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Nonlinear Memory Effect
Gravitational memory effects, also known as gravitational-wave memory effects are predicted persistent changes in the relative position of pairs of masses in space due to the passing of a gravitational wave. Detection of gravitational memory effects has been suggested as a way of validating general relativity. In 2014 Andrew Strominger and Alexander Zhiboedov showed that the formula related to the memory effect is the Fourier transform in time of Weinberg's soft graviton theorem. Linear and non linear effect There are two kinds of predicted gravitational memory effects: one based on a linear approximation of Einstein's equations, first proposed in 1974 by the Soviet scientists Yakov Zeldovich and A. G. Polnarev, developed also by Vladimir Braginsky and L. P. Grishchuk, and a non-linear phenomenon known as the non-linear memory effect, which was first proposed in the 1990s by Demetrios Christodoulou. The non-linear memory effect could be exploited to determine the inclina ...
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Orbital Plane
The orbital plane of a revolving body is the geometric plane in which its orbit lies. Three non-collinear points in space suffice to determine an orbital plane. A common example would be the positions of the centers of a massive body (host) and of an orbiting celestial body at two different times/points of its orbit. The orbital plane is defined in relation to a reference plane by two parameters: inclination (''i'') and longitude of the ascending node (Ω). By definition, the reference plane for the Solar System is usually considered to be Earth's orbital plane, which defines the ecliptic, the circular path on the celestial sphere that the Sun appears to follow over the course of a year. In other cases, for instance a moon or artificial satellite orbiting another planet, it is convenient to define the inclination of the object's orbit as the angle between its orbital plane and the planet's equatorial plane. The coordinate system defined that uses the orbital plane as ...
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Astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest include planets, natural satellite, moons, stars, nebulae, galaxy, galaxies, meteoroids, asteroids, and comets. Relevant phenomena include supernova explosions, gamma ray bursts, quasars, blazars, pulsars, and cosmic microwave background radiation. More generally, astronomy studies everything that originates beyond atmosphere of Earth, Earth's atmosphere. Cosmology is a branch of astronomy that studies the universe as a whole. Astronomy is one of the oldest natural sciences. The early civilizations in recorded history made methodical observations of the night sky. These include the Egyptian astronomy, Egyptians, Babylonian astronomy, Babylonians, Greek astronomy, Greeks, Indian astronomy, Indians, Chinese astronomy, Chinese, Maya civilization, M ...
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LIGO
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Prior to LIGO, all data about the universe has come in the form of light and other forms of electromagnetic radiation, from limited direct exploration on relatively nearby Solar System objects such as the Moon, Mars, Venus, Jupiter and their moons, asteroids etc, and from high energy cosmic particles. Initially, two large observatories were built in the United States with the aim of detecting gravitational waves by laser interferometry. Two additional, smaller gravity wave observatories are now operational in Japan KAGRA, (KAGRA) and Italy Virgo interferometer, (Virgo). The two LIGO observatories use mirrors spaced four kilometers apart to measure changes in length—over an effective span of 1120 km—of less than one ten-thousandth the charge radius, ...
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Laser Interferometer Space Antenna
The Laser Interferometer Space Antenna (LISA) is a planned space probe to detect and measure gravitational waves—tiny ripples in the fabric of spacetime—from astronomical sources. LISA will be the first dedicated space-based gravitational-wave observatory. It aims to measure gravitational waves directly by using laser interferometry. The LISA concept features three spacecraft arranged in an equilateral triangle with each side 2.5 million kilometers long, flying in an Earth-like heliocentric orbit. The distance between the satellites is precisely monitored to detect a passing gravitational wave. The LISA project started out as a joint effort between NASA and the European Space Agency (ESA). However, in 2011, NASA announced that it would be unable to continue its original LISA partnership with the European Space Agency due to funding limitations. In response, ESA continued developing the mission and in 2017, NASA re-engaged with LISA, contributing technology and scientific e ...
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Laurent Series
In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Laurent series was named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass had previously described it in a paper written in 1841 but not published until 1894. Definition The Laurent series for a complex function f(z) about an arbitrary point c is given by f(z) = \sum_^\infty a_n(z-c)^n, where the coefficients a_n are defined by a contour integral that generalizes Cauchy's integral formula: a_n =\frac\oint_\gamma \frac \, dz. The path of integration \gamma is counterclockwise around a Jordan curve enclosing c and lying in an annulus A in which f(z) is holomorphic ( analytic). The expansion for f(z) will then be valid anywhere inside the annulus. The annulus is shown in red in th ...
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Angular Momentum
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction (geometry), direction and a magnitude, and both are conserved. Bicycle and motorcycle dynamics, Bicycles and motorcycles, flying discs, Rifling, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it. The three-dimensional angular momentum for a point particle is classically represented as a pseudovector , the cross product of the particle's position vector (relative to some origin) and its mo ...
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Sabrina Gonzalez Pasterski
Sabrina Gonzalez Pasterski (born June 3, 1993) is an American theoretical physicist from Chicago who studies high energy physics. She describes herself as "a proud first-generation Cuban-American and Chicago Public Schools alumna". Her first few months at Harvard's Center for the Fundamental Laws of Nature (2014) resulted in discovery of the spin memory effect which predates LIGO's reported discoveries and may be proven as an inexpensive way to detect as well as verify gravitational waves and their net effects during a very rare celestial gravitational lensing event the first week of May 2028 if not sooner via Advanced LIGO Since leaving Harvard, Pasterski has pioneered Celestial Holography. She completed her undergraduate studies in three years while still a teenager at the Massachusetts Institute of Technology (MIT), earned her PhD from Harvard University and was a PCTS Postdoctoral Fellow at Princeton University before joining the faculty of the Perimeter Institute at age 27. ...
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Nova (American TV Program)
''Nova'' (stylized as ''NOVΛ'') is an American popular science television program produced by WGBH in Boston, Massachusetts, since 1974. It is broadcast on PBS in the United States, and in more than 100 other countries. The program has won many major television awards. ''Nova'' often includes interviews with scientists doing research in the subject areas covered and occasionally includes footage of a particular discovery. Some episodes have focused on the history of science. Examples of topics covered include the following: Colditz Castle, the Drake equation, elementary particles, the 1980 eruption of Mount St. Helens, Fermat's Last Theorem, the AIDS epidemic, global warming, moissanite, Project Jennifer, storm chasing, Unterseeboot 869, Vinland, Tarim mummies, and the COVID-19 pandemic. The ''Nova'' programs have been praised for their pacing, writing, and editing. Websites that accompany the segments have also won awards. Episodes History ''Nova'' was first aired ...
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Gravitational Wave
Gravitational waves are oscillations of the gravitational field that Wave propagation, travel through space at the speed of light; they are generated by the relative motion of gravity, gravitating masses. They were proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as the gravitational equivalent of Electromagnetic radiation, electromagnetic waves. In 1916, Albert Einstein demonstrated that gravitational waves result from his general theory of relativity as ripples in spacetime. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, instead asserting that gravity has instantaneous effect everywhere. Gravitational waves therefore stand as an important relativistic phenomenon that is absent from Newtonian physics. Gravitational-wave astronomy has the advantage that, unlike elec ...
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Demetrios Christodoulou
Demetrios Christodoulou (; born 19 October 1951) is a Greek mathematician and physicist, who first became well known for his proof, together with Sergiu Klainerman, of the nonlinear stability of the Minkowski spacetime of special relativity in the framework of general relativity. Christodoulou is a 1993 MacArthur Fellow. Early life Christodoulou was born in Athens and received his doctorate in physics from Princeton University in 1971 under the direction of John Archibald Wheeler. After a temporary position at Caltech, a full professor position at the physics department of the University of Athens shortly followed. Then, after visiting CERN and the Max Planck Institute for Physics, he became professor of mathematics, first at Syracuse University, then at the Courant Institute, and at Princeton University, before taking up his last position as professor of mathematics and physics at the ETH Zurich in Switzerland. He is emeritus professor since January 2017. He holds dual Gree ...
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