Nova
A nova or classical nova is a transient astronomical event that causes the sudden appearance of a bright "new" star, that fades over several weeks or many months. Novae involve an interaction between two stars that cause the flareup, perceived as a new entity, much brighter than the stars involved. Causes of the dramatic appearance of a nova vary, depending on the circumstances of the two progenitor stars. All observed novae involve located binary stars, either a pair of red dwarfs in the process of merging, or a white dwarf and another star; the main sub-classes of novae are classical novae, recurrent novae, dwarf novae. They are all considered to be cataclysmic variable stars. Luminous red novae share the name and are cataclysmic variables, but are a different type of event caused by a stellar merger. With similar names are the much more energetic supernovae and kilonovae. Classical nova eruptions are the most common type of nova, they are created in a close binary star system consisting of a white dwarf and either a main sequence, sub-giant, or red giant star.
When the orbital period falls in the range of several days to one day, the white dwarf is close enough to its companion star to start drawing accreted matter onto the surface of the white dwarf, which creates a dense but shallow atmosphere. This atmosphere is hydrogen and is thermally heated by the hot white dwarf, which reaches a critical temperature causing rapid runaway ignition by fusion. From the dramatic and sudden energies created, the now hydrogen-burnt atmosphere is dramatically expelled into interstellar space, its brightened envelope is seen as the visible light created from the nova event, was mistaken as a "new" star. A few novae produce short-lived nova remnants, lasting for several centuries. Recurrent nova processes are the same as the classical nova, except that the fusion ignition may be repetitive because the companion star can again feed the dense atmosphere of the white dwarf. Novae most occur in the sky along the path of the Milky Way near the observed galactic centre in Sagittarius.
They occur far more than galactic supernovae, averaging about ten per year. Most are found telescopically only one every year to eighteen months reaching naked-eye visibility. Novae reaching first or second magnitude occur only several times per century; the last bright nova was V1369 Centauri reaching 3.3 magnitude on 14 December 2013. During the sixteenth century, astronomer Tycho Brahe observed the supernova SN 1572 in the constellation Cassiopeia, he described it in his book De nova stella. In this work he argued that a nearby object should be seen to move relative to the fixed stars, that the nova had to be far away. Although this event was a supernova and not a nova, the terms were considered interchangeable until the 1930s. After this, novae were classified as classical novae to distinguish them from supernovae, as their causes and energies were thought to be different, based in the observational evidence. Despite the term "stella nova" meaning "new star", novae most take place as a result of white dwarfs: remnants of old stars.
Evolution of potential novae begins with two main sequence stars in a binary system. One of the two evolves into a red giant, leaving its remnant white dwarf core in orbit with the remaining star; the second star—which may be either a main sequence star or an aging giant—begins to shed its envelope onto its white dwarf companion when it overflows its Roche lobe. As a result, the white dwarf captures matter from the companion's outer atmosphere in an accretion disk, in turn, the accreted matter falls into the atmosphere; as the white dwarf consists of degenerate matter, the accreted hydrogen does not inflate, but its temperature increases. Runaway fusion occurs when the temperature of this atmospheric layer reaches ~20 million K, initiating nuclear burning, via the CNO cycle. Hydrogen fusion may occur in a stable manner on the surface of the white dwarf for a narrow range of accretion rates, giving rise to a super soft X-ray source, but for most binary system parameters, the hydrogen burning is unstable thermally and converts a large amount of the hydrogen into other, heavier chemical elements in a runaway reaction, liberating an enormous amount of energy.
This blows the remaining gases away from the surface of the white dwarf surface and produces an bright outburst of light. The rise to peak brightness may be rapid, or gradual; this is related to the speed class of the nova. The time taken for a nova to decay by around 2 or 3 magnitudes from maximum optical brightness is used for classification, via its speed class. Fast novae will take fewer than 25 days to decay by 2 magnitudes, while slow novae will take more than 80 days. In spite of their violence the amount of material ejected in novae is only about 1⁄10,000 of a solar mass, quite small relative to the mass of the white dwarf. Furthermore, only five percent of the accreted mass is fused during the power outburst. Nonetheless, this is enough energy to accelerate nova ejecta to velocities as high as several thousand kilometers per second—higher for fast novae than slow ones—with a concurrent rise in luminosity from a few times solar to 50,000–100,000 times solar. In 2010 scientists using NASA's Fermi Gamma-ray Space Telescope discovered that a nova can emit gamma-rays.
A white dwarf can generate multiple novae over t
Horseshoe orbit
A horseshoe orbit is a type of co-orbital motion of a small orbiting body relative to a larger orbiting body. The orbital period of the smaller body is nearly the same as for the larger body, its path appears to have a horseshoe shape as viewed from the larger object in a rotating reference frame; the loop is not closed but will drift forward or backward each time, so that the point it circles will appear to move smoothly along the larger body's orbit over a long period of time. When the object approaches the larger body at either end of its trajectory, its apparent direction changes. Over an entire cycle the center traces the outline of a horseshoe, with the larger body between the'horns'. Asteroids in horseshoe orbits with respect to Earth include 54509 YORP, 2002 AA29, 2010 SO16, 2015 SO2 and 2001 GO2. A broader definition includes 3753 Cruithne, which can be said to be in a compound and/or transition orbit, or 1998 UP1 and 2003 YN107. By 2016, 12 horseshoe librators of Earth have been discovered.
Saturn's moons Epimetheus and Janus occupy horseshoe orbits with respect to each other. The following explanation relates to an asteroid, in such an orbit around the Sun, is affected by the Earth; the asteroid is in the same solar orbit as Earth. Both take one year to orbit the Sun, it is necessary to grasp two rules of orbit dynamics: A body closer to the Sun completes an orbit more than a body further away. If a body accelerates along its orbit, its orbit moves outwards from the Sun. If it decelerates, the orbital radius decreases; the horseshoe orbit arises because the gravitational attraction of the Earth changes the shape of the elliptical orbit of the asteroid. The shape changes are small but result in significant changes relative to the Earth; the horseshoe becomes apparent only when mapping the movement of the asteroid relative to both the Sun and the Earth. The asteroid always orbits the Sun in the same direction. However, it goes through a cycle of catching up with the Earth and falling behind, so that its movement relative to both the Sun and the Earth traces a shape like the outline of a horseshoe.
Starting at point A, on the inner ring between L5 and Earth, the satellite is orbiting faster than the Earth and is on its way toward passing between the Earth and the Sun. But Earth's gravity exerts an outward accelerating force, pulling the satellite into a higher orbit which decreases its angular speed; when the satellite gets to point B, it is traveling at the same speed as Earth. Earth's gravity is still accelerating the satellite along the orbital path, continues to pull the satellite into a higher orbit. At Point C, the satellite reaches a high and slow enough orbit such that it starts to lag behind Earth, it spends the next century or more appearing to drift'backwards' around the orbit when viewed relative to the Earth. Its orbit around the Sun still takes only more than one Earth year. Given enough time, the Earth and the satellite will be on opposite sides of the Sun; the satellite comes around to point D where Earth's gravity is now reducing the satellite's orbital velocity. This causes it to fall into a lower orbit, which increases the angular speed of the satellite around the Sun.
This continues until point E where the satellite's orbit is now lower and faster than Earth's orbit, it begins moving out ahead of Earth. Over the next few centuries it completes its journey back to point A. On the longer term, asteroids can transfer between quasi-satellite orbits. Quasi-satellites aren't gravitationally bound to their planet, but appear to circle it in a retrograde direction as they circle the Sun with the same orbital period as the planet. By 2016, orbital calculations showed that four of Earth's horseshoe librators and all five of its known quasi-satellites transfer between horseshoe and quasi-satellite orbits. A somewhat different, but equivalent, view of the situation may be noted by considering conservation of energy, it is a theorem of classical mechanics that a body moving in a time-independent potential field will have its total energy, E = T + V, where E is total energy, T is kinetic energy and V is potential energy, negative. It is apparent since V = -GM/R near a gravitating body of mass M and orbital radius R, that seen from a stationary frame, V will be increasing for the region behind M, decreasing for the region in front of it.
However, orbits with lower total energy have shorter periods, so a body moving on the forward side of a planet will lose energy, fall into a shorter-period orbit, thus move away, or be "repelled" from it. Bodies moving on the trailing side of the planet will gain energy, rise to a higher, slower and thereby fall behind repelled, thus a small body can move back and forth between a leading and a trailing position, never approaching too close to the planet that dominates the region. See trojan. Figure 1 above shows shorter orbits around the Lagrangian points L4 and L5; these are called tadpole orbits and can be explained in a similar way, except that the asteroid's distance from the Earth does not oscillate as far as the L3 point on the other side of the Sun. As it moves closer to or farther from the Earth, the changing pull of Earth's gravitational field causes it to accelerate or decelerate, causing a change in its orbit known as libration. An example of a body in a tadpole orbit is Polydeuces, a small moon of Saturn which librates around the
Millisecond pulsar
A millisecond pulsar is a pulsar with a rotational period in the range of about 1–10 milliseconds. Millisecond pulsars have been detected in the radio, X-ray, gamma ray portions of the electromagnetic spectrum; the leading theory for the origin of millisecond pulsars is that they are old rotating neutron stars which have been spun up or "recycled" through accretion of matter from a companion star in a close binary system. For this reason, millisecond pulsars are sometimes called recycled pulsars. Millisecond pulsars are thought to be related to low-mass X-ray binary systems, it is thought that the X-rays in these systems are emitted by the accretion disk of a neutron star produced by the outer layers of a companion star that has overflowed its Roche lobe. The transfer of angular momentum from this accretion event can theoretically increase the rotation rate of the pulsar to hundreds of times a second, as is observed in millisecond pulsars. However, there has been recent evidence that the standard evolutionary model fails to explain the evolution of all millisecond pulsars young millisecond pulsars with high magnetic fields, e.g. PSR B1937+21.
Bülent Kiziltan and S. E. Thorsett showed that different millisecond pulsars must form by at least two distinct processes, but the nature of the other process remains a mystery. Many millisecond pulsars are found in globular clusters; this is consistent with the spin-up theory of their formation, as the high stellar density of these clusters implies a much higher likelihood of a pulsar having a giant companion star. There are 130 millisecond pulsars known in globular clusters; the globular cluster Terzan 5 alone contains 37 of these, followed by 47 Tucanae with 22 and M28 and M15 with 8 pulsars each. Millisecond pulsars, which can be timed with high precision, are better clocks than the best atomic clocks of 1997; this makes them sensitive probes of their environments. For example, anything placed in orbit around them causes periodic Doppler shifts in their pulses' arrival times on Earth, which can be analyzed to reveal the presence of the companion and, with enough data, provide precise measurements of the orbit and the object's mass.
The technique is so sensitive that objects as small as asteroids can be detected if they happen to orbit a millisecond pulsar. The first confirmed exoplanets, discovered several years before the first detections of exoplanets around "normal" solar-like stars, were found in orbit around a millisecond pulsar, PSR B1257+12; these planets remained for many years the only Earth-mass objects known outside the Solar System. One of them, PSR B1257+12 D, has an smaller mass, comparable to that of our Moon, is still today the smallest-mass object known beyond the Solar System; the first millisecond pulsar, PSR B1937 +21, was discovered in 1982 by al.. Spinning 641 times a second, it remains the second fastest-spinning millisecond pulsar of the 200 that have been discovered. Pulsar PSR J1748-2446ad, discovered in 2005, is, as of 2012, the fastest-spinning pulsar known, spinning 716 times a second. Current theories of neutron star structure and evolution predict that pulsars would break apart if they spun at a rate of c. 1500 rotations per second or more, that at a rate of above about 1000 rotations per second they would lose energy by gravitational radiation faster than the accretion process would speed them up.
However, in early 2007 data from the Rossi X-ray Timing Explorer and INTEGRAL spacecraft discovered a neutron star XTE J1739-285 rotating at 1122 Hz. The result is not statistically significant, with a significance level of only 3 sigma. Therefore, while it is an interesting candidate for further observations, current results are inconclusive. Still, it is believed. Furthermore, one X-ray pulsar that spins at 599 revolutions per second, IGR J00291+5934, is a prime candidate for helping detect such waves in the future. "Pinning Down a Pulsar's Age". Science News. "How Millisecond Pulsars Spin So Fast". Universe Today. "Fast-Spinning Star Could Test Gravitational Waves". New Scientist. "Astronomical whirling dervishes hide their age well". Astronomy Now. Audio: Cain/Gay - Pulsars Astronomy Cast - Nov 2009
Mass
Mass is both a property of a physical body and a measure of its resistance to acceleration when a net force is applied. The object's mass determines the strength of its gravitational attraction to other bodies; the basic SI unit of mass is the kilogram. In physics, mass is not the same as weight though mass is determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass; this is because weight is a force, while mass is the property that determines the strength of this force. There are several distinct phenomena. Although some theorists have speculated that some of these phenomena could be independent of each other, current experiments have found no difference in results regardless of how it is measured: Inertial mass measures an object's resistance to being accelerated by a force. Active gravitational mass measures the gravitational force exerted by an object.
Passive gravitational mass measures the gravitational force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force; the inertia and the inertial mass describe the same properties of physical bodies at the qualitative and quantitative level by other words, the mass quantitatively describes the inertia. According to Newton's second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A body's mass determines the degree to which it generates or is affected by a gravitational field. If a first body of mass mA is placed at a distance r from a second body of mass mB, each body is subject to an attractive force Fg = GmAmB/r2, where G = 6.67×10−11 N kg−2 m2 is the "universal gravitational constant". This is sometimes referred to as gravitational mass. Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are identical.
The standard International System of Units unit of mass is the kilogram. The kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. However, because precise measurement of a decimeter of water at the proper temperature and pressure was difficult, in 1889 the kilogram was redefined as the mass of the international prototype kilogram of cast iron, thus became independent of the meter and the properties of water. However, the mass of the international prototype and its identical national copies have been found to be drifting over time, it is expected that the re-definition of the kilogram and several other units will occur on May 20, 2019, following a final vote by the CGPM in November 2018. The new definition will use only invariant quantities of nature: the speed of light, the caesium hyperfine frequency, the Planck constant. Other units are accepted for use in SI: the tonne is equal to 1000 kg. the electronvolt is a unit of energy, but because of the mass–energy equivalence it can be converted to a unit of mass, is used like one.
In this context, the mass has units of eV/c2. The electronvolt and its multiples, such as the MeV, are used in particle physics; the atomic mass unit is 1/12 of the mass of a carbon-12 atom 1.66×10−27 kg. The atomic mass unit is convenient for expressing the masses of molecules. Outside the SI system, other units of mass include: the slug is an Imperial unit of mass; the pound is a unit of both mass and force, used in the United States. In scientific contexts where pound and pound need to be distinguished, SI units are used instead; the Planck mass is the maximum mass of point particles. It is used in particle physics; the solar mass is defined as the mass of the Sun. It is used in astronomy to compare large masses such as stars or galaxies; the mass of a small particle may be identified by its inverse Compton wavelength. The mass of a large star or black hole may be identified with its Schwarzschild radius. In physical science, one may distinguish conceptually between at least seven different aspects of mass, or seven physical notions that involve the concept of mass.
Every experiment to date has shown these seven values to be proportional, in some cases equal, this proportionality gives rise to the abstract concept of mass. There are a number of ways mass can be measured or operationally defined: Inertial mass is a measure of an object's resistance to acceleration when a force is applied, it is determined by applying a force to an object and measuring the acceleration that results from that force. An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force. One says. Active gravitational mass is a measure of the strength of an object's gravitational flux. Gravitational field can be measured by allowing a small "test object" to fall and measuring its free-fall acceleration. For example, an object in free fall near the Moon is subject to a smaller gravitational field, hence
Coriolis force
In physics, the Coriolis force is an inertial or fictitious force that seems to act on objects that are in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology. Newton's laws of motion describe the motion of an object in an inertial frame of reference; when Newton's laws are transformed to a rotating frame of reference, the Coriolis force and centrifugal force appear. Both forces are proportional to the mass of the object; the Coriolis force is proportional to the rotation rate and the centrifugal force is proportional to the square of the rotation rate.
The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object's speed in the rotating frame. The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame; these additional forces are termed fictitious forces or pseudo forces. They allow the application of Newton's laws to a rotating system, they are correction factors that do not exist in a inertial reference frame. In popular usage of the term "Coriolis effect", the rotating reference frame implied is always the Earth; because the Earth spins, Earth-bound observers need to account for the Coriolis force to analyze the motion of objects. The Earth completes one rotation per day, so for motions of everyday objects the Coriolis force is quite small compared to other forces; such motions are constrained by the surface of the Earth, so only the horizontal component of the Coriolis force is important.
This force causes moving objects on the surface of the Earth to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. The horizontal deflection effect is greater near the poles, since the effective rotation rate about a local vertical axis is largest there, decreases to zero at the equator. Rather than flowing directly from areas of high pressure to low pressure, as they would in a non-rotating system and currents tend to flow to the right of this direction north of the equator and to the left of this direction south of it; this effect is responsible for the rotation of large cyclones. For an intuitive explanation of the origin of the Coriolis force, consider an object, constrained to follow the Earth's surface and moving northward in the northern hemisphere. Viewed from outer space, the object has an eastward motion; the further north you go, the smaller the "horizontal diameter" of the Earth, so the slower the eastward motion of its surface. As the object moves north, to higher latitudes, it has a tendency to maintain the eastward speed it started with, so it veers east.
For objects moving east-west in the northern hemisphere, the Coriolis deflection can be intuitively explained as follows. The speed of an object moving east at a given latitude is faster than the rotation of the earth at that latitude; this means. In the northern hemisphere this deflects the object to the south. An object moving west in the northern hemisphere is moving too slow relative to the rotation of the earth and takes a path of decreasing radius; this deflects the object to the north. Italian scientist Giovanni Battista Riccioli and his assistant Francesco Maria Grimaldi described the effect in connection with artillery in the 1651 Almagestum Novum, writing that rotation of the Earth should cause a cannonball fired to the north to deflect to the east. In 1674 Claude François Milliet Dechales described in his Cursus seu Mundus Mathematicus how the rotation of the Earth should cause a deflection in the trajectories of both falling bodies and projectiles aimed toward one of the planet's poles.
Riccioli and Dechales all described the effect as part of an argument against the heliocentric system of Copernicus. In other words, they argued that the Earth's rotation should create the effect, so failure to detect the effect was evidence for an immobile Earth; the Coriolis acceleration equation was derived by Euler in 1749 and the effect was described in the tidal equations of Pierre-Simon Laplace in 1778. Gaspard-Gustave Coriolis published a paper in 1835 on the energy yield of machines with rotating parts, such as waterwheels; that paper considered the supplementary forces. Coriolis divided these suppleme
Equipotential
Equipotential or isopotential in mathematics and physics refers to a region in space where every point in it is at the same potential. This refers to a scalar potential, although it can be applied to vector potentials. An equipotential of a scalar potential function in n-dimensional space is an dimensional space; the del operator illustrates the relationship between a vector field and its associated scalar potential field. An equipotential region might be referred as being'of equipotential' or be called'an equipotential'. An equipotential region of a scalar potential in three-dimensional space is an equipotential surface, but it can be a three-dimensional region in space; the gradient of the scalar potential is everywhere perpendicular to the equipotential surface, zero inside a three-dimensional equipotential region. Electrical conductors offer an intuitive example. If a and b are any two points within or at the surface of a given conductor, given there is no flow of charge being exchanged between the two points the potential difference is zero between the two points.
Thus, an equipotential would contain both points a. Extending this definition, an isopotential is the locus of all points that are of the same potential. Gravity is perpendicular to the equipotential surfaces of the gravity potential, in electrostatics and in the case of steady currents the electric field is perpendicular to the equipotential surfaces of the electric potential. In gravity, a hollow sphere has a three-dimensional equipotential region inside, with no gravity. In electrostatics a conductor is a three-dimensional equipotential region. In the case of a hollow conductor, the equipotential region includes the space inside. A ball will not be accelerated by the force of gravity if it is resting on a flat, horizontal surface, because it is an equipotential surface. Equipotential surface Potential flow Potential gradient Isopotential map Scalar potential Electric Field Applet
Perturbation (astronomy)
In astronomy, perturbation is the complex motion of a massive body subject to forces other than the gravitational attraction of a single other massive body. The other forces can include a third body, resistance, as from an atmosphere, the off-center attraction of an oblate or otherwise misshapen body; the study of perturbations began with the first attempts to predict planetary motions in the sky. In ancient times the causes were a mystery. Newton, at the time he formulated his laws of motion and of gravitation, applied them to the first analysis of perturbations, recognizing the complex difficulties of their calculation. Many of the great mathematicians since have given attention to the various problems involved; the complex motions of gravitational perturbations can be broken down. The hypothetical motion that the body follows under the gravitational effect of one other body only is a conic section, can be described with the methods of geometry; this is called an unperturbed Keplerian orbit.
The differences between that and the actual motion of the body are perturbations due to the additional gravitational effects of the remaining body or bodies. If there is only one other significant body the perturbed motion is a three-body problem. A general analytical solution exists for the two-body problem; the two-body problem becomes insoluble if one of the bodies is irregular in shape. Most systems that involve multiple gravitational attractions present one primary body, dominant in its effects; the gravitational effects of the other bodies can be treated as perturbations of the hypothetical unperturbed motion of the planet or satellite around its primary body. In methods of general perturbations, general differential equations, either of motion or of change in the orbital elements, are solved analytically by series expansions; the result is expressed in terms of algebraic and trigonometric functions of the orbital elements of the body in question and the perturbing bodies. This can be applied to many different sets of conditions, is not specific to any particular set of gravitating objects.
General perturbations were investigated first. The classical methods are known as variation of the elements, variation of parameters or variation of the constants of integration. In these methods, it is considered that the body is always moving in a conic section, however the conic section is changing due to the perturbations. If all perturbations were to cease at any particular instant, the body would continue in this conic section indefinitely. General perturbations takes advantage of the fact that in many problems of celestial mechanics, the two-body orbit changes rather due to the perturbations. General perturbations is applicable only if the perturbing forces are about one order of magnitude smaller, or less, than the gravitational force of the primary body. In the Solar System, this is the case. General perturbation methods are preferred for some types of problems, as the source of certain observed motions are found; this is not so for special perturbations. In methods of special perturbations, numerical datasets, representing values for the positions and accelerative forces on the bodies of interest, are made the basis of numerical integration of the differential equations of motion.
In effect, the positions and velocities are perturbed directly, no attempt is made to calculate the curves of the orbits or the orbital elements. Special perturbations can be applied to any problem in celestial mechanics, as it is not limited to cases where the perturbing forces are small. Once applied only to comets and minor planets, special perturbation methods are now the basis of the most accurate machine-generated planetary ephemerides of the great astronomical almanacs. Special perturbations are used for modeling an orbit with computers. Cowell's formulation is the simplest of the special perturbation methods. In a system of n mutually interacting bodies, this method mathematically solves for the Newtonian forces on body i by summing the individual interactions from the other j bodies: r ¨ i = ∑ j = 1 j ≠ i n G m j r i j
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