1.
Galactic Center
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The Galactic Center is the rotational center of the Milky Way. The estimates for its range from 7.6 to 8.7 kiloparsecs from Earth in the direction of the constellations Sagittarius, Ophiuchus. There is strong evidence consistent with the existence of a black hole at the Galactic Center of the Milky Way. Because of interstellar dust along the line of sight, the Galactic Center cannot be studied at visible, the available information about the Galactic Center comes from observations at gamma ray, hard X-ray, infrared, sub-millimetre and radio wavelengths. In the early 1940s Walter Baade at Mount Wilson Observatory took advantage of wartime conditions in nearby Los Angeles to conduct a search for the center with the 100 inch Hooker Telescope. This gap has been known as Baades Window ever since, by 1954 they had built an 80 feet fixed dish antenna and used it to make a detailed study of an extended, extremely powerful belt of radio emission that was detected in Sagittarius. In 1958 the International Astronomical Union decided to adopt the position of Sagittarius A as the true zero co-ordinate point for the system of latitude and longitude. In the equatorial system the location is, RA 17h 45m 40. 04s. The exact distance between the Solar System and the Galactic Center is not certain, although estimates since 2000 have remained within the range 7. 2–8.8 kpc. The nature of the Milky Ways bar, which extends across the Galactic Center, is also debated, with estimates for its half-length. Certain authors advocate that the Milky Way features two bars, one nestled within the other. The bar is delineated by red-clump stars, however, RR Lyr variables do not trace a prominent Galactic bar. The bar may be surrounded by a called the 5-kpc ring that contains a large fraction of the molecular hydrogen present in the Milky Way. Viewed from the Andromeda Galaxy, it would be the brightest feature of the Milky Way, accretion of gas onto the black hole, probably involving a disk around it, would release energy to power the radio source, itself much larger than the black hole. The latter is too small to see with present instruments, a study in 2008 which linked radio telescopes in Hawaii, Arizona and California measured the diameter of Sagittarius A* to be 44 million kilometers. For comparison, the radius of Earths orbit around the Sun is about 150 million kilometers, thus the diameter of the radio source is slightly less than the distance from Mercury to the Sun.3 million solar masses. On 5 January 2015, NASA reported observing an X-ray flare 400 times brighter than usual, the central cubic parsec around Sagittarius A* contains around 10 million stars. Although most of them are old red giant stars, the Galactic Center is also rich in massive stars, more than 100 OB and Wolf–Rayet stars have been identified there so far

2.
Center of balance (horse)
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In horsemanship, the center of balance of a horse is a position on the horses back which correlates closely to the center of gravity of the horse itself. The term may refer to the horses center of gravity. For the best performance by the horse, as well as for better balance of the rider, the location of the horses center of balance depends on a combination of speed and degree of collection. For a standing or quietly walking horse, it is slightly behind the heart girth, if a horse is moving at a trot or canter, the center of balance shifts slightly forward, and it moves even more forward when the horse is galloping or jumping. If a horse is highly collected, the center of balance will be back, regardless of gait. For example, a close contact style of English saddle, designed for show jumping, places the riders seat farther forward than does a dressage style English saddle

3.
Locating the center of mass
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There are several methods for locating the center of mass of a body. This method is useful when one wishes to find the centroid of a complex shape with unknown dimensions. It relies on finding the center of mass of a body of homogeneous density having the same shape as the complex planar shape. This is a method of determining the center of mass of an L-shaped object, divide the shape into two rectangles, as shown in fig 2. Find the center of masses of two rectangles by drawing the diagonals. Draw a line joining the centers of mass, the center of mass of the shape must lie on this line AB. Divide the shape into two rectangles, as shown in fig 3. Find the centers of mass of two rectangles by drawing the diagonals. Draw a line joining the centers of mass, the center of mass of the L-shape must lie on this line CD. As the center of mass of the shape must lie along AB and also along CD, it is obvious that it is at the intersection of these two lines, at O. This method is useful when one wishes to find the location of the centroid or center of mass of an object that is divided into elementary shapes. Here the center of mass will only be found in the x direction, the same procedure may be followed to locate the center of mass in the y direction. It is easily divided into a square, triangle, and circle, note that the circle will have negative area. From the List of centroids, we note the coordinates of the individual centroid. From equation 1 above,3 × +5 ×102 +13.33 ×1022 −2.52 π +102 +1022 ≈8.5 units. The center of mass of this figure is at a distance of 8.5 units from the corner of the figure. A direct development of the known as an integraph, or integerometer. This method can be applied to a shape with an irregular and it was regularly used by ship builders to ensure the ship would not capsize

4.
Center of mass
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The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. Calculations in mechanics are simplified when formulated with respect to the center of mass. It is a point where entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the equivalent of a given object for application of Newtons laws of motion. In the case of a rigid body, the center of mass is fixed in relation to the body. The center of mass may be located outside the body, as is sometimes the case for hollow or open-shaped objects. In the case of a distribution of separate bodies, such as the planets of the Solar System, in orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass frame is a frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system. The concept of center of mass in the form of the center of gravity was first introduced by the ancient Greek physicist, mathematician, and engineer Archimedes of Syracuse. He worked with simplified assumptions about gravity that amount to a uniform field, in work on floating bodies he demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes, Newtons second law is reformulated with respect to the center of mass in Eulers first law. The center of mass is the point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the location of a distribution of mass in space. Solving this equation for R yields the formula R =1 M ∑ i =1 n m i r i, solve this equation for the coordinates R to obtain R =1 M ∭ Q ρ r d V, where M is the total mass in the volume. If a continuous mass distribution has density, which means ρ is constant. The center of mass is not generally the point at which a plane separates the distribution of mass into two equal halves, in analogy with statistics, the median is not the same as the mean. The coordinates R of the center of mass of a system, P1 and P2, with masses m1. The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, another way of interpreting the process here is the mechanical balancing of moments about an arbitrary point

5.
Mass point geometry
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Coincidence - We say that two points m P and n Q coincide if and only if m = n and P = Q. Addition - The sum of two points m P and n Q has mass m + n and point R where R is the point on P Q such that P R, R Q = n, m. In other words, R is the point that perfectly balances the points P and Q. An example of mass point addition is shown at right, mass point addition is closed, commutative, and associative. Scalar Multiplication - Given a mass point m P and a real scalar k. Mass point scalar multiplication is distributive over mass point addition, first, a point is assigned with a mass in the way that other masses are also whole numbers. The principle of calculation is that the foot of a cevian is the addition of the two vertices, for each cevian, the point of concurrency is the sum of the vertex and the foot. Each length ratio may then be calculated from the masses at the points, see Problem One for an example. Splitting masses is the more complicated method necessary when a problem contains transversals in addition to cevians. Any vertex that is on both sides the transversal crosses will have a split mass, see Problem Two for an example. Rouths theorem - Many problems involving triangles with cevians will ask for areas, however, Rouths theorem, which goes hand in hand with mass points, uses ratios of lengths to calculate the ratio of areas between a triangle and a triangle formed by three cevians. Special cevians - When given cevians with special properties, like an angle bisector or an altitude, One very common theorem used likewise is the angle bisector theorem. In triangle A B C, E is on A C so that C E =3 A E and F is on A B so that B F =3 A F. If B E and C F intersect at O and line A O intersects B C at D and we may arbitrarily assign the mass of point A to be 3. By ratios of lengths, the masses at B and C must both be 1, by summing masses, the masses at E and F are both 4. Furthermore, the mass at O is 4 +1 =5, if D E and C F intersect at O, compute O D O E and O C O F. Solution. As this problem involves a transversal, we must use split masses on point C and we may arbitrarily assign the mass of point A to be 15. By ratios of lengths, the mass at B must be 6, by summing masses, we get the masses at D, E, and F to be 15,25, and 21, respectively

6.
Center of gravity of an aircraft
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The center of gravity of an aircraft is the point over which the aircraft would balance. Its position is calculated after supporting the aircraft on at least two sets of weighing scales or load cells and noting the weight shown on set of scales or load cells. The center of gravity affects the stability of the aircraft, to ensure the aircraft is safe to fly, the center of gravity must fall within specified limits established by the aircraft manufacturer. Ballast Ballast is removable or permanently installed weight in a used to bring the center of gravity into the allowable range. Center-of-Gravity Limits Center of gravity limits are specified longitudinal and/or lateral limits within which the center of gravity must be located during flight. The CG limits are indicated in the flight manual. The area between the limits is called the CG range of the aircraft, different maximum weights may be defined for different situations, for example, large aircraft may have maximum landing weights that are lower than maximum take-off weights. The center of gravity may change over the duration of the flight as the weight changes due to fuel burn or by passengers moving forward or aft in the cabin. Reference Datum The reference datum is a plane that allows accurate. The location of the datum is established by the manufacturer and is defined in the aircraft flight manual. There is no fixed rule for its location, and it may be located forward of the nose of the aircraft, for helicopters, it may be located at the rotor mast, the nose of the helicopter, or even at a point in space ahead of the helicopter. This is to all the computed values positive. The lateral reference datum is usually located at the center of the helicopter, arm The arm is the horizontal distance from the reference datum to the center of gravity of an item. The algebraic sign is plus if measured aft of the datum or to the side of the center line when considering a lateral calculation. The algebraic sign is minus if measured forward of the datum or the side of the center line when considering a lateral calculation. Moment The moment is the moment of force, or torque, moment is also referred to as the tendency of an object to rotate or pivot about a point. The further an object is from this point, the greater the force it exerts, moment is calculated by multiplying the weight of an object by its arm. Mean Aerodynamic Chord A specific chord line of a tapered wing, at the mean aerodynamic chord, the center of pressure has the same aerodynamic force, position, and area as it does on the rest of the wing