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Porkchop Plot
In orbital mechanics, a porkchop plot (also pork-chop plot) is a chart that shows level curves of equal characteristic energy (C3) against combinations of launch date and arrival date for a particular interplanetary flight. The chart shows the characteristic energy ranges in zones around the local minima, which resembles the shape of a porkchop slice. By examining the results of the porkchop plot, engineers can determine when a launch opportunity exists (a 'launch window') that is compatible with the capabilities of a particular spacecraft. A given contour, called a porkchop curve, represents constant C3, and the center of the porkchop the optimal minimum C3. The orbital elements of the solution, where the fixed values are the departure date, the arrival date, and the length of the flight, were first solved mathematically in 1761 by Johann Heinrich Lambert, and the equation is generally known as Lambert's problem (or theorem). Math The general form of ''characteristic energy'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Orbital Energy
In the gravitational two-body problem, the specific orbital energy \varepsilon (or specific ''vis-viva'' energy) of two orbiting bodies is the constant quotient of their mechanical energy (the sum of their mutual potential energy, \varepsilon_p, and their kinetic energy, \varepsilon_k) to their reduced mass. According to the orbital energy conservation equation (also referred to as ''vis-viva'' equation), it does not vary with time: \begin \varepsilon &= \varepsilon_k + \varepsilon_p \\ &= \frac - \frac = -\frac \frac \left(1 - e^2\right) = -\frac \end where *v is the relative orbital speed; *r is the orbital distance between the bodies; *\mu = (m_1 + m_2) is the sum of the standard gravitational parameters of the bodies; *h is the specific relative angular momentum in the sense of relative angular momentum divided by the reduced mass; *e is the orbital eccentricity; *a is the semi-major axis. It is a kind of specific energy, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Trajectory
In astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola. In more technical terms this can be expressed by the condition that the orbital eccentricity is greater than one. Under simplistic assumptions a body traveling along this trajectory will coast towards infinity, settling to a final excess velocity relative to the central body. Similarly to parabolic trajectories, all hyperbolic trajectories are also escape trajectories. The specific energy of a hyperbolic trajectory orbit is positive. Planetary flybys, used for gravitational slingshots, can be described within the planet's sphere of influence using hyperbolic trajectories. Parameters describing a hyperbolic trajectory Like an elliptical orbit, a hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Trajectory
In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the Orbital eccentricity, eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a C3 = 0 orbit (see Characteristic energy). Under standard assumptions a body traveling along an escape orbit will coast along a Parabola, parabolic trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return. Parabolic trajectories are minimum-energy escape trajectories, separating positive-characteristic energy, energy hyperbolic trajectory, hyperbolic trajectories from negative-energy elliptic orbits. Velocity The Kinetic energy, orbital velocity (v) of a body travelling along a parabolic trajectory can be computed as: :v = \sqrt where: *r is the radial distance of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbit
In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yale University Press
Yale University Press is the university press of Yale University. It was founded in 1908 by George Parmly Day and Clarence Day, grandsons of Benjamin Day, and became a department of Yale University in 1961, but it remains financially and operationally autonomous. , Yale University Press publishes approximately 300 new hardcover A hardcover, hard cover, or hardback (also known as hardbound, and sometimes as casebound (At p. 247.)) book is one bookbinding, bound with rigid protective covers (typically of binder's board or heavy paperboard covered with buckram or other clo ... and 150 new paperback books annually and has a backlist of about 5,000 books in print. Its books have won five National Book Awards, two National Book Critics Circle Awards and eight Pulitzer Prizes. The press maintains offices in New Haven, Connecticut and London, England. Yale is the only American university press with a full-scale publishing operation in Europe. It was a co-founder of the dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fiscal Year
A fiscal year (also known as a financial year, or sometimes budget year) is used in government accounting, which varies between countries, and for budget purposes. It is also used for financial reporting by businesses and other organizations. Laws in many jurisdictions require company financial reports to be prepared and published on an annual basis but generally with the reporting period not aligning with the calendar year (1 January to 31 December). Taxation laws generally require accounting records to be maintained and taxes calculated on an annual basis, which usually corresponds to the fiscal year used for government purposes. The calculation of tax on an annual basis is especially relevant for direct taxes, such as income tax. Many annual government fees—such as council tax and license fees are also levied on a fiscal year basis, but others are charged on an anniversary basis. Some companies, such as Cisco Systems, end their fiscal year on the same day of the week each ye ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christmas
Christmas is an annual festival commemorating Nativity of Jesus, the birth of Jesus Christ, observed primarily on December 25 as a Religion, religious and Culture, cultural celebration among billions of people Observance of Christmas by country, around the world. A liturgical year, liturgical feast central to Christianity, Christmas preparation begins on the Advent Sunday, First Sunday of Advent and it is followed by Christmastide, which historically in the West lasts Twelve Days of Christmas, twelve days and culminates on Twelfth Night (holiday), Twelfth Night. Christmas Day is a public holiday in List of holidays by country, many countries, is observed religiously by a majority of Christians, as well as celebrated culturally by many non-Christians, and forms an integral part of the annual Christmas and holiday season, holiday season. The traditional Christmas narrative recounted in the New Testament, known as the Nativity of Jesus, says that Jesus was born in Bethlehem, in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thanksgiving
Thanksgiving is a national holiday celebrated on various dates in October and November in the United States, Canada, Saint Lucia, Liberia, and unofficially in countries like Brazil and Germany. It is also observed in the Australian territory of Norfolk Island. It began as a day of giving thanks for the blessings of the harvest and of the preceding year. Various similarly named harvest festival holidays occur throughout the world during autumn. Although Thanksgiving has historical roots in religious and cultural traditions, it has long been celebrated as a Secularity, secular holiday as well. History Prayers of thanks and special thanksgiving ceremonies are common among most religions after harvests and at other times of the year. The Thanksgiving holiday's history in North America is rooted in English traditions dating from the Protestant Reformation. It also has aspects of a harvest festival, even though the harvest in New England occurs well before the late-November date on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voyager Program
The Voyager program is an American scientific program that employs two interstellar probes, ''Voyager 1'' and ''Voyager 2''. They were launched in 1977 to take advantage of a favorable planetary alignment to explore the two gas giants Jupiter and Saturn and potentially also the ice giants, Uranus and Neptune—to Flyby (spaceflight), fly near them while collecting data for transmission back to Earth. After ''Voyager 1'' successfully completed its flyby of Saturn and its moon Titan (moon), Titan, it was decided to send ''Voyager 2'' on flybys of Uranus and Neptune. After the planetary flybys were complete, decisions were made to keep the probes in operation to explore Outer space, interstellar space and the outer regions of the Solar System. On 25 August 2012, data from ''Voyager 1'' indicated that it had entered interstellar space. On 5 November 2019, data from ''Voyager 2'' indicated that it also had entered interstellar space. On 4 November 2019, scientists reported that on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Speed
In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter (the combined center of mass) or, if one body is much more massive than the other bodies of the system combined, its speed relative to the center of mass of the most massive body. The term can be used to refer to either the mean orbital speed (i.e. the average speed over an entire orbit) or its instantaneous speed at a particular point in its orbit. The maximum (instantaneous) orbital speed occurs at periapsis (perigee, perihelion, etc.), while the minimum speed for objects in closed orbits occurs at apoapsis (apogee, aphelion, etc.). In ideal two-body systems, objects in open orbits continue to slow down forever as their distance to the barycenter increases. When a system approximates a two-body system, instantaneous orbital speed at a given point of the orbit can b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Mechanics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Astrodynamics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and it is sometimes necessary to use it for greater accuracy or in high-gravity situations (e.g. orbits near the Sun). History Until th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
