in chapters 8–9 of the Book of Jubilees, sometimes known as the "Lesser Genesis," a work from the early Second Temple period. Jubilees is considered pseudepigraphical by most Christian and Jewish denominations but thought to have been held in regard by many of the Church Fathers. Its division of the descendants throughout the world are thought to have been heavily influenced by the "Ionian world map" described in the Histories of Herodotus, and the anomalous treatment of Canaan and Madai are thought to have been "propaganda for the territorial expansion of the Hasmonean state".

Septuagint version

The Hebrew bible was translated into Greek in Alexandria at the request of Ptolemy II, who reigned over Egypt 285–246 BCE. Its version of the Table of Nations is substantially the same as that in the Hebrew text, but with the following differences:

• It lists Elisa as an extra son of Japheth, giving him eight instead of seven, while continuing to list him also as a son of Javan, as in the Masoretic text.
• Whereas the Hebrew text lists Shelah as the son of Arpachshad in the line of Shem, the Septuagint has a Cainan as the son of Arpachshad and father of Shelah – the Book of Jubilees gives considerable scope to this figure. Cainan appears again at the end of the list of the sons of Shem.
• Obal, Joktan's eighth son in the Masoretic text, does not appear.

1 Peter

In the First Epistle of Peter, 3:20, the author says that eight righteous persons were saved from the Great Flood, referring to the four named males, and their wives aboard Noah's Ark not enumerated elsewhere in the Bible.

Sons of Noah: Shem, Ham and Japheth

1823 map by Robert Wilkinson (see also 1797 version here). Prior to the mid-19th century, Shem was associated with all of Asia, Ham with all of Africa and Japheth with all of Europe.

The Genesis flood narrative tells how Noah and his three sons Shem, Ham, and Japheth, together with their wives, were saved from the Deluge to repopulate the Earth.

• Shem's descendants: Genesis chapter 10 verses 21–30 gives one list of descendants of Shem. In chapter 11 verses 10–26 a second list of descendants of Shem names Abraham and thus the Arabs and Israelites. In the view of some 17th-century European scholars (e.g., John Webb), the Native American peoples of North and South America, eastern Persia and "the Indias" descended from Shem, possibly through his descendant Joktan. Some modern creationists identify Shem as the progenitor of Y-chromosomal haplogroup IJ, and hence haplogroups I (common in northern Europe) and J (common in the Middle East).

• Ham's descendants: The forefather of Cush, Egypt, and Put, and of Canaan, whose lands include portions of Africa. The Aboriginal Australians and indigenous people of New Guinea have also been tied to Ham. The etymology of his name is uncertain; some scholars have linked it to terms connected with divinity, but a divine or semi-divine status for Ham is unlikely.
• Japheth's descendants: His name is associated with the mythological Greek Titan Iapetus, and his sons include Javan, the Greek-speaking cities of Ionia. In Genesis 9:27 it forms a pun with the Hebrew root yph: "May God make room [the hiphil of the yph root] for Japheth, that he may live in Shem's tents and Canaan may be his slave."

Based on an old Jewish tradition contained in the Aramaic Targum of pseudo-Jonathan ben Uzziel, an anecdotal reference to the Origines gentium in Genesis 10:2–ff has been passed down, and which, in one form or another, has also been relayed by Josephus in his Antiquities, repeated in the Talmud, and further elaborated by medieval Jewish scholars, such as in works written by Saadia Gaon, Josippon, and Don Isaac Abarbanel, who, based on their own knowledge of the nations, showed their migratory patterns at the time of their compositions:

"The sons of Japheth are Gomer, and Magog, and Madai, and Javan, and Tuval, and Meshech and Tiras, while the names of their diocese are Africa proper, and Germania, and Media, and Macedonia, and Bithynia, and Moesia (var. Mysia) and Thrace. Now, the sons of Gomer were Ashkenaz, and Rifath and Togarmah, while the names of their diocese are Asia, and Parthia and the 'land of the barbarians.' The sons of Javan were Elisha, and Tarshish, Kitim and Dodanim, while the names of their diocese are Elis, and Tarsus, Achaia and Dardania." ---Targum Pseudo-Jonathan on Genesis 10:2–5

"The sons of Ḥam are Kūš, and Miṣrayim, and Fūṭ (Phut), and Kenaʻan, while the names of their diocese are Arabia, and Egypt, and Elīḥerūq and Canaan. The sons of Kūš are Sebā and Ḥawīlah and Savtah and Raʻamah and Savteḫā, [while the sons of Raʻamah are Ševā and Dedan]. The names of their diocese are called Sīnīrae, and Hīndīqī, Samarae, Lūbae, Zinğae, while the sons of Mauretinos are [the inhabitants of] Zemarğad and [the inhabitants of] Mezağ." ---Targum Pseudo-Jonathan on Genesis 10:6–7

"The sons of Shem are Elam, and Ashur, and Arphaxad, and Lud, and Aram. [And the children of Aram are these: Uz, and Hul, and Gether, and Mash.] Now, Arphaxad begat Shelah (Salah), and Shelah begat Eber. Unto Eber were born two sons, the one named Peleg, since in his days the [nations of the] earth were divided, while the name of his brother is Joktan. Joktan begat Almodad, who measured the earth with ropes; Sheleph, who drew out the waters of rivers; and Hazarmaveth, and Jerah, and Hadoram, and Uzal, and Diklah, and Obal, and Abimael, and Sheba, and Ophir, and Havilah, and Jobab, all of whom are the sons of Joktan." ---Targum Pseudo-Jonathan on Genesis 10: 22–28

Noahic descandant (Gen. 10:2 – 10:23)	Proposed historical identifications
Gomer	Cimmerians
Magog	Lydia (Mermnad dynasty)
Madai	Uncertain, usually reckoned as the Medes, but other proposals include Matiene, Mannaea, and Mitanni.
Javan	Ionians
Tubal	Tabal
Tiras	Thrace
Meshech	Muski
Ashkenaz	Scythians
Riphath	Uncertain, proposals include Paphlagonia, and the semihistorical Arimaspi.
Togarmah	Tegarama
Elishah	Uncertain, usually reckoned as Alashiya, but other proposals include Magna Graecia, the Sicels, the Aeolians and Carthage.
Tarshish	Tarshish, though its location has been debated for centuries and remains uncertain.
Kittim	Kition
Dodanim	Uncertain, further complicated by its later attestation as Rodanim. Those assuming Dodanim represents the original form have proposed Dodona, Dardania, and Dardanus; whereas those assuming Rodanim represents the original have almost universally proposed Rhodes.
Cush	Kush
Mizraim	Egypt
Put	Ancient Libya
Canaan	Canaan
Seba	Uncertain
Havilah	Uncertain, proposals include Nubia, Arabia, Somalia, and Bahrain Island.
Sabtah	Uncertain
Raamah	Uncertain
Sabtecha	Uncertain
Sheba	Sabaʾ
Dedan	Lihyan
Nimrod	Uncertain, various proposals exist imagining Nimrod as an ethnic group, person, city, and deity.
Ludim	Uncertain, sometimes suggested to represent Libya
Anamim	Uncertain
Lehabim	Uncertain, sometimes synchronized with Ludim.
Naphtuhim	Uncertain
Pathrusim	Pathros
"the Casluhites"	Kasluḥet of Egypt, modern identification uncertain.
"the Caphtorites"	Caphtor, modern identification uncertain, proposals include Cilicia, Cyprus, and Crete.
Sidon	Sidon
Heth	Biblical Hittites
"the Jebusites"	Jebus, traditionally identified as Jerusalem
"the Amorites"	Amurru
"the Girgashites"	Possibly Karkisa.
"the Hivites"	Uncertain
"the Arkites"	Arqa
"the Sinites"	Uncertain
"the Arvadites"	Arwad
"the Zemarites"	Sumur
"the Hamathites"	Hama
Elam	Elam
Ashur	Aššur
Lud	Lydia
Aram	Aram
Uz	"Land of Uz", hypothesized locations include Aram and Edom
Hul	Uncertain
Gether	Uncertain
Mash	Uncertain

Problems with identification

Because of the traditional grouping of people based on their alleged descent from the three major biblical progenitors (Shem, Ham, and Japheth) by the three Abrahamic religions, in former years there was an attempt to classify these family groups and to divide humankind into three races called Caucasoid, Mongoloid, and Negroid (originally named "Ethiopian"), terms which were introduced in the 1780s by members of the Göttingen school of history. It is now recognized that determining precise descent-groups based strictly on patrilineal descent is problematic, owing to the fact that nations are not stationary. People are often multi-lingual and multi-ethnic, and people sometimes migrate from one country to another - whether voluntarily or involuntarily. Some nations have intermingled with other nations and can no longer trace their paternal descent, or have assimilated and abandoned their mother's tongue for another language. In addition, phenotypes cannot always be used to determine one's ethnicity because of interracial marriages. A nation today is defined as "a large aggregate of people inhabiting a particular territory united by a common descent, history, culture, or language." The biblical line of descent is irrespective of language, place of nativity, or cultural influences, as all that is binding is one's patrilineal line of descent. For these reasons, attempting to determine precise blood relation of any one group in today's Modern Age may prove futile. Sometimes people sharing a common patrilineal descent spoke two separate languages, whereas, at other times, a language spoken by a people of common descent may have been learnt and spoken by multiple other nations of different descent.

Another problem associated with determining precise descent-groups based strictly on patrilineal descent is the realization that, for some of the prototypical family groups, certain sub-groups have sprung forth, and are considered diverse from each other (such as Ismael, the progenitor of the Arab nations, and Isaac, the progenitor of the Israelite nation, although both family groups are derived from Shem's patrilineal line through Eber. The total number of other sub-groups, or splinter groups, each with its distinct language and culture is unknown.

Ethnological interpretations

Main article: Biblical terminology for race

Identifying geographically-defined groups of people in terms of their biblical lineage, based on the Generations of Noah, has been common since antiquity.

The early modern biblical division of the world's "races" into Semites, Hamites and Japhetites was coined at the Göttingen school of history in the late 18th century – in parallel with the color terminology for race which divided mankind into five colored races ("Caucasian or White", "Mongolian or Yellow", "Aethiopian or Black", "American or Red" and "Malayan or Brown").

Extrabiblical sons of Noah

There exist various traditions in post-biblical and talmudic sources claiming that Noah had children other than Shem, Ham, and Japheth who were born before the Deluge.

According to the Quran (Hud 42–43), Noah had another unnamed son who refused to come aboard the Ark, instead preferring to climb a mountain, where he drowned. Some later Islamic commentators give his name as either Yam or Kan'an.

According to Irish mythology, as found in the Annals of the Four Masters and elsewhere, Noah had another son named Bith who was not allowed aboard the Ark, and who attempted to colonise Ireland with 54 persons, only to be wiped out in the Deluge.

Some 9th-century manuscripts of the Anglo-Saxon Chronicle assert that Sceafa was the fourth son of Noah, born aboard the Ark, from whom the House of Wessex traced their ancestry; in William of Malmesbury's version of this genealogy (c. 1120), Sceaf is instead made a descendant of Strephius, the fourth son born aboard the Ark (Gesta Regnum Anglorum).

An early Arabic work known as Kitab al-Magall "Book of Rolls" (part of Clementine literature) mentions Bouniter, the fourth son of Noah, born after the flood, who allegedly invented astronomy and instructed Nimrod. Variants of this story with often similar names for Noah's fourth son are also found in the c. fifth century Ge'ez work Conflict of Adam and Eve with Satan (Barvin), the c. sixth century Syriac book Cave of Treasures (Yonton), the seventh century Apocalypse of Pseudo-Methodius (Ionitus), the Syriac Book of the Bee 1221 (Yônatôn), the Hebrew Chronicles of Jerahmeel, c. 12th–14th century (Jonithes), and throughout Armenian apocryphal literature, where he is usually referred to as Maniton; as well as in works by Petrus Comestor c. 1160 (Jonithus), Godfrey of Viterbo 1185 (Ihonitus), Michael the Syrian 1196 (Maniton), Abu al-Makarim c. 1208 (Abu Naiţur); Jacob van Maerlant c. 1270 (Jonitus), and Abraham Zacuto 1504 (Yoniko).

Martin of Opava (c. 1250), later versions of the Mirabilia Urbis Romae, and the Chronica Boemorum of Giovanni de' Marignolli (1355) make Janus (the Roman deity) the fourth son of Noah, who moved to Italy, invented astrology, and instructed Nimrod.

According to the monk Annio da Viterbo (1498), the Hellenistic Babylonian writer Berossus had mentioned 30 children born to Noah after the Deluge, including Macrus, Iapetus Iunior (Iapetus the Younger), Prometheus Priscus (Prometheus the Elder), Tuyscon Gygas (Tuyscon the Giant), Crana, Cranus, Granaus, 17 Tytanes (Titans), Araxa Prisca (Araxa the Elder), Regina, Pandora Iunior (Pandora the Younger), Thetis, Oceanus, and Typhoeus. However, Annio's manuscript is widely regarded today as having been a forgery.

Historian William Whiston stated in his book A New Theory of the Earth that Noah, who is to be identified with Fuxi, migrated with his wife and children born after the deluge to China, and founded Chinese civilization.