In astronomy, absolute magnitude is a measure of the luminosity of a celestial object on an inverse logarithmic astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs, without extinction of its light due to absorption by interstellar matter and cosmic dust. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared among each other on a magnitude scale. For Solar System bodies that shine in reflected light, a different definition of absolute magnitude (H) is used, based on a standard reference distance of one astronomical unit.
The number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of natural logarithms. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the computation of compound interest. It can also be calculated as the sum of the infinite series
The exponential function is a mathematical function denoted by or . Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation, but modern definitions allow it to be rigorously extended to all real arguments, including irrational numbers. Its ubiquitous occurrence in pure and applied mathematics led mathematician Walter Rudin to opine that the exponential function is "the most important function in mathematics".
In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal; I = I0 cos θ. The law is also known as the cosine emission law or Lambert's emission law. It is named after Johann Heinrich Lambert, from his Photometria, published in 1760.
A meteor shower is a celestial event in which a number of meteors are observed to radiate, or originate, from one point in the night sky. These meteors are caused by streams of cosmic debris called meteoroids entering Earth's atmosphere at extremely high speeds on parallel trajectories. Most meteors are smaller than a grain of sand, so almost all of them disintegrate and never hit the Earth's surface. Very intense or unusual meteor showers are known as meteor outbursts and meteor storms, which produce at least 1,000 meteors an hour, most notably from the Leonids. The Meteor Data Centre lists over 900 suspected meteor showers of which about 100 are well established. Several organizations point to viewing opportunities on the Internet. NASA maintains a daily map of active meteor showers.
Johnson–Nyquist noise is the electronic noise generated by the thermal agitation of the charge carriers inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. Thermal noise is present in all electrical circuits, and in sensitive electronic equipment can drown out weak signals, and can be the limiting factor on sensitivity of electrical measuring instruments. Thermal noise increases with temperature. Some sensitive electronic equipment such as radio telescope receivers are cooled to cryogenic temperatures to reduce thermal noise in their circuits. The generic, statistical physical derivation of this noise is called the fluctuation-dissipation theorem, where generalized impedance or generalized susceptibility is used to characterize the medium.
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller than any relevant dimension of the body; so that its geometry and the constitutive properties of the material at each point of space can be assumed to be unchanged by the deformation.
The Quadrantids (QUA) are a meteor shower that peaks in early January and whose radiant lies in the constellation Boötes. The zenithal hourly rate (ZHR) of this shower can be as high as that of two other reliably rich meteor showers, the Perseids in August and the Geminids in December, yet Quadrantid meteors are not seen as often as those of the two other showers because the time frame of the peak is exceedingly narrow, sometimes lasting only hours. Moreover, the meteors are quite faint, with mean apparent magnitudes between 3.0 and 6.0.
Draco is a constellation in the far northern sky. Its name is Latin for dragon. It was one of the 48 constellations listed by the 2nd century Greek astronomer Ptolemy, and remains one of the 88 modern constellations today. The north pole of the ecliptic is in Draco. Draco is circumpolar from northern latitudes, meaning that it never sets and can be seen at any time of year.
In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible at each point. This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and back. The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved.
In applied mechanics, bending characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.
In geometry, a pentadecagon or pentakaidecagon or 15-gon is a fifteen-sided polygon.
The Eta Aquariids are a meteor shower associated with Halley's Comet. The shower is visible from about April 19 to about May 28 each year with peak activity on or around May 5. Unlike most major annual meteor showers, there is no sharp peak for this shower, but rather a broad maximum with good rates that last approximately one week centered on May 5. The meteors we currently see as members of the Eta Aquariid shower separated from Halley's Comet hundreds of years ago. The current orbit of Halley's Comet does not pass close enough to the Earth to be a source of meteoric activity.
The June Boötids are a meteor shower occurring every year between 22 June and 2 July that peak around June 27. In most years their activity is weak, with a zenithal hourly rate (ZHR) of only 1 or 2. However, occasional outbursts have been seen, with the outburst of 1916 drawing attention to the previously unrecorded meteor shower. The most recent outburst occurred in 1998, when the ZHR reached up to 100.
The Southern Delta Aquariids are a meteor shower visible from mid July to mid August each year with peak activity on 28 or 29 July. The comet of origin is not known with certainty. A suspected candidate is Comet 96P Machholz. Earlier, it was thought to have originated from the Marsden and Kracht Sungrazing comets.
The Alpha Monocerotids is a meteor shower active from 15 to 25 November, with its peak occurring on 21 or 22 November. The speed of its meteors is 65 km/s, which is close to the maximum possible speed for meteors of about 73 km/s. Normally it has a low Zenithal Hourly Rate (ZHR), but occasionally it produces much more intense meteor storms that last less than an hour: such outbursts were observed in 1925, 1935, 1985, and 1995. The 1925 and 1935 storms both reached levels passing 1,000 ZHR.
Kappa Cygni, Latinized from κ Cygni, is a star in the northern constellation of Cygnus. It has an apparent visual magnitude of 3.8, which is bright enough to be seen with the naked eye. In the constellation, it forms the tip of Cygnus's left wing. The radiant of the minor Kappa Cygnids meteor shower is located about 5° north of this star.
The Calabi triangle is a special triangle found by Eugenio Calabi and defined by its property of having three different placements for the largest square that it contains. It is an isosceles triangle which is obtuse with an irrational but algebraic ratio between the lengths of its sides and its base.
The Gamma Normids (GNO) are a weak meteor shower, active from March 7 to 23, peaking on March 15. The radiant is located near the star Gamma2 Normae in the constellation Norma.
