1.
Classical mechanics
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In physics, classical mechanics is one of the two major sub-fields of mechanics, along with quantum mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology. Classical mechanics describes the motion of objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars. Within classical mechanics are fields of study that describe the behavior of solids, liquids and gases, Classical mechanics also provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When both quantum and classical mechanics cannot apply, such as at the level with high speeds. Since these aspects of physics were developed long before the emergence of quantum physics and relativity, however, a number of modern sources do include relativistic mechanics, which in their view represents classical mechanics in its most developed and accurate form. Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and these advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newtons work, particularly through their use of analytical mechanics. The following introduces the concepts of classical mechanics. For simplicity, it often models real-world objects as point particles, the motion of a point particle is characterized by a small number of parameters, its position, mass, and the forces applied to it. Each of these parameters is discussed in turn, in reality, the kind of objects that classical mechanics can describe always have a non-zero size. Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the degrees of freedom. However, the results for point particles can be used to such objects by treating them as composite objects. The center of mass of a composite object behaves like a point particle, Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as where an object is in space, non-relativistic mechanics also assumes that forces act instantaneously. The position of a point particle is defined with respect to a fixed reference point in space called the origin O, in space. A simple coordinate system might describe the position of a point P by means of a designated as r. In general, the point particle need not be stationary relative to O, such that r is a function of t, the time

2.
Astrodynamics
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Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of objects is usually calculated from Newtons laws of motion. It is a discipline within space mission design and control. General relativity is an exact theory than Newtons laws for calculating orbits. Until the rise of space travel in the century, there was little distinction between orbital and celestial mechanics. At the time of Sputnik, the field was termed space dynamics, the fundamental techniques, such as those used to solve the Keplerian problem, are therefore the same in both fields. Furthermore, the history of the fields is almost entirely shared, johannes Kepler was the first to successfully model planetary orbits to a high degree of accuracy, publishing his laws in 1605. Isaac Newton published more general laws of motion in his 1687 book. The following rules of thumb are useful for situations approximated by classical mechanics under the assumptions of astrodynamics outlined below the rules. The specific example discussed is of a satellite orbiting a planet, Keplers laws of planetary motion, Orbits are elliptical, with the heavier body at one focus of the ellipse. Special case of this is an orbit with the planet at the center. A line drawn from the planet to the satellite sweeps out equal areas in equal times no matter which portion of the orbit is measured, the square of a satellites orbital period is proportional to the cube of its average distance from the planet. Without applying force, the period and shape of the satellites orbit wont change, a satellite in a low orbit moves more quickly with respect to the surface of the planet than a satellite in a higher orbit, due to the stronger gravitational attraction closer to the planet. If thrust is applied at one point in the satellites orbit, it will return to that same point on each subsequent orbit. Thus one cannot move from one orbit to another with only one brief application of thrust. Thrust applied in the direction of the satellites motion creates an elliptical orbit with an apoapse 180 degrees away from the firing point, the consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecraft are in the circular orbit and wish to dock, unless they are very close. This will change the shape of its orbit, causing it to gain altitude and actually slow down relative to the leading craft, the space rendezvous before docking normally takes multiple precisely calculated engine firings in multiple orbital periods requiring hours or even days to complete

3.
Orbital mechanics
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Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of objects is usually calculated from Newtons laws of motion. It is a discipline within space mission design and control. General relativity is an exact theory than Newtons laws for calculating orbits. Until the rise of space travel in the century, there was little distinction between orbital and celestial mechanics. At the time of Sputnik, the field was termed space dynamics, the fundamental techniques, such as those used to solve the Keplerian problem, are therefore the same in both fields. Furthermore, the history of the fields is almost entirely shared, johannes Kepler was the first to successfully model planetary orbits to a high degree of accuracy, publishing his laws in 1605. Isaac Newton published more general laws of motion in his 1687 book. The following rules of thumb are useful for situations approximated by classical mechanics under the assumptions of astrodynamics outlined below the rules. The specific example discussed is of a satellite orbiting a planet, Keplers laws of planetary motion, Orbits are elliptical, with the heavier body at one focus of the ellipse. Special case of this is an orbit with the planet at the center. A line drawn from the planet to the satellite sweeps out equal areas in equal times no matter which portion of the orbit is measured, the square of a satellites orbital period is proportional to the cube of its average distance from the planet. Without applying force, the period and shape of the satellites orbit wont change, a satellite in a low orbit moves more quickly with respect to the surface of the planet than a satellite in a higher orbit, due to the stronger gravitational attraction closer to the planet. If thrust is applied at one point in the satellites orbit, it will return to that same point on each subsequent orbit. Thus one cannot move from one orbit to another with only one brief application of thrust. Thrust applied in the direction of the satellites motion creates an elliptical orbit with an apoapse 180 degrees away from the firing point, the consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecraft are in the circular orbit and wish to dock, unless they are very close. This will change the shape of its orbit, causing it to gain altitude and actually slow down relative to the leading craft, the space rendezvous before docking normally takes multiple precisely calculated engine firings in multiple orbital periods requiring hours or even days to complete

4.
Apparent retrograde motion
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Apparent retrograde motion is the apparent motion of a planet in a direction opposite to that of other bodies within its system, as observed from a particular vantage point. Direct motion or prograde motion is motion in the direction as other bodies. While the terms direct and prograde are equivalent in this context, the earliest recorded use of prograde was in the early 18th century, although the term is now less common. The term retrograde is from the Latin word retrogradus – backward-step, retrograde is most commonly an adjective used to describe the path of a planet as it travels through the night sky, with respect to the zodiac, stars, and other bodies of the celestial canopy. Mercury in retrograde is an example of the used as a noun for retrograde motion. Retrograde is also used as an intransitive verb meaning to become, to appear. Although planets can sometimes be mistaken for stars as one observes the night sky, retrograde and prograde are observed as though the stars revolve around the Earth. Like the sun, the appear to rise in the East. When a planet travels eastward in relation to the stars, it is called prograde, when the planet travels westward in relation to the stars it is called retrograde. In Earths sky, the Sun, Moon, and stars appear to move from east to west because of the rotation of Earth, however, orbiters such as the Space Shuttle and many artificial satellites appear to move from west to east. These are direct satellites, but they orbit Earth faster than Earth itself rotates, Mars has a natural satellite Phobos, with a similar orbit. From the surface of Mars it appears to move in the direction because its orbital period is less than a Martian day. There are also numbers of truly retrograde artificial satellites orbiting Earth which counter-intuitively appear to move westward. As seen from Earth, all the objects in the Solar System appear to periodically switch direction as they cross the sky. Though all stars and planets appear to move from east to west on a basis in response to the rotation of Earth. Asteroids and Kuiper Belt objects exhibit apparent retrogradation and this motion is normal for the planets, and so is considered direct motion. However, since Earth completes its orbit in a period of time than the planets outside its orbit, it periodically overtakes them. When this occurs, the planet being passed will first appear to stop its eastward drift, then, as Earth swings past the planet in its orbit, it appears to resume its normal motion west to east

5.
Attitude control
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Attitude control is controlling the orientation of an object with respect to an inertial frame of reference or another entity. The integrated field that studies the combination of sensors, actuators and algorithms is called Guidance, Navigation, a spacecrafts attitude must typically be stabilized and controlled for a variety of reasons. Propulsion system thrusters are fired only occasionally to make desired changes in spin rate, if desired, the spinning may be stopped through the use of thrusters or by yo-yo de-spin. The Pioneer 10 and Pioneer 11 probes in the solar system are examples of spin-stabilized spacecraft. Three-axis stabilization is a method of spacecraft attitude control in which the spacecraft is held fixed in the desired orientation without any rotation. One method is to use thrusters to continually nudge the spacecraft back. Thrusters may also be referred to as control systems, or reaction control systems. The space probes Voyager 1 and Voyager 2 employ this method, another method for achieving three-axis stabilization is to use electrically powered reaction wheels, also called momentum wheels, which are mounted on three orthogonal axes aboard the spacecraft. They provide a means to trade angular momentum back and forth between spacecraft and wheels, to rotate the vehicle on a given axis, the reaction wheel on that axis is accelerated in the opposite direction. To rotate the back, the wheel is slowed. This is done during maneuvers called momentum desaturation or momentum unload maneuvers, most spacecraft use a system of thrusters to apply the torque for desaturation maneuvers. A different approach was used by the Hubble Space Telescope, which had sensitive optics that could be contaminated by thruster exhaust, there are advantages and disadvantages to both spin stabilization and three-axis stabilization. Many spacecraft have components that require articulation, Voyager and Galileo, for example, were designed with scan platforms for pointing optical instruments at their targets largely independently of spacecraft orientation. Many spacecraft, such as Mars orbiters, have solar panels that must track the Sun so they can provide power to the spacecraft. Cassinis main engine nozzles are steerable, knowing where to point a solar panel, or scan platform, or a nozzle — that is, how to articulate it—requires knowledge of the spacecrafts attitude. Because AACS keeps track of the attitude, the Suns location. It logically falls to one subsystem, then, to manage both attitude and articulation, the name AACS may even be carried over to a spacecraft even if it has no appendages to articulate. Many sensors generate outputs that reflect the rate of change in attitude and these require a known initial attitude, or external information to use them to determine attitude

6.
Beta angle
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The beta angle is a measurement that is used most notably in spaceflight. The beta angle determines the percentage of time an object such as a spacecraft in low Earth orbit spends in direct sunlight, Beta angle is defined as the angle between the orbital plane of the spacecraft and the vector to the sun. The beta angle is the angle between the Sun vector and the plane of the objects orbit. The beta angle varies between +90° and −90°, and the direction the satellite revolves around the body it orbits determines whether the beta angle sign is positive or negative. An imaginary observer standing on the Sun defines a beta angle as positive if the satellite in question orbits in a clockwise direction. The maximum amount of time that a satellite in a normal low Earth orbit mission can spend in the Earths shadow occurs at a angle of zero. In such an orbit, the satellite is in no more than 59% of the time. The degree of orbital shadowing an object in LEO experiences is determined by that objects beta angle. An object launched into an orbit with an inclination equal to the complement of the Earths inclination to the ecliptic results in an initial beta angle of 0 degrees for the orbiting object. This allows the object to spend the maximum amount of its orbital period in the Earths shadow. An example would be a polar orbit initiated at local dawn or dusk on an equinox, Beta angles describing non-geocentric orbits are important when space agencies launch satellites into orbits around other bodies in the Solar System. When the orbiter was in-flight and it flew to an angle greater than 60 degrees, the orbiter went into rotisserie mode. For flights to ISS, the shuttle could launch during an ISS beta cutout if the ISS would be at a less than 60 degrees at dock. Therefore, the mission duration affected launch timing when the beta cutout dates were approaching, international Space Station Low Earth Orbit Launch window NASA, ISS Beta Angle

7.
Bi-elliptic transfer
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The bi-elliptic transfer consists of two half elliptic orbits. The idea of the bi-elliptical transfer trajectory was first published by Ary Sternfeld in 1934. e. The final retrograde burn requires a delta-v of magnitude, Δ v 3 =2 μ r 2 − μ a 2 − μ r 2 If r b = r 2, then the maneuver reduces to a Hohmann transfer. Thus the bi-elliptic transfer constitutes a general class of orbital transfers. The maximum savings possible can be computed by assuming that r b = ∞, in this case one also speaks of a bi-parabolic transfer because the two transfer trajectories no longer are ellipses but parabola. The transfer time increases to infinity too, like the Hohmann transfer, both transfer orbits used in the bi-elliptic transfer constitute exactly one half of an elliptic orbit. This means that the required to execute each phase of the transfer is half the orbital period of each transfer ellipse. Using the equation for the period and the notation from above. The inset shows a close-up of the region where the bi-elliptic curves cross the Hohmann curve for the first time, one sees that the Hohmann transfer is always more efficient if the ratio of radii R is smaller than 11.94. Between the ratios of 11.94 and 15.58, for any given R in this range, there is a value of r b above which the bi-elliptic transfer is superior and below which the Hohmann transfer is better. The following table lists this value of α ≡ r b / r 1 for some selected cases, the long Transfer time of the bi-elliptic transfer t = π a 13 μ + π a 23 μ is a major drawback for this maneuver. It even becomes infinite for the bi-parabolic transfer limiting case. 02+1308. 70=4133.72 m/s, however, because r1=14r0 >11. 94r0, it is possible to do better with a bi-elliptic transfer. The Δv saving could be improved by increasing the intermediate apogee. For example, an apogee of 75. 8r0=507,688 km would result in a 1% Δv saving over a Hohmann transfer, but require a transit time of 17 days. As an impractical extreme example, an apogee of 1757r0=11,770,000 km would result in a 2% Δv saving over a Hohmann transfer, for comparison, the Hohmann transfer requires 15 hours and 34 minutes. Δv applied prograde Δv applied retrograde Evidently, the bi-elliptic orbit spends more of its delta-v early on and this yields a higher contribution to the specific orbital energy and, due to the Oberth effect, is responsible for the net reduction in required delta-v. Delta-v budget Oberth effect