Imaginary unit

From Wikipedia, the free encyclopedia

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

The imaginary unit i in the complex plane: Real numbers are conventionally drawn on the horizontal axis, and imaginary numbers on the vertical axis.

The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x² + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is 2 + 3i.

Imaginary numbers are an important mathematical concept; they extend the real number system ${\displaystyle \mathbb{R}}$ to the complex number system ${\displaystyle \mathbb{C},}$ in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square.

There are two complex square roots of −1: i and −i, just as there are two complex square roots of every real number other than zero (which has one double square root).

In contexts in which use of the letter i is ambiguous or problematic, the letter j is sometimes used instead. For example, in electrical engineering and control systems engineering, the imaginary unit is normally denoted by j instead of i, because i is commonly used to denote electric current.

Terminology

Further information: Complex number § History

Square roots of negative numbers are called imaginary because in early-modern mathematics, only what are now called real numbers, obtainable by physical measurements or basic arithmetic, were considered to be numbers at all – even negative numbers were treated with skepticism – so the square root of a negative number was previously considered undefined or nonsensical. The name imaginary is generally credited to René Descartes, and Isaac Newton used the term as early as 1670. The i notation was introduced by Leonhard Euler.

A unit is an undivided whole, and unity or the unit number is the number one (1).

Definition

The powers of i are cyclic:
${\displaystyle ⋮}$
${\displaystyle i^{-4}=\phantom{}1\phantom{}}$
${\displaystyle i^{-3}=\phantom{}i\phantom{\mathrm{}}}$
${\displaystyle i^{-2}=-1\phantom{}}$
${\displaystyle i^{-1}=-i\phantom{\mathrm{}}}$
${\displaystyle i^0=\phantom{}1\phantom{}}$
${\displaystyle i^1=\phantom{}i\phantom{\mathrm{}}}$
${\displaystyle i^2=-1\phantom{}}$
${\displaystyle i^3=-i\phantom{\mathrm{}}}$
${\displaystyle i^4=\phantom{}1\phantom{}}$
${\displaystyle i^5=\phantom{}i\phantom{\mathrm{}}}$
${\displaystyle i^6=-1\phantom{}}$
${\displaystyle i^7=-i\phantom{\mathrm{}}}$
${\displaystyle ⋮}$

The imaginary unit i is defined solely by the property that its square is −1:

$${\displaystyle i^2=-1.}$$

With i defined this way, it follows directly from algebra that i and −i are both square roots of −1.

Although the construction is called "imaginary", and although the concept of an imaginary number may be intuitively more difficult to grasp than that of a real number, the construction is valid from a mathematical standpoint. Real number operations can be extended to imaginary and complex numbers, by treating i as an unknown quantity while manipulating an expression (and using the definition to replace any occurrence of i² with −1). Higher integral powers of i are thus

$${\displaystyle \begin{array}{rlrlrl}{i}^3& =i^{2}i& & =(-1)i& & =-i,\\ i^4& =i^{3}i& & =(-i)i& & =1,\\ i^5& =i^{4}i& & =(1)i& & =i,\end{array}}$$

and so on, cycling through the four values 1, i, −1, and −i. As with any non-zero real number, i⁰ = 1.

As a complex number, i can be represented in rectangular form as 0 + 1i, with a zero real component and a unit imaginary component. In polar form, i can be represented as 1 × e^{πi /2} (or just e^{πi /2}), with an absolute value (or magnitude) of 1 and an argument (or angle) of ${\displaystyle \frac{\pi }{2}}$ radians. (Adding any integer multiple of 2π to this angle works as well.) In the complex plane, which is a special interpretation of a Cartesian plane, i is the point located one unit from the origin along the imaginary axis (which is orthogonal to the real axis).

i vs. −i

Being a quadratic polynomial with no multiple root, the defining equation x² = −1 has two distinct solutions, which are equally valid and which happen to be additive and multiplicative inverses of each other. Although the two solutions are distinct numbers, their properties are indistinguishable; there is no property that one has that the other does not. One of these two solutions is labelled +i (or simply i) and the other is labelled −i, though which is which is inherently ambiguous.

The only differences between +i and −i arise from this labelling. For example, by convention +i is said to have an argument of ${\displaystyle +\frac{\pi }{2}}$ and −i is said to have an argument of ${\displaystyle -\frac{\pi }{2},}$ related to the convention of labelling orientations in the Cartesian plane relative to the positive x-axis with positive angles turning anticlockwise in the direction of the positive y-axis. Despite the signs written with them, neither +i nor −i is inherently positive or negative in the sense that real numbers are.

A more formal expression of this indistinguishability of +i and −i is that, although the complex field is unique (as an extension of the real numbers) up to isomorphism, it is not unique up to a unique isomorphism. That is, there are two field automorphisms of the complex numbers ${\displaystyle \mathbb{C}}$ that keep each real number fixed, namely the identity and complex conjugation. For more on this general phenomenon, see Galois group.

Matrices

Using the concepts of matrices and matrix multiplication, complex numbers can be represented in linear algebra. The real unit 1 and imaginary unit i can be represented by any pair of matrices I and J satisfying I² = I, IJ = JI = J, and J² = −I. Then a complex number a + bi can be represented by the matrix aI + bJ, and all of the ordinary rules of complex arithmetic can be derived from the rules of matrix arithmetic.

The most common choice is to represent 1 and i by the 2 × 2 identity matrix I and the matrix J,

$${\displaystyle I=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right),J=\left(\begin{array}{cc}0& -1\\ 1& 0\end{array}\right).}$$

Then an arbitrary complex number a + bi can be represented by:

$${\displaystyle aI+bJ=\left(\begin{array}{cc}a& -b\\ b& a\end{array}\right).}$$

More generally, any real-valued 2 × 2 matrix with a trace of zero and a determinant of one squares to −I, so could be chosen for J. Larger matrices could also be used, for example 1 could be represented by the 4 × 4 identity matrix and i could be represented by any of the Dirac matrices for spatial dimensions.

Root of x² + 1

Polynomials (weighted sums of the powers of a variable) are a basic tool in algebra. Polynomials whose coefficients are real numbers form a ring, denoted ${\displaystyle \mathbb{R}[x],}$ an algebraic structure with addition and multiplication and sharing many properties with the ring of integers.

The polynomial ${\displaystyle x^2+1}$ has no real-number roots, but the set of all real-coefficient polynomials divisible by ${\displaystyle x^2+1}$ forms an ideal, and so there is a quotient ring ${\displaystyle \mathbb{R}[x]/⟨x^2+1⟩.}$ This quotient ring is isomorphic to the complex numbers, and the variable ${\displaystyle x}$ expresses the imaginary unit.

Graphic representation

Main article: Complex plane

The complex numbers can be represented graphically by drawing the real number line as the horizontal axis and the imaginary numbers as the vertical axis of a Cartesian plane called the complex plane. In this representation, the numbers 1 and i are at the same distance from 0, with a right angle between them. Addition by a complex number corresponds to translation in the plane, while multiplication by a unit-magnitude complex number corresponds to rotation about the origin. Every similarity transformation of the plane can be represented by a complex-linear function ${\displaystyle z\mapsto az+b.}$

Geometric algebra

In the geometric algebra of the Euclidean plane, the geometric product or quotient of two arbitrary vectors is a sum of a scalar (real number) part and a bivector part. (A scalar is a quantity with no orientation, a vector is a quantity oriented like a line, and a bivector is a quantity oriented like a plane.) The square of any vector is a positive scalar, representing its length squared, while the square of any bivector is a negative scalar.

The quotient of a vector with itself is the scalar 1 = u/u, and when multiplied by any vector leaves it unchanged (the identity transformation). The quotient of any two perpendicular vectors of the same magnitude, J = u/v, which when multiplied rotates the divisor a quarter turn into the dividend, Jv = u, is a unit bivector which squares to −1, and can thus be taken as a representative of the imaginary unit. Any sum of a scalar and bivector can be multiplied by a vector to scale and rotate it, and the algebra of such sums is isomorphic to the algebra of complex numbers. In this interpretation points, vectors, and sums of scalars and bivectors are all distinct types of geometric objects.

More generally, in the geometric algebra of any higher-dimensional Euclidean space, a unit bivector of any arbitrary planar orientation squares to −1, so can be taken to represent the imaginary unit i.

Proper use

The imaginary unit was historically written $\sqrt{-1},$ and still is in some modern works. However, great care needs to be taken when manipulating formulas involving radicals. The radical sign notation $\sqrt{x}$ is reserved either for the principal square root function, which is defined for only real x ≥ 0, or for the principal branch of the complex square root function. Attempting to apply the calculation rules of the principal (real) square root function to manipulate the principal branch of the complex square root function can produce false results:

$${\displaystyle -1=i\cdot i=\sqrt{-1}\cdot \sqrt{-1}\stackrel{\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{y}}{=}\sqrt{(-1)\cdot (-1)}=\sqrt{1}=1\text{(incorrect).}}$$

Generally, the calculation rules $\sqrt{x\phantom{}}\cdot \sqrt{y\phantom{}}=\sqrt{x\cdot y\phantom{}}$ and $\sqrt{x\phantom{}}/\sqrt{y\phantom{}}=\sqrt{x/y}$ are guaranteed to be valid for real, positive values of x and y only. When x or y is real but negative, these problems can be avoided by writing and manipulating expressions like $i\sqrt{7}$, rather than $\sqrt{-7}$. For a more thorough discussion, see square root and branch point.

Properties

As a complex number, the imaginary unit follows all of the rules of complex arithmetic.

Imaginary integers and imaginary numbers

When the imaginary unit is repeatedly added or subtracted, the result is some integer times the imaginary unit, an imaginary integer; any such numbers can be added and the result is also an imaginary integer:

$${\displaystyle ai+bi=(a+b)i.}$$

Thus, the imaginary unit is the generator of a group under addition, specifically an infinite cyclic group.

The imaginary unit can also be multiplied by any arbitrary real number to form an imaginary number. These numbers can be pictured on a number line, the imaginary axis, which as part of the complex plane is typically drawn with a vertical orientation, perpendicular to the real axis which is drawn horizontally.

Gaussian integers

Integer sums of the real unit 1 and the imaginary unit i form a square lattice in the complex plane called the Gaussian integers. The sum, difference, or product of Gaussian integers is also a Gaussian integer:

$${\displaystyle \begin{array}{rl}(a+bi)+(c+di)& =(a+c)+(b+d)i,\\ (a+bi)(c+di)& =(ac-bd)+(ad+bc)i.\end{array}}$$

Quarter-turn rotation

When multiplied by the imaginary unit i, any arbitrary complex number in the complex plane is rotated by a quarter turn (${\displaystyle \frac{1}{2}\pi }$ radians or 90°) anticlockwise. When multiplied by −i, any arbitrary complex number is rotated by a quarter turn clockwise. In polar form:

$${\displaystyle ir{e}^{\phi i}=r{e}^{(\phi +\pi /2)i},-ir{e}^{\phi i}=r{e}^{(\phi -\pi /2)i}.}$$

In rectangular form,

$${\displaystyle i(a+bi)=-b+ai,-i(a+bi)=b-ai.}$$

Integer powers

The powers of i repeat in a cycle expressible with the following pattern, where n is any integer:

$${\displaystyle i^{4n}=1,i^{4n+1}=i,i^{4n+2}=-1,i^{4n+3}=-i.}$$

Thus, under multiplication, i is a generator of a cyclic group of order 4, a discrete subgroup of the continuous circle group of the unit complex numbers under multiplication.

Written as a special case of Euler's formula for an integer n,

$${\displaystyle i^n=\exp (\frac{1}{2}\pi i{)}^n=\exp (\frac{1}{2}n\pi i)=\cos (\frac{1}{2}n\pi )+i\sin (\frac{1}{2}n\pi ).}$$

With a careful choice of branch cuts and principal values, this last equation can also apply to arbitrary complex values of n, including cases like n = i.

Roots

The two square roots of i in the complex plane

Just like all nonzero complex numbers, $i=e^{\pi i/2}$ has two distinct square roots which are additive inverses. In polar form, they are

$${\displaystyle \begin{array}{rlrl}\sqrt{i}& =\exp (\frac{1}{2}\pi i{)}^{1/2}& & =\exp (\frac{1}{4}\pi i),\\ -\sqrt{i}& =\exp (\frac{1}{4}\pi i-\pi i)& & =\exp (-\frac{3}{4}\pi i).\end{array}}$$

In rectangular form, they are

$${\displaystyle \begin{array}{rlrl}\sqrt{i}& =(1+i)/\sqrt{2}& & =\phantom{}\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i,\\ -\sqrt{i}& =-(1+i)/\sqrt{2}& & =-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i.\end{array}}$$

Squaring either expression yields

$${\displaystyle {\left(\pm \frac{1+i}{\sqrt{2}}\right)}^2=\frac{1+2i-1}{2}=\frac{2i}{2}=i.}$$

The three cube roots of i in the complex plane

The three cube roots of i are

$${\displaystyle \sqrt[3]{i}=\exp (\frac{1}{6}\pi i)=\frac{\sqrt{3}}{2}+\frac{1}{2}i,\exp (\frac{5}{6}\pi i)=-\frac{\sqrt{3}}{2}+\frac{1}{2}i,\exp (-\frac{1}{2}\pi i)=-i.}$$

For a general positive integer n, the n-th roots of i are, for k = 0, 1, ..., n − 1,

$${\displaystyle \exp \left(2\pi i\frac{k+\frac{1}{4}}{n}\right)=\cos \left(\frac{4k+1}{2n}\pi \right)+i\sin \left(\frac{4k+1}{2n}\pi \right).}$$

The value associated with k = 0 is the principal n-th root of i. The set of roots equals the corresponding set of roots of unity rotated by the principal n-th root of i. These are the vertices of a regular polygon inscribed within the complex unit circle.

Exponential and logarithm

The complex exponential function relates complex addition in the domain to complex multiplication in the codomain. Real values in the domain represent scaling in the codomain (multiplication by a real scalar) with 1 representing multiplication by e, while imaginary values in the domain represent rotation in the codomain (multiplication by a unit complex number) with i representing a rotation by 1 radian. The complex exponential is thus a periodic function in the imaginary direction, with period 2πi and image 1 at points 2kπi for all integers k, a real multiple of the lattice of imaginary integers.

The complex exponential can be broken into even and odd components, the hyperbolic functions cosh and sinh or the trigonometric functions cos and sin:

$${\displaystyle \exp z=\cosh z+\sinh z=\cos (-iz)+i\sin (-iz)}$$

Euler's formula decomposes the exponential of an imaginary number representing a rotation:

$${\displaystyle \exp i\phi =\cos \phi +i\sin \phi .}$$

The quotient coth z = cosh z / sinh z, with appropriate scaling, can be represented as an infinite partial fraction decomposition as the sum of reciprocal functions translated by imaginary integers:

$${\displaystyle \pi \coth \pi z=\underset{n\to \mathrm{\infty }}{lim}\sum _{k=-n}^n\frac{1}{z+ki}.}$$

Other functions based on the complex exponential are well-defined with imaginary inputs. For example, a number raised to the ni power is:

$${\displaystyle x^{ni}=\cos (n\ln x)+i\sin (n\ln x).}$$

Because the exponential is periodic, its inverse the complex logarithm is a multi-valued function, with each complex number in the domain corresponding to multiple values in the codomain, separated from each-other by any integer multiple of 2πi. One way of obtaining a single-valued function is to treat the codomain as a cylinder, with complex values separated by any integer multiple of 2πi treated as the same value; another is to take the domain to be a Riemann surface consisting of multiple copies of the complex plane stitched together along the negative real axis as a branch cut, with each branch in the domain corresponding to one infinite strip in the codomain. Functions depending on the complex logarithm therefore depend on careful choice of branch to define and evaluate clearly.

For example, if one chooses any branch where ${\displaystyle \ln i=\frac{1}{2}\pi i}$ then when x is a positive real number,

$${\displaystyle {\log }_{i}x=-\frac{2i\ln x}{\pi }.}$$

Factorial

The factorial of the imaginary unit i is most often given in terms of the gamma function evaluated at 1 + i:

$${\displaystyle i!=\mathrm{\Gamma }(1+i)=i\mathrm{\Gamma }(i)\approx 0.4980-0.1549i.}$$

The magnitude and argument of this number are:

$${\displaystyle |\mathrm{\Gamma }(1+i)|=\sqrt{\frac{\pi }{\sinh \pi }}\approx 0.5216,\arg \mathrm{\Gamma }(1+i)\approx -\mathrm{0.3016.}}$$

Spaceplane

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Spaceplane

A spaceplane is a vehicle that can fly and glide like an aircraft in Earth's atmosphere and maneuver like a spacecraft in outer space. To do so, spaceplanes must incorporate features of both aircraft and spacecraft. Orbital spaceplanes tend to be more similar to conventional spacecraft, while sub-orbital spaceplanes tend to be more similar to fixed-wing aircraft. All spaceplanes to date have been rocket-powered for takeoff and climb, but have then landed as unpowered gliders.

Four types of spaceplanes have successfully launched to orbit, reentered Earth's atmosphere, and landed: the U.S. Space Shuttle, Russian Buran, U.S. X-37, and the Chinese CSSHQ. Another, Dream Chaser, is under development in the U.S. As of 2019 all past, current, and planned orbital vehicles launch vertically on a separate rocket. Orbital spaceflight takes place at high velocities, with orbital kinetic energies typically greater than suborbital trajectories. This kinetic energy is shed as heat during reentry. Many more spaceplanes have been proposed, but none have reached flight status.

At least two suborbital rocket-powered aircraft have been launched horizontally into sub-orbital spaceflight from an airborne carrier aircraft before rocketing beyond the Kármán line: the X-15 and SpaceShipOne.

Operational principles

Landing of Space Shuttle Atlantis, a crewed orbital spaceplane

Spaceplanes must operate in space, like traditional spacecraft, but also must be capable of atmospheric flight, like an aircraft. These requirements drive up the complexity, risk, dry mass, and cost of spaceplane designs. The following sections will draw heavily on the US Space Shuttle as the biggest, deadliest, most complex, most expensive, most flown, and only crewed orbital spaceplane, but other designs have been successfully flown.

Launch to space

The flight trajectory required to reach orbit results in significant aerodynamic loads, vibrations, and accelerations, all of which have to be withstood by the vehicle structure.

If the launch vehicle suffers a catastrophic malfunction, a conventional capsule spacecraft is propelled to safety by a launch escape system. The Space Shuttle was far too big and heavy for this approach to be viable, resulting in a number of abort modes that may or may not have been survivable. In any case, the Challenger disaster demonstrated that the Space Shuttle lacked survivability on ascent.

Space environment

Once on-orbit, a spaceplane must be supplied with power by solar panels and batteries or fuel cells, maneuvered in space, kept in thermal equilibrium, oriented, and communicated with. On-orbit thermal and radiological environments impose additional stresses. This is in addition to accomplishing the task the spaceplane was launched to complete, such as satellite deployment or science experiments.

The Space Shuttle used dedicated engines to accomplish orbital maneuvers. These engines used toxic hypergolic propellants that required special handling precautions. Various gases, including helium for pressurization and nitrogen for life support, were stored under high pressure in composite overwrapped pressure vessels.

Atmospheric reentry

Main article: Atmospheric entry

Buran spaceplane rear showing rocket engine nozzles, attitude control thrusters, aerodynamic surfaces, and heat shielding

Orbital spacecraft reentering the Earth's atmosphere must shed significant velocity, resulting in extreme heating. For example, the Space Shuttle thermal protection system (TPS) protects the orbiter's interior structure from surface temperatures that reach as high as 1,650 °C (3,000 °F), well above the melting point of steel. Suborbital spaceplanes fly lower energy trajectories that do not put as much stress on the spacecraft thermal protection system.

The Space Shuttle Columbia disaster was the direct result of a TPS failure.

Aerodynamic flight and horizontal landing

Aerodynamic control surfaces must be actuated. Landing gear must be included at the cost of additional mass.

Air-breathing orbital spaceplane concept

An air-breathing orbital spaceplane would have to fly what is known as a 'depressed trajectory,' which places the vehicle in the high-altitude hypersonic flight regime of the atmosphere for an extended period of time. This environment induces high dynamic pressure, high temperature, and high heat flow loads particularly upon the leading edge surfaces of the spaceplane, requiring exterior surfaces to be constructed from advanced materials and/or use active cooling.

Orbital spaceplanes

Space Shuttle

Discovery lifts off at the start of the STS-120 mission.

The Space Shuttle is a retired, partially reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. Its official program name was Space Transportation System (STS), taken from a 1969 plan for a system of reusable spacecraft where it was the only item funded for development.

The first (STS-1) of four orbital test flights occurred in 1981, leading to operational flights (STS-5) beginning in 1982. Five complete Space Shuttle orbiter vehicles were built and flown on a total of 135 missions from 1981 to 2011. They launched from the Kennedy Space Center (KSC) in Florida. Operational missions launched numerous satellites, interplanetary probes, and the Hubble Space Telescope (HST), conducted science experiments in orbit, participated in the Shuttle-Mir program with Russia, and participated in the construction and servicing of the International Space Station (ISS). The Space Shuttle fleet's total mission time was 1,323 days.

Space Shuttle components include the Orbiter Vehicle (OV) with three clustered Rocketdyne RS-25 main engines, a pair of recoverable solid rocket boosters (SRBs), and the expendable external tank (ET) containing liquid hydrogen and liquid oxygen. The Space Shuttle was launched vertically, like a conventional rocket, with the two SRBs operating in parallel with the orbiter's three main engines, which were fueled from the ET. The SRBs were jettisoned before the vehicle reached orbit, while the main engines continued to operate, and the ET was jettisoned after main engine cutoff and just before orbit insertion, which used the orbiter's two Orbital Maneuvering System (OMS) engines. At the conclusion of the mission, the orbiter fired its OMS to deorbit and reenter the atmosphere. The orbiter was protected during reentry by its thermal protection system tiles, and it glided as a spaceplane to a runway landing, usually to the Shuttle Landing Facility at KSC, Florida, or to Rogers Dry Lake in Edwards Air Force Base, California. If the landing occurred at Edwards, the orbiter was flown back to the KSC atop the Shuttle Carrier Aircraft (SCA), a specially modified Boeing 747 designed to carry the shuttle above it.

The first orbiter, Enterprise, was built in 1976 and used in Approach and Landing Tests (ALT), but had no orbital capability. Four fully operational orbiters were initially built: Columbia, Challenger, Discovery, and Atlantis. Of these, two were lost in mission accidents: Challenger in 1986 and Columbia in 2003, with a total of 14 astronauts killed. A fifth operational (and sixth in total) orbiter, Endeavour, was built in 1991 to replace Challenger. The three surviving operational vehicles were retired from service following Atlantis's final flight on July 21, 2011. The U.S. relied on the Russian Soyuz spacecraft to transport astronauts to the ISS from the last Shuttle flight until the launch of the Crew Dragon Demo-2 mission in May 2020.

Buran

The Antonov An-225 Mriya carrying a Buran orbiter in 1989.

The Buran programme (Russian: Буран, IPA: [bʊˈran], "Snowstorm", "Blizzard"), also known as the "VKK Space Orbiter programme" (Russian: ВКК «Воздушно-Космический Корабль», lit. 'Air and Space Ship'), was a Soviet and later Russian reusable spacecraft project that began in 1974 at the Central Aerohydrodynamic Institute in Moscow and was formally suspended in 1993. In addition to being the designation for the whole Soviet/Russian reusable spacecraft project, Buran was also the name given to orbiter 1K, which completed one uncrewed spaceflight in 1988 and was the only Soviet reusable spacecraft to be launched into space. The Buran-class orbiters used the expendable Energia rocket as a launch vehicle.

The Buran programme was started by the Soviet Union as a response to the United States Space Shuttle program and benefited from extensive espionage undertaken by the KGB of the unclassified US Space Shuttle program, resulting in many superficial and functional similarities between American and Soviet Shuttle designs. Although the Buran class was similar in appearance to NASA's Space Shuttle orbiter, and could similarly operate as a re-entry spaceplane, its final internal and functional design was different. For example, the main engines during launch were on the Energia rocket and were not taken into orbit by the spacecraft. Smaller rocket engines on the craft's body provided propulsion in orbit and de-orbital burns, similar to the Space Shuttle's OMS pods. Unlike the Space Shuttle, Buran had a capability of flying uncrewed missions, as well as performing fully automated landings. The project was the largest and the most expensive in the history of Soviet space exploration.

X-37

The sixth X-37B mission with a Service module placed inside its payload fairing

The Boeing X-37, also known as the Orbital Test Vehicle (OTV), is a reusable robotic spacecraft. It is boosted into space by a launch vehicle, then re-enters Earth's atmosphere and lands as a spaceplane. The X-37 is operated by the Department of the Air Force Rapid Capabilities Office, in collaboration with United States Space Force, for orbital spaceflight missions intended to demonstrate reusable space technologies. It is a 120-percent-scaled derivative of the earlier Boeing X-40. The X-37 began as a NASA project in 1999, before being transferred to the United States Department of Defense in 2004. Until 2019, the program was managed by Air Force Space Command.

An X-37 first flew during a drop test in 2006; its first orbital mission was launched in April 2010 on an Atlas V rocket, and returned to Earth in December 2010. Subsequent flights gradually extended the mission duration, reaching 780 days in orbit for the fifth mission, the first to launch on a Falcon 9 rocket. The sixth mission launched on an Atlas V on 17 May 2020 and concluded on 12 November 2022, reaching a total of 908 days in orbit. The seventh mission launched on 28 December 2023 on a Falcon Heavy rocket, entering a highly elliptical high Earth orbit.

Chongfu Shiyong Shiyan Hangtian Qi

The Chinese reusable experimental spacecraft (Chinese: 可重复使用试验航天器; pinyin: Kě chóngfù shǐyòng shìyàn hángtiān qì; lit. 'Reusable Experimental Spacecraft'; CSSHQ) is the first reusable spacecraft produced by China. It embarked upon its initial orbital mission on 4 September 2020. According to media reports, the CSSHQ is launched into Earth orbit in a vertical configuration while enclosed within the payload fairings of a rocket like a traditional satellite or space capsule, but it returns to Earth via a runway landing like a conventional aircraft; the landing is conducted autonomously (unlike the Space Shuttle). In the absence of any official descriptions of the spacecraft or photographic depictions thereof, some observers have speculated that the CSSHQ may resemble the X-37B spaceplane of the United States in both form and function.

Suborbital rocket planes

An X-15 in flight

Main article: Rocket-powered aircraft

Two piloted suborbital rocket-powered aircraft have reached space: the North American X-15 and SpaceShipOne; a third, SpaceShipTwo, has crossed the US-defined boundary of space but has not reached the higher internationally recognised boundary. None of these crafts were capable of entering orbit, and all were first lifted to high altitude by a carrier aircraft.

On 7 December 2009, Scaled Composites and Virgin Galactic unveiled SpaceShipTwo, along with its atmospheric mothership "Eve". On 13 December 2018, SpaceShipTwo VSS Unity successfully crossed the US-defined boundary of space (although it has not reached space using the internationally recognised definition of this boundary, which lies at a higher altitude than the US boundary). SpaceShipThree is the new spacecraft of Virgin Galactic, launched on 30 March 2021. It is also known as VSS Imagine. On 11 July 2021 VSS Unity completed its first fully crewed mission including Sir Richard Branson.

The Mikoyan-Gurevich MiG-105 was an atmospheric prototype of an intended orbital spaceplane, with the suborbital BOR-4 subscale heat shield test vehicle successfully reentering the atmosphere before program cancellation. HYFLEX was a miniaturized suborbital demonstrator launched in 1996, flying to 110 km altitude, achieving hypersonic flight, and successfully reentering the atmosphere.

History of unflown concepts

United States Gemini tested the use of a Rogallo wing rather than a parachute. August 1964.

Various types of spaceplanes have been suggested since the early twentieth century. Notable early designs include a spaceplane equipped with wings made of combustible alloys that it would burn during its ascent, and the Silbervogel bomber concept. World War II Germany and the postwar US considered winged versions of the V-2 rocket, and in the 1950s and '60s winged rocket designs inspired science fiction artists, filmmakers, and the general public.

United States (1950s–2010s)

The U.S. Air Force invested some effort in a paper study of a variety of spaceplane projects under their Aerospaceplane efforts of the late 1950s, but later reduced the scope of the project. The result, the Boeing X-20 Dyna-Soar, was to have been the first orbital spaceplane, but was canceled in the early 1960s in lieu of NASA's Project Gemini and the U.S. Air Force's crewed spaceflight program.

In 1961, NASA originally planned to have the Gemini spacecraft land on a runway with a Rogallo wing airfoil, rather than an ocean landing under parachutes. The test vehicle became known as the Paraglider Research Vehicle. Development work on both parachutes and the paraglider began in 1963. By December 1963, the parachute was ready to undergo full-scale deployment testing, while the paraglider had run into technical difficulties. Though attempts to revive the paraglider concept persisted within NASA and North American Aviation, in 1964 development was definitively discontinued due to the expense of overcoming the technical hurdles.

United States STS concepts, circa 1970s

The Space Shuttle underwent many variations during its conceptual design phase. Some early concepts are illustrated.

Illustration of NASP taking off

The Rockwell X-30 National Aero-Space Plane (NASP), begun in the 1980s, was an attempt to build a scramjet vehicle capable of operating like an aircraft and achieving orbit like the shuttle. Introduced to the public in 1986, the concept was intended to reach Mach 25, enabling flights between Dulles Airport to Tokyo in two hours, while also being capable of low Earth orbit. Six critical technologies were identified, three relating to the propulsion system, which would consist of a hydrogen-fueled scramjet.

The NASP program became the Hypersonic Systems Technology Program (HySTP) in late 1994. HySTP was designed to transfer the accomplishments made in hypersonic flight into a technology development program. On 27 January 1995 the Air Force terminated participation in (HySTP).

In 1994, a USAF captain proposed an F-16 sized single-stage-to-orbit peroxide/kerosene spaceplane called "Black Horse". It was to take off almost empty and undergo aerial refueling before rocketing to orbit.

The Lockheed Martin X-33 was a 1/3 scale prototype made as part of an attempt by NASA to build a SSTO hydrogen-fuelled spaceplane VentureStar that failed when the hydrogen tank design could not be constructed as intended.

On 5 March 2006, Aviation Week & Space Technology published a story purporting to be the "outing" of a highly classified U.S. military two-stage-to-orbit spaceplane system with the code name Blackstar.

In 2011, Boeing proposed the X-37C, a 165 to 180 percent scale X-37B built to carry up to six passengers to low Earth orbit. The spaceplane was also intended to carry cargo, with both upmass and downmass capacity.

Soviet Union (1960s–1991)

Further information: Buran program § Background

The Soviet reusable spacecraft programme has its roots in the late 1950s, at the very beginning of the space age. The idea of Soviet reusable space flight is very old, though it was neither continuous nor consistently organized. Before Buran, no project of the programme reached operational status.

The first step toward a reusable Soviet spacecraft was the 1954 Burya, a high-altitude prototype jet aircraft/cruise missile. Several test flights were made before it was cancelled by order of the Central Committee. The Burya had the goal of delivering a nuclear payload, presumably to the United States, and then returning to base. The Burya programme was cancelled by the USSR in favor of a decision to develop ICBMs instead. The next iteration of a reusable spacecraft was the Zvezda design, which also reached a prototype stage. Decades later, another project with the same name would be used as a service module for the International Space Station. After Zvezda, there was a hiatus in reusable projects until Buran.

The Buran orbital vehicle programme was developed in response to the U.S. Space Shuttle program, which raised considerable concerns among the Soviet military and especially Defense Minister Dmitry Ustinov. An authoritative chronicler of the Soviet and later Russian space programme, the academic Boris Chertok, recounts how the programme came into being. According to Chertok, after the U.S. developed its Space Shuttle program, the Soviet military became suspicious that it could be used for military purposes, due to its enormous payload, several times that of previous U.S. launch vehicles. Officially, the Buran orbital vehicle was designed for the delivery to orbit and return to Earth of spacecraft, cosmonauts, and supplies. Both Chertok and Gleb Lozino-Lozinskiy (General Designer and General Director of NPO Molniya) suggest that from the beginning, the programme was military in nature; however, the exact military capabilities, or intended capabilities, of the Buran programme remain classified.

Like its American counterpart, the Buran orbital vehicle, when in transit from its landing sites back to the launch complex, was transported on the back of a large jet aeroplane – the Antonov An-225 Mriya transport aircraft, which was designed in part for this task and was the largest aircraft in the world to fly multiple times. Before the Mriya was ready (after the Buran had flown), the Myasishchev VM-T Atlant, a variant on the Soviet Myasishchev M-4 Molot (Hammer) bomber (NATO code: Bison), fulfilled the same role.

MiG-105 crewed aerodynamics test vehicle

The Soviet Union first considered a preliminary design of rocket-launch small spaceplane Lapotok in early 1960s. The Spiral airspace system with small orbital spaceplane and rocket as second stage was developed in the 1960s–1980s. Mikoyan-Gurevich MiG-105 was a crewed test vehicle to explore low-speed handling and landing.

Russia

Main articles: Buran program and Kliper

In the early 2000s the orbital 'cosmoplane' (Russian: космоплан) was proposed by Russia's Institute of Applied Mechanics as a passenger transport. According to researchers, it could take about 20 minutes to fly from Moscow to Paris, using hydrogen and oxygen-fueled engines.

United Kingdom

An artist's depiction of HOTOL

The Multi-Unit Space Transport And Recovery Device (MUSTARD) was a concept explored by the British Aircraft Corporation (BAC) around 1968 for launching payloads weighing as much as 2,300 kg (5,000 lb) into orbit. It was never constructed.

In the 1980s, British Aerospace began development of HOTOL, an SSTO spaceplane powered by a revolutionary SABRE air-breathing rocket engine, but the project was canceled due to technical and financial uncertainties. The inventor of SABRE set up Reaction Engines to develop SABRE and proposed a twin-engined SSTO spaceplane called Skylon. One NASA analysis showed possible issues with the hot rocket exhaust plumes causing heating of the tail structure at high Mach numbers. although the CEO of Skylon Enterprises Ltd has claimed that reviews by NASA were "quite positive".

Bristol Spaceplanes has undertaken design and prototyping of three potential spaceplanes since its founding by David Ashford in 1991. The European Space Agency has endorsed these designs on several occasions.

European Space Agency (1985–)

France worked on the Hermes crewed spaceplane launched by Ariane rocket in the late 20th century, and proposed in January 1985 to go through with Hermes development under the auspices of the ESA.

In the 1980s, West Germany funded design work on the MBB Sänger II with the Hypersonic Technology Program. Development continued on MBB/Deutsche Aerospace Sänger II/HORUS until the late 1980s when it was canceled. Germany went on to participate in the Ariane rocket, Columbus space station and Hermes spaceplane of ESA, Spacelab of ESA-NASA and Deutschland missions (non-U.S. funded Space Shuttle flights with Spacelab). The Sänger II had predicted cost savings of up to 30 percent over expendable rockets.

Hopper was one of several proposals for a European reusable launch vehicle (RLV) planned to cheaply ferry satellites into orbit by 2015. One of those was 'Phoenix', a German project which is a one-seventh scale model of the Hopper concept vehicle. The suborbital Hopper was a Future European Space Transportation Investigations Programme system study design A test project, the Intermediate eXperimental Vehicle (IXV), has demonstrated lifting reentry technologies and will be extended under the PRIDE programme.

Japan

HOPE was a Japanese experimental spaceplane project designed by a partnership between NASDA and NAL (both now part of JAXA), started in the 1980s. It was positioned for most of its lifetime as one of the main Japanese contributions to the International Space Station, the other being the Japanese Experiment Module. The project was eventually cancelled in 2003, by which point test flights of a sub-scale testbed had flown successfully.

India

AVATAR (Aerobic Vehicle for Hypersonic Aerospace Transportation; Sanskrit: अवतार) was a concept study for an uncrewed single-stage reusable spaceplane capable of horizontal takeoff and landing, presented to India's Defence Research and Development Organisation. The mission concept was for low cost military and commercial satellite launches.

Current development programs

China

Main articles: Shenlong (spacecraft) and Shadow Dragon (aircraft)

Shenlong (Chinese: 神龙; pinyin: shén lóng; lit. 'divine dragon') is a proposed Chinese robotic spaceplane that is similar to the Boeing X-37. Only a few images have been released since late 2007.

European Union

A test project, the Intermediate eXperimental Vehicle (IXV), has demonstrated lifting reentry technologies and will be extended under the PRIDE programme. The FAST20XX Future High-Altitude High Speed Transport 20XX aims to establish sound technological foundations for the introduction of advanced concepts in suborbital high-speed transportation with air-launch-to-orbit ALPHA vehicle.

The Daimler-Chrysler Aerospace RLV is a small reusable spaceplane prototype for the ESA Future Launchers Preparatory Programme/FLTP program. SpaceLiner is the most recent project.

The Space Rider (Space Reusable Integrated Demonstrator for Europe Return) is a planned uncrewed orbital lifting body spaceplane aiming to provide the European Space Agency (ESA) with affordable and routine access to space. Contracts for construction of the vehicle and ground infrastructure were signed in December 2020. Its maiden flight is currently scheduled for the third quarter of 2025.

Development of Space Rider is being led by the Italian Programme for Reusable In-orbit Demonstrator in Europe (PRIDE programme) in collaboration with ESA, and is the continuation of the Intermediate eXperimental Vehicle (IXV) experience, launched on 11 February 2015. The cost of this phase, not including the launcher, is at least US$36.7 million. At the ESA Ministerial Council held in Seville in November 2019, the development of the Space Rider was subscribed by the participating member states with an allocation of €195.73 million.

India

As of 2016, the Indian Space Research Organisation is developing a launch system named the Reusable Launch Vehicle (RLV). It is India's first step towards realizing a two-stage-to-orbit reusable launch system. A space plane serves as the second stage. The plane is expected to have air-breathing scramjet engines as well as rocket engines. Tests with miniature spaceplanes and a working scramjet have been conducted by ISRO in 2016. In April 2023, India successfully conducted an autonomous landing mission of a scaled-down prototype of the spaceplane. The RLV prototype was dropped from a Chinook helicopter at an altitude of 4.5 kms and was made to autonomously glide down to a purpose-built runway at the Chitradurga Aeronautical Test Range, Karnataka.

Japan

As of 2018, Japan is developing the Winged Reusable Sounding rocket (WIRES), which if successful, may be used as a recoverable first-stage or as a crewed sub-orbital spaceplane.

US

Dream Chaser flight test vehicle in 2013

Dream Chaser is an American reusable lifting-body spaceplane developed by Sierra Space. Originally intended as a crewed vehicle, the Dream Chaser Space System is set to be produced after the Dream Chaser Cargo System cargo variant is operational. The crewed variant is planned to carry up to seven people and cargo to and from low Earth orbit.

The cargo Dream Chaser is designed to resupply the International Space Station with both pressurized and unpressurized cargo. It is intended to launch vertically on the Vulcan Centaur rocket and autonomously land horizontally on conventional runways. A proposed version to be operated by ESA would launch on an Arianespace vehicle.

International

The Dawn Mk-II Aurora is a suborbital spaceplane being developed by Dawn Aerospace to demonstrate multiple suborbital flights per day. Dawn is based in the Netherlands and New Zealand, and is working closely with the American CAA. On December 9, 2020, the Civil Aviation Authority of New Zealand, working alongside the New Zealand Space Agency, issued a license allowing the vehicle to fly from a conventional airport. On August 25, 2021, the first test-flight campaign of five successful flights using surrogate jet engines was announced. As of August 15, 2022, 35 test flights have been complete, validating the vehicles aerodynamics, avionics, rapid deployment and various piloting modes. A qualified 2.5 kN.s pump-fed HTP/kerosene engine is being installed for high-performance high-altitude flights. Dawn Aerospace previously demonstrated multiple low-altitude rocket-powered flights per day on their Mk-I vehicle.

Suprachiasmatic nucleus

From Wikipedia, the free encyclopedia

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

The suprachiasmatic nucleus or nuclei (SCN) is a small region of the brain in the hypothalamus, situated directly above the optic chiasm. It is the principal circadian pacemaker in mammals, responsible for generating circadian rhythms. Reception of light inputs from photosensitive retinal ganglion cells allow it to coordinate the subordinate cellular clocks of the body and entrain to the environment. The neuronal and hormonal activities it generates regulate many different body functions in an approximately 24-hour cycle.

The idea that the SCN is the main circadian pacemaker in mammals was proposed by Robert Moore, who conducted experiments using radioactive amino acids to find where the termination of the retinohypothalamic projection occurs in rodents. Early lesioning experiments in mouse, guinea pig, cat, and opossum established how removal of the SCN results in ablation of circadian rhythm in mammals.

Moreover, the SCN interacts with many other regions of the brain. It contains several cell types and several different peptides (including vasopressin and vasoactive intestinal peptide) and neurotransmitters.

Disruptions or damage to the SCN has been associated with different mood disorders and sleep disorders, suggesting the significance of the SCN in regulating circadian timing.

Neuroanatomy

The SCN is situated in the anterior part of the hypothalamus immediately dorsal, or superior (hence supra) to the optic chiasm bilateral to (on either side of) the third ventricle. It consists of two nuclei composed of approximately 10,000 neurons.

The morphology of the SCN is species dependent. Distribution of different cell phenotypes across specific SCN regions, such as the concentration of VP-IR neurons, can cause the shape of the SCN to change.

The nucleus can be divided into ventrolateral and dorsolateral portions, also known as the core and shell, respectively. These regions differ in their expression of the clock genes, the core expresses them in response to stimuli whereas the shell expresses them constitutively.

In terms of projections, the core receives innervation via three main pathways, the retinohypothalamic tract, geniculohypothalamic tract, and projections from some raphe nuclei. The dorsomedial SCN is mainly innervated by the core and also by other hypothalamic areas. Lastly, its output is mainly to the subparaventricular zone and dorsomedial hypothalamic nucleus which both mediate the influence SCN exerts over circadian regulation of the body.

The most abundant peptides found within the SCN are arginine-vasopressin (AVP), vasoactive intestinal polypeptide (VIP), and peptide histidine-isoleucine (PHI). Each of these peptides are localized in different regions. Neurons with AVP are found dorsomedially, whereas VIP-containing and PHI-containing neurons are found ventrolaterally.

Circadian clock

Main article: Circadian clock

Different organisms such as bacteria, plants, fungi, and animals, show genetically based near-24-hour rhythms. Although all of these clocks appear to be based on a similar type of genetic feedback loop, the specific genes involved are thought to have evolved independently in each kingdom. Many aspects of mammalian behavior and physiology show circadian rhythmicity, including sleep, physical activity, alertness, hormone levels, body temperature, immune function, and digestive activity. Early experiments on the function of the SCN involved lesioning the SCN in hamsters. SCN lesioned hamsters lost their daily activity rhythms. Further, when the SCN of a hamster was transplanted into an SCN lesioned hamster, the hamster adopted the rhythms of the hamster from which the SCN was transplanted. Together, these experiments suggest that the SCN is sufficient for generating circadian rhythms in hamsters.

Later studies have shown that skeletal, muscle, liver, and lung tissues in rats generate 24-hour rhythms, which dampen over time when isolated in a dish, where the SCN maintains its rhythms. Together, these data suggest a model whereby the SCN maintains control across the body by synchronizing "slave oscillators," which exhibit their own near-24-hour rhythms and control circadian phenomena in local tissue.

The SCN receives input from specialized photosensitive ganglion cells in the retina via the retinohypothalamic tract. Neurons in the ventrolateral SCN (vlSCN) have the ability for light-induced gene expression. Melanopsin-containing ganglion cells in the retina have a direct connection to the ventrolateral SCN via the retinohypothalamic tract. When the retina receives light, the vlSCN relays this information throughout the SCN allowing entrainment, synchronization, of the person's or animal's daily rhythms to the 24-hour cycle in nature. The importance of entraining organisms, including humans, to exogenous cues such as the light/dark cycle, is reflected by several circadian rhythm sleep disorders, where this process does not function normally.

Neurons in the dorsomedial SCN (dmSCN) are believed to have an endogenous 24-hour rhythm that can persist under constant darkness (in humans averaging about 24 hours 11 min). A GABAergic mechanism is involved in the coupling of the ventral and dorsal regions of the SCN.

Circadian rhythms of endothermic (warm-blooded) and ectothermic (cold-blooded) vertebrates

A thermographic image of an ectothermic snake wrapping around the hand of an endothermic human

Information about the direct neuronal regulation of metabolic processes and circadian rhythm-controlled behaviors is not well known among either endothermic or ectothermic vertebrates, although extensive research has been done on the SCN in model animals such as the mammalian mouse and ectothermic reptiles, particularly lizards. The SCN is known to be involved not only in photoreception through innervation from the retinohypothalamic tract, but also in thermoregulation of vertebrates capable of homeothermy as well as regulating locomotion and other behavioral outputs of the circadian clock within ectothermic vertebrates. The behavioral differences between both classes of vertebrates when compared to the respective structures and properties of the SCN as well as various other nuclei proximate to the hypothalamus provide insight into how these behaviors are the consequence of differing circadian regulation. Ultimately, many neuroethological studies must be done to completely ascertain the direct and indirect roles of the SCN on circadian-regulated behaviors of vertebrates.

The SCN of endotherms and ectotherms

In general, external temperature does not influence endothermic animal circadian rhythm because of the ability of these animals to keep their internal body temperature constant through homeostatic thermoregulation; however, peripheral oscillators (see Circadian rhythm) in mammals are sensitive to temperature pulses and will experience resetting of the circadian clock phase and associated genetic expression, suggesting how peripheral circadian oscillators may be separate entities from one another despite having a master oscillator within the SCN. Furthermore, when individual neurons of the SCN from a mouse were treated with heat pulses, a similar resetting of oscillators was observed, but when an intact SCN was treated with the same heat pulse treatment the SCN was resistant to temperature change by exhibiting an unaltered circadian oscillating phase. In ectothermic animals, particularly the ruin lizard, Podarcis siculus, temperature has been shown to affect the circadian oscillators within the SCN. This reflects a potential evolutionary relationship among endothermic and ectothermic vertebrates as ectotherms rely on environmental temperature to affect their circadian rhythms and behavior while endotherms have an evolved SCN that is resistant to external temperature fluctuations and uses photoreception as a means for entraining the circadian oscillators within their SCN. In addition, the differences of the SCN between endothermic and ectothermic vertebrates suggest that the neuronal organization of the temperature-resistant SCN in endotherms is responsible for driving thermoregulatory behaviors in those animals differently from those of ectotherms, since they rely on external temperature for engaging in certain behaviors.

Behaviors controlled by the SCN of vertebrates

Significant research has been conducted on the genes responsible for controlling circadian rhythm, in particular within the SCN. Knowledge of the gene expression of Clock (Clk) and Period2 (Per2), two of the many genes responsible for regulating circadian rhythm within the individual cells of the SCN, has allowed for a greater understanding of how genetic expression influences the regulation of circadian rhythm-controlled behaviors. Studies on thermoregulation of ruin lizards and mice have informed some connections between the neural and genetic components of both vertebrates when experiencing induced hypothermic conditions. Certain findings have reflected how evolution of SCN both structurally and genetically has resulted in the engagement of characteristic and stereotyped thermoregulatory behavior in both classes of vertebrates.

• Mice: Among vertebrates, it is known that mammals are endotherms that are capable of homeostatic thermoregulation. It has been shown that mice display thermosensitivity within the SCN. However, the regulation of body temperature in hypothermic mice is more sensitive to the amount of light in their environment. Even while fasted, mice in darkened conditions and experiencing hypothermia maintained a stable internal body temperature. In light conditions, mice showed a drop in body temperature under the same fasting and hypothermic conditions. Through analyzing genetic expression of Clock genes in wild-type and knockout strains, as well as analyzing the activity of neurons within the SCN and connections to proximate nuclei of the hypothalamus in the aforementioned conditions, it has been shown that the SCN is the center of control for circadian body temperature rhythm. This circadian control, thus, includes both direct and indirect influence of many of the thermoregulatory behaviors that mammals engage in to maintain homeostasis.
• Ruin lizards: Several studies have been conducted on the genes expressed in circadian oscillating cells of the SCN during various light and dark conditions, as well as effects from inducing mild hypothermia in reptiles. In terms of structure, the SCNs of lizards have a closer resemblance to those of mice, possessing a dorsomedial portion and a ventrolateral core. However, genetic expression of the circadian-related Per2 gene in lizards is similar to that in reptiles and birds, despite the fact that birds have been known to have a distinct SCN structure consisting of a lateral and medial portion. Studying the lizard SCN because of the lizard's small body size and ectothermy is invaluable to understanding how this class of vertebrates modifies its behavior within the dynamics of circadian rhythm, but it has not yet been determined whether the systems of cold-blooded vertebrates were slowed as a result of decreased activity in the SCN or showed decreases in metabolic activity as a result of hypothermia.

Other signals from the retina

A variation of an eskinogram showing the influence of light and darkness on circadian rhythms and related physiology and behavior through the SCN in humans

The SCN is one of many nuclei that receive nerve signals directly from the retina.

Some of the others are the lateral geniculate nucleus (LGN), the superior colliculus, the basal optic system, and the pretectum:

• The LGN passes information about color, contrast, shape, and movement on to the visual cortex and itself signals to the SCN.
• The superior colliculus controls the movement and orientation of the eye.
• The basal optic system also controls eye movements.
• The pretectum controls the size of the pupil.

Genetic Basis of SCN Function

The SCN is the central circadian pacemaker of mammals, serving as the coordinator of mammalian circadian rhythms. Neurons in an intact SCN show coordinated circadian rhythms in electrical activity. Neurons isolated from the SCN have been shown to produce and sustain circadian rhythms in vitro, suggesting that each individual neuron of the SCN can function as an independent circadian oscillator at the cellular level. Each cell of the SCN synchronizes its oscillations to the cells around it, resulting in a network of mutually reinforced and precise oscillations constituting the SCN master clock.

Mammals

The SCN functions as a circadian biological clock in vertebrates including teleosts, reptiles, birds, and mammals. In mammals, the rhythms produced by the SCN are driven by a transcription-translation negative feedback loop (TTFL) composed of interacting positive and negative transcriptional feedback loops. Within the nucleus of an SCN cell, the genes Clock and Bmal1 (mop3) encode the BHLH-PAS transcription factors CLOCK and BMAL1 (MOP3), respectively. CLOCK and BMAL1 are positive activators that form CLOCK-BMAL1 heterodimers. These heterodimers then bind to E-boxes upstream of multiple genes, including per and cry, to enhance and promote their transcription and eventual translation. In mammals, there are three known homologs for the period gene in Drosophila, namely per1, per2, and per3.

As per and cry are transcribed and translated into PER and CRY, the proteins accumulate and form heterodimers in the cytoplasm. The heterodimers are phosphorylated at a rate that determines the length of the transcription-translation feedback loop (TTFL) and then translocate back into the nucleus where the phosphorylated PER-CRY heterodimers act on CLOCK and/or BMAL1 to inhibit their activity. Although the role of phosphorylation in the TTFL mechanism is known, the specific kinetics are yet to be elucidated. As a result, PER and CRY function as negative repressors and inhibit the transcription of per and cry. Over time, the PER-CRY heterodimers degrade and the cycle begins again with a period of about 24.5 hours. The integral genes involved, termed “clock genes," are highly conserved throughout both SCN-bearing vertebrates like mice, rats, and birds as well as in non-SCN bearing animals such as Drosophila.

Electrophysiology

Neurons in the SCN fire action potentials in a 24-hour rhythm, even under constant conditions. At mid-day, the firing rate reaches a maximum, and, during the night, it falls again. Rhythmic expression of circadian regulatory genes in the SCN requires depolarization in the SCN neurons via calcium and cAMP. Thus, depolarization of SCN neurons via cAMP and calcium contributes to the magnitude of the rhythmic gene expression in the SCN.

Further, the SCN synchronizes nerve impulses which spread to various parasympathetic and sympathetic nuclei. The sympathetic nuclei drive glucocorticoid output from the adrenal gland which activates Per1 in the body cells, thus resetting the circadian cycle of cells in the body. Without the SCN, rhythms in body cells dampen over time, which may be due to lack of synchrony between cells.

Many SCN neurons are sensitive to light stimulation via the retina. The photic response is likely linked to effects of light on circadian rhythms. In addition, application of melatonin in live rats and isolated SCN cells can decrease the firing rate of these neurons. Variances in light input due to jet lag, seasonal changes, and constant light conditions all change the firing rhythm in SCN neurons demonstrating the relationship between light and SCN neuronal functioning.

Clinical significance

Irregular sleep-wake rhythm disorder

Irregular sleep-wake rhythm (ISWR) disorder is thought to be caused by structural damage to the SCN, decreased responsiveness of the circadian clock to light and other stimuli, and decreased exposure to light. People who tend to stay indoors and limit their exposure to light experience decreased nocturnal melatonin production. The decrease in melatonin production at night corresponds with greater expression of SCN-generated wakefulness during night, causing irregular sleep patterns.

Major depressive disorder

Major depressive disorder (MDD) has been associated with altered circadian rhythms. Patients with MDD have weaker rhythms that express clock genes in the brain. When SCN rhythms were disturbed, anxiety-like behavior, weight gain, helplessness, and despair were reported in a study conducted with mice. Abnormal glucocorticoid levels occurred in mice with no Bmal1 expression in the SCN.

Alzheimer's disease

The functional disruption of the SCN can be observed in early stages of Alzheimer's disease (AD). Changes in the SCN and melatonin secretion are major factors that cause circadian rhythm disturbances. These disturbances cause the normal physiology of sleep to change, such as the biological clock and body temperature during rest. Patients with AD experience insomnia, hypersomnia, and other sleep disorders as a result of the degeneration of the SCN and changes in critical neurotransmitter concentrations.