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Circular Orbit
A circular orbit is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle. In this case, not only the distance, but also the speed, angular speed, Potential energy, potential and kinetic energy are constant. There is no periapsis or apoapsis. This orbit has no Radial orbit, radial version. Listed below is a circular orbit in astrodynamics or celestial mechanics under standard assumptions. Here the centripetal force is the gravitational force, and the axis mentioned above is the line through the Center of mass, center of the central mass perpendicular to the orbital plane. Circular acceleration :wikt:transverse, Transverse acceleration (perpendicular to velocity) causes a change in direction. If it is constant in magnitude and changing in direction with the velocity, circular motion ensues. Taking two derivatives of the particle's coordinates concerning time gives the centripetal acceleration : a\, = \frac \, = where: *v\, is Kinetic e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Newton Cannon
Newton Cannon (May 22, 1781 – September 16, 1841) was an American politician who served as the eighth Governor of Tennessee from 1835 to 1839. He also served several terms in the United States House of Representatives, from 1814 to 1817, and from 1819 to 1823. Cannon was a long-time foe of Andrew Jackson, and spent much of his political career opposing Jacksonite policies. Cannon was succeeded as Governor of Tennessee by James K. Polk in 1839, who later became President of the United States. Early life Born in Guilford County, North Carolina, Cannon was the son of Minos Cannon, who served as a soldier in the Continental Army. The family moved to the area that later became Williamson County, Tennessee, around 1790.Jonathan M. Atkins"Newton Cannon" in ''Tennessee Encyclopedia of History and Culture'' (online edition). Last accessed June 3, 2011. Cannon received a common school education and tried several occupations as a young man, working as a saddler, merchant and surveying, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Circular Motion
In physics, circular motion is movement of an object along the circumference of a circle or rotation along a circular arc. It can be uniform, with a constant rate of rotation and constant tangential speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves the circular motion of its parts. The equations of motion describe the movement of the center of mass of a body, which remains at a constant distance from the axis of rotation. In circular motion, the distance between the body and a fixed point on its surface remains the same, i.e., the body is assumed rigid. Examples of circular motion include: special satellite orbits around the Earth (circular orbits), a ceiling fan's blades rotating around a hub, a stone that is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a mechani ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Radial Parabolic Orbit
In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the 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 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-energy hyperbolic trajectories from negative-energy elliptic orbits. Velocity The orbital velocity (v) of a body travelling along a parabolic trajectory can be computed as: :v = \sqrt where: *r is the radial distance of the orbiting body from the central body, *\mu is the standard gravitational parameter. At ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Free-fall Time
The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse. As such, it plays a fundamental role in setting the timescale for a wide variety of astrophysical processes—from star formation to helioseismology to supernovae—in which gravity plays a dominant role. Derivation Infall to a point source of gravity It is relatively simple to derive the free-fall time by applying Kepler's Third Law of planetary motion to a degenerate elliptic orbit. Consider a point mass m at distance R from a point source of mass M which falls radially inward to it. (Crucially, Kepler's Third Law depends only on the semi-major axis of the orbit, and does not depend on the eccentricity). A purely radial trajectory is an example of a degenerate ellipse with an eccentricity of 1 and semi-major axis R/2. Therefore, the time it would take a body to fall inward, turn around, and return to its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Orbital Period
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars. It may also refer to the time it takes a satellite orbiting a planet or moon to complete one orbit. For celestial objects in general, the orbital period is determined by a 360° revolution of one body around its primary, ''e.g.'' Earth around the Sun. Periods in astronomy are expressed in units of time, usually hours, days, or years. Its reciprocal is the orbital frequency, a kind of revolution frequency, in units of hertz. Small body orbiting a central body According to Kepler's Third Law, the orbital period ''T'' of two point masses orbiting each other in a circular or elliptic orbit is: :T = 2\pi\sqrt where: * ''a'' is the orbit's semi-major axis * ''G'' is the gravitationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Specific Angular Momentum
In celestial mechanics, the specific relative angular momentum (often denoted \vec or \mathbf) of a body is the angular momentum of that body divided by its mass. In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum, divided by the mass of the body in question. Specific relative angular momentum plays a pivotal role in the analysis of the two-body problem, as it remains constant for a given orbit under ideal conditions. "Specific" in this context indicates angular momentum per unit mass. The SI unit for specific relative angular momentum is square meter per second. Definition The specific relative angular momentum is defined as the cross product of the relative position vector \mathbf and the relative velocity vector \mathbf . \mathbf = \mathbf\times \mathbf = \frac where \mathbf is the angular momentum vector, defined as \mathbf \times m \mathbf. The \mathbf vector is always perpendicular to the instantaneo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Orbit Equation
In astrodynamics, an orbit equation defines the path of orbiting body m_2\,\! around central body m_1\,\! relative to m_1\,\!, without specifying position as a function of time. Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular orbit, elliptic orbit, parabolic trajectory, hyperbolic trajectory, or radial trajectory) with the central body located at one of the two foci, or ''the'' focus ( Kepler's first law). If the conic section intersects the central body, then the actual trajectory can only be the part above the surface, but for that part the orbit equation and many related formulas still apply, as long as it is a freefall (situation of weightlessness). Central, inverse-square law force Consider a two-body system consisting of a central body of mass ''M'' and a much smaller, orbiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Standard Gravitational Parameter
The standard gravitational parameter ''μ'' of a celestial body is the product of the gravitational constant ''G'' and the mass ''M'' of that body. For two bodies, the parameter may be expressed as , or as when one body is much larger than the other: \mu=G(M+m)\approx GM . For several objects in the Solar System, the value of ''μ'' is known to greater accuracy than either ''G'' or ''M''. The SI unit of the standard gravitational parameter is . However, the unit is frequently used in the scientific literature and in spacecraft navigation. Definition Small body orbiting a central body The central body in an orbital system can be defined as the one whose mass (''M'') is much larger than the mass of the orbiting body (''m''), or . This approximation is standard for planets orbiting the Sun or most moons and greatly simplifies equations. Under Newton's law of universal gravitation, if the distance between the bodies is ''r'', the force exerted on the smaller body is: F = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particle, elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple Mass in special relativity, definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure (mathematics), measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied. The object's mass also determines the Force, strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is Mass versus weight, not the same as weight, even though mass is often determined by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Gravitational Constant
The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general relativity, theory of general relativity. It is also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant, denoted by the capital letter . In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse-square law, inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor). The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately The modern notation of Newton's law involving was introduced i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dimensionless Quantity
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined Unit of measurement, units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific Unit of volume, units of volume used, such as in milliliters per milliliter (mL/mL). The 1, number one is recognized as a dimensionless Base unit of measurement, base quantity. Radians serve as dimensionless units for Angle, angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference. Dimensionless quantities play a crucial role serving as parameters in differential equations in various technical disciplines. In calculus, concepts like the unitless ratios ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at the centre of a circle by an Circular arc, arc that is equal in length to the radius. The unit was formerly an SI supplementary unit and is currently a dimensionless unit, dimensionless SI derived unit,: "The CGPM decided to interpret the supplementary units in the SI, namely the radian and the steradian, as dimensionless derived units." defined in the SI as 1 rad = 1 and expressed in terms of the SI base unit metre (m) as . Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing. Definition One radian is defined as the angle at the center of a circle in a plane that wikt:subtend, subtends an arc whose length equals the radius of the circle. More generally, the magnit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
