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

8.
Delta-v
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It is a scalar that has the units of speed. As used in context, it is not the same as the physical change in velocity of the vehicle. For multiple maneuvers, delta-v sums linearly, for interplanetary missions delta-v is often plotted on a porkchop plot which displays the required mission delta-v as a function of launch date. Δ v = ∫ t 0 t 1 | T | m d t where T is the instantaneous thrust at time, M is the instantaneous mass at time, t. In the absence of forces, Δ v = ∫ t 0 t 1 | v ˙ | d t where v ˙ is the coordinate acceleration. When thrust is applied in a constant direction this simplifies to, orbit maneuvers are made by firing a thruster to produce a reaction force acting on the spacecraft. e. If for example 20% of the mass is fuel giving a constant v exh of 2100 m/s the capacity of the reaction control system is Δ v =2100 ln m/s =460 m/s. But for many purposes, typically for studies or for maneuver optimization, like this one can for example use a patched conics approach modeling the maneuver as a shift from one Kepler orbit to another by an instantaneous change of the velocity vector. This approximation with impulsive maneuvers is in most cases very accurate, for low thrust systems, typically electrical propulsion systems, this approximation is less accurate. But even for geostationary spacecraft using electrical propulsion for out-of-plane control with thruster burn periods extending over several hours around the nodes this approximation is fair, delta-v is typically provided by the thrust of a rocket engine, but can be created by other engines. The time-rate of change of delta-v is the magnitude of the caused by the engines. The actual acceleration vector would be found by adding thrust per mass on to the gravity vector, the total delta-v needed is a good starting point for early design decisions since consideration of the added complexities are deferred to later times in the design process. The rocket equation shows that the amount of propellant dramatically increases with increasing delta-v. Which is just the rocket equation applied to the sum of the two maneuvers and this is convenient since it means that delta-v’s can be calculated and simply added and the mass ratio calculated only for the overall vehicle for the entire mission. Thus delta-v is commonly quoted rather than mass ratios which would require multiplication, when designing a trajectory, delta-v budget is used as a good indicator of how much propellant will be required. Propellant usage is a function of delta-v in accordance with the rocket equation. For example, most spacecraft are launched in an orbit with inclination fairly near to the latitude at the launch site, for examples of calculating delta-v, see Hohmann transfer orbit, gravitational slingshot, and Interplanetary Transport Network. It is also notable that large thrust can reduce gravity drag, delta-v is also required to keep satellites in orbit and is expended in propulsive orbital stationkeeping maneuvers

9.
Delta-v budget
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In astrodynamics and aerospace, a delta-v budget is an estimate of the total delta-v required for a space mission. Delta-v is a scalar quantity dependent only on the desired trajectory, for example, although more fuel is needed to transfer a heavier communication satellite from low Earth orbit to geosynchronous orbit than for a lighter one, the delta-v required is the same. Also delta-v is additive, as contrasted to rocket burn time, tables of the delta-v required to move between different space venues are useful in the conceptual planning of space missions. In the absence of an atmosphere, the delta-v is typically the same for changes in orbit in either direction, in particular, an atmosphere can be used to slow a spacecraft by aerobraking. The simplest delta-v budget can be calculated with Hohmann transfer, which moves from one orbit to another coplanar circular orbit via an elliptical transfer orbit. In some cases a bi-elliptic transfer can give a lower delta-v. A more complex transfer occurs when the orbits are not coplanar, in that case there is an additional delta-v necessary to change the plane of the orbit. The velocity of the vehicle needs substantial burns at the intersection of the two planes and the delta-v is usually extremely high. However, these changes can be almost free in some cases if the gravity. In other cases, boosting up to a high altitude apoapsis gives low speed before performing the plane change. Another effect is the Oberth effect—this can be used to decrease the delta-v needed. A less used effect is low energy transfers and these are highly nonlinear effects that work by orbital resonances and by choosing trajectories close to Lagrange points. They can be slow, but use very little delta-v. Because delta-v depends on the position and motion of bodies, particularly when using the slingshot effect and Oberth effect. These can be plotted on a porkchop plot, course corrections usually also require some propellant budget. Propulsion systems never provide precisely the right propulsion in precisely the direction at all times. Some propellant needs to be reserved to correct variations from the optimum trajectory, the delta-v requirements for sub-orbital spaceflight are much lower than for orbital spaceflight. For the Ansari X Prize altitude of 100 km, Space Ship One required a delta-v of roughly 1.4 km/s, to reach low Earth orbit of the space station of 300 km, the delta-v is over six times higher about 9.4 km/s. Because of the nature of the rocket equation the orbital rocket needs to be considerably bigger

10.
Escape velocity
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The escape velocity from Earth is about 11.186 km/s at the surface. More generally, escape velocity is the speed at which the sum of a kinetic energy. With escape velocity in a direction pointing away from the ground of a massive body, once escape velocity is achieved, no further impulse need be applied for it to continue in its escape. When given a speed V greater than the speed v e. In these equations atmospheric friction is not taken into account, escape velocity is only required to send a ballistic object on a trajectory that will allow the object to escape the gravity well of the mass M. The existence of escape velocity is a consequence of conservation of energy, by adding speed to the object it expands the possible places that can be reached until with enough energy they become infinite. For a given gravitational potential energy at a position, the escape velocity is the minimum speed an object without propulsion needs to be able to escape from the gravity. Escape velocity is actually a speed because it does not specify a direction, no matter what the direction of travel is, the simplest way of deriving the formula for escape velocity is to use conservation of energy. Imagine that a spaceship of mass m is at a distance r from the center of mass of the planet and its initial speed is equal to its escape velocity, v e. At its final state, it will be a distance away from the planet. The same result is obtained by a calculation, in which case the variable r represents the radial coordinate or reduced circumference of the Schwarzschild metric. All speeds and velocities measured with respect to the field, additionally, the escape velocity at a point in space is equal to the speed that an object would have if it started at rest from an infinite distance and was pulled by gravity to that point. In common usage, the point is on the surface of a planet or moon. On the surface of the Earth, the velocity is about 11.2 km/s. However, at 9,000 km altitude in space, it is less than 7.1 km/s. The escape velocity is independent of the mass of the escaping object and it does not matter if the mass is 1 kg or 1,000 kg, what differs is the amount of energy required. For an object of mass m the energy required to escape the Earths gravitational field is GMm / r, a related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by the mass. An object has reached escape velocity when the orbital energy is greater or equal to zero

11.
Flight dynamics (spacecraft)
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Spacecraft flight dynamics is the science of space vehicle performance, stability, and control. Dynamics is the modeling of the position and orientation of a vehicle. For a spacecraft, these forces are of three types, propulsive force, gravitational force exerted by the Earth or other celestial bodies, the vehicles attitude must be taken into account because of its effect on the aerodynamic and propulsive forces. There are other reasons, unrelated to flight dynamics, for controlling the attitude in non-powered flight. The principles of flight dynamics are used to control a spacecraft by means of an inertial navigation system in conjunction with an attitude control system. Together, they create a subsystem of the bus often called ADCS. Solving for a, acceleration equals the sum divided by mass. Acceleration is integrated over time to get velocity, and velocity is in turn integrated to get position, for preliminary studies, some simplifying assumptions can be made with reasonably small loss of accuracy. The general case of a launch from Earth must take engine thrust, aerodynamic forces, the acceleration equation can be reduced from vector to scalar form by resolving it into tangential and angular components. For most launch vehicles, relatively small levels of lift are generated, in the gravity turn, pitch-over is initiated by applying an increasing angle of attack, followed by a gradual decrease in angle of attack through the remainder of the flight. A powered descent analysis would use the procedure, with reverse boundary conditions. Attitude control is the exercise of control over the orientation of an object with respect to a frame of reference or another entity. The attitude of a craft can be described using three mutually perpendicular axes of rotation, generally referred to as roll, pitch, and yaw angles respectively. Orientation is a quantity described by three angles for the instantaneous direction, and the instantaneous rates of roll in all three axes of rotation. The three principal moments of inertia Ix, Iy, and Iz about the roll, pitch, attitude control torque, absent aerodynamic forces, is frequently applied by a reaction control system, a set of thrusters located about the vehicle. Orbital mechanics are used to calculate flight in orbit about a central body and this can be shown to result in the trajectory being ideally a conic section with the central body located at one focus. Orbital trajectories are either circles or ellipses, the parabolic trajectory represents first escape of the vehicle from the central bodys gravitational field, hyperbolic trajectories are escape trajectories with excess velocity, and will be covered under Interplanetary flight below. Elliptical orbits are characterized by three elements, the argument of periapsis ω, measured in the orbital plane counter-clockwise looking southward, from the ascending node to the periapsis

12.
Frozen orbit
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In orbital mechanics, a frozen orbit is an orbit for an artificial satellite in which natural drifting due to the central bodys shape has been minimized by careful selection of the orbital parameters. This results in a stable orbit that minimizes the use of stationkeeping propellant. For many spacecraft, changes to orbits are caused by the oblateness of the Earth, gravitational attraction from the Sun and Moon, solar radiation pressure and they must be counteracted by maneuvers to keep the spacecraft in the desired orbit. For a geostationary spacecraft, correction maneuvers on the order of 40–50 m/s per year are required to counteract these forces, for Sun-synchronous spacecraft, intentional shifting of the orbit plane can be used for the benefit of the mission. For these missions, an orbit with an altitude of 600–900 km is used. An appropriate inclination is selected so that the precession of the plane is equal to the rate of movement of the Earth around the Sun - or about 1 degree per day. As a result, the spacecraft will pass over points on the Earth that have the time of day during every orbit. For instance, if the orbit is square to the Sun, the vehicle will always pass over points at which it is 6 a. m. on the north-bound portion and this is called a Dawn-Dusk orbit. Alternatively, if the plane is perpendicular to the Sun, the vehicle will always pass over Earth noon on the north-bound leg. Such orbits are desirable for many Earth observation missions such as weather, imagery, perturbing forces caused by the oblateness of the Earth will also change the shape of the orbit. To compensate, there are near-circular orbits where there are no secular/long periodic perturbations of the eccentricity, such an orbit is called a frozen orbit. These orbits are often the choice for Earth observation missions where repeated observations under constant conditions are desirable. The Earth observation satellites ERS-1, ERS-2 and Envisat are operated in Sun-synchronous frozen orbits, similarly the quadratic terms of the eccentricity vector components in can be ignored for almost circular orbits, i. e. The latter figure means that the eccentricity vector will have described a circle in 1569 orbits. In this way the secular perturbation of the eccentricity vector caused by the J2 term is used to counteract all secular perturbations, applying this algorithm for the case discussed above, i. e. e. Including also the forces due to the higher zonal terms the value changes to. With the modern theory this explicit closed form expression is not directly used and these directions r ^ and λ ^ are illustrated in Figure 1. e. Towards the blue point of Figure 2

13.
Geostationary orbit
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A geostationary orbit, geostationary Earth orbit or geosynchronous equatorial orbit is a circular orbit 35,786 kilometres above the Earths equator and following the direction of the Earths rotation. An object in such an orbit has a period equal to the Earths rotational period and thus appears motionless, at a fixed position in the sky. Using this characteristic, ocean color satellites with visible and near-infrared light sensors can also be operated in geostationary orbit in order to monitor sensitive changes of ocean environments, the notion of a geostationary space station equipped with radio communication was published in 1928 by Herman Potočnik. The first appearance of an orbit in popular literature was in the first Venus Equilateral story by George O. Smith. Clarke acknowledged the connection in his introduction to The Complete Venus Equilateral, the orbit, which Clarke first described as useful for broadcast and relay communications satellites, is sometimes called the Clarke Orbit. Similarly, the Clarke Belt is the part of space about 35,786 km above sea level, in the plane of the equator, the Clarke Orbit is about 265,000 km in circumference. Most commercial communications satellites, broadcast satellites and SBAS satellites operate in geostationary orbits, a geostationary transfer orbit is used to move a satellite from low Earth orbit into a geostationary orbit. The first satellite placed into an orbit was the Syncom-3. A worldwide network of operational geostationary meteorological satellites is used to provide visible and infrared images of Earths surface, a geostationary orbit can only be achieved at an altitude very close to 35,786 km and directly above the equator. This equates to a velocity of 3.07 km/s and an orbital period of 1,436 minutes. This ensures that the satellite will match the Earths rotational period and has a footprint on the ground. All geostationary satellites have to be located on this ring. 85° per year, to correct for this orbital perturbation, regular orbital stationkeeping manoeuvres are necessary, amounting to a delta-v of approximately 50 m/s per year. A second effect to be taken into account is the longitude drift, there are two stable and two unstable equilibrium points. Any geostationary object placed between the points would be slowly accelerated towards the stable equilibrium position, causing a periodic longitude variation. The correction of this effect requires station-keeping maneuvers with a maximal delta-v of about 2 m/s per year, solar wind and radiation pressure also exert small forces on satellites, over time, these cause them to slowly drift away from their prescribed orbits. In the absence of servicing missions from the Earth or a renewable propulsion method, hall-effect thrusters, which are currently in use, have the potential to prolong the service life of a satellite by providing high-efficiency electric propulsion. This delay presents problems for latency-sensitive applications such as voice communication, geostationary satellites are directly overhead at the equator and become lower in the sky the further north or south one travels. At latitudes above about 81°, geostationary satellites are below the horizon, because of this, some Russian communication satellites have used elliptical Molniya and Tundra orbits, which have excellent visibility at high latitudes

14.
Gravity assist
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Gravity assistance can be used to accelerate a spacecraft, that is, to increase or decrease its speed or redirect its path. The assist is provided by the motion of the body as it pulls on the spacecraft. It was used by interplanetary probes from Mariner 10 onwards, including the two Voyager probes notable flybys of Jupiter and Saturn, a gravity assist around a planet changes a spacecrafts velocity by entering and leaving the gravitational field of a planet. The spacecrafts speed increases as it approaches the planet and decreases while escaping its gravitational pull, because the planet orbits the sun, the spacecraft is affected by this motion during the maneuver. To increase speed, the flies with the movement of the planet, to decrease speed. The sum of the energies of both bodies remains constant. A slingshot maneuver can therefore be used to change the spaceships trajectory, a close terrestrial analogy is provided by a tennis ball bouncing off the front of a moving train. Imagine standing on a platform, and throwing a ball at 30 km/h toward a train approaching at 50 km/h. The driver of the sees the ball approaching at 80 km/h. Because of the motion, however, that departure is at 130 km/h relative to the train platform. Translating this analogy into space, in the reference frame. After the slingshot occurs and the leaves the planet, it will still have a velocity of v. In the Sun reference frame, the planet has a velocity of v, and by using the Pythagorean Theorem. After the spaceship leaves the planet, it will have a velocity of v + v = 2v and this example is also one of many trajectories and gained speeds the spaceship can have. The linear momentum gained by the spaceship is equal in magnitude to that lost by the planet, so the spacecraft gains velocity, however, the planets enormous mass compared to the spacecraft makes the resulting change in its speed negligibly small. These effects on the planet are so slight that they can be ignored in the calculation, realistic portrayals of encounters in space require the consideration of three dimensions. The same principles apply, only adding the planets velocity to that of the spacecraft requires vector addition, due to the reversibility of orbits, gravitational slingshots can also be used to reduce the speed of a spacecraft. Both Mariner 10 and MESSENGER performed this maneuver to reach Mercury, if even more speed is needed than available from gravity assist alone, the most economical way to utilize a rocket burn is to do it near the periapsis

15.
Gravity drag
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In astrodynamics and rocketry, gravity drag is a measure of the loss in the net performance of a rocket while it is thrusting in a gravitational field. In other words, it is the cost of having to hold the rocket up in a gravity field, gravity losses depend on the time over which thrust is applied as well the direction the thrust is applied in. Gravity losses as a proportion of delta-v are minimised if maximum thrust is applied for a short time, or if thrust is applied in a direction perpendicular to the local gravitational field. During the launch and ascent phase, however, thrust must be applied over a period with a major component of thrust in the opposite direction to gravity. For example, to reach a speed of 7.8 km/s in low Earth orbit requires a delta-v of between 9 and 10 km/s, the additional 1.5 to 2 km/s delta-v is due to gravity losses and atmospheric drag. Consider the simplified case of a vehicle with constant mass accelerating vertically with a constant thrust per unit mass a in a field of strength g. The actual acceleration of the craft is a-g and it is using delta-v at a rate of a per unit time, over a time t the change in speed of the spacecraft is t, whereas the delta-v expended is at. The gravity drag is the difference between these figures, which is gt, as a proportion of delta-v, the gravity drag is g/a. A very large thrust over a short time will achieve a desired speed increase with little gravity drag. Efficiency drops drastically with increasing time spent thrusting against gravity, therefore, it is advisable to minimize the burn time. These effects apply whenever climbing to an orbit with higher specific orbital energy, thrust is a vector quantity, and the direction of the thrust has a large impact on the size of gravity losses. For instance, gravity drag on a rocket of mass m would reduce a 3mg thrust directed upward to an acceleration of 2g and its important to note that minimising gravity losses is not the only objective of a launching spacecraft. Rather, the objective is achieve the position/velocity combination for the desired orbit, for instance, the way to maximize acceleration is to thrust straight downward, however, thrusting downward is clearly not a viable course of action for a rocket intending to reach orbit. These facts sometimes inspire ideas to launch rockets from high flying airplanes, to minimize atmospheric drag. Delta-v budget Oberth effect Turner, Martin J. L. Rocket and Spacecraft Propulsion, Principles, Practice and New Developments, Springer, general Theory of Optimal Trajectory for Rocket Flight in a Resisting Medium

16.
Ground track
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A ground track or ground trace is the path on the surface of the Earth directly below an aircraft or satellite. In the case of a satellite, it is the projection of the orbit onto the surface of the Earth. A satellite ground track may be thought of as a path along the Earths surface which traces the movement of a line between the satellite and the center of the Earth. In other words, the track is the set of points at which the satellite will pass directly overhead, or cross the zenith. In air navigation, ground tracks typically approximate an arc of a great circle, in order to follow a specified ground track, a pilot must adjust their heading in order to compensate for the effect of wind. Aircraft routes are planned to avoid restricted airspace and dangerous areas, typically, satellites have a roughly sinusoidal ground track. A satellite with an inclination between 90° and 180° is said to be in a retrograde orbit. A satellite in an orbit with an orbital period less than one day will tend to move from west to east along its ground track. This is called apparent direct motion, a satellite in a direct orbit with an orbital period greater than one day will tend to move from east to west along its ground track, in what is called apparent retrograde motion. This effect occurs because the satellite orbits more slowly than the speed at which the Earth rotates beneath it, any satellite in a true retrograde orbit will always move from east to west along its ground track, regardless of the length of its orbital period. Because a satellite in an orbit moves faster near perigee and slower near apogee, it is possible for a satellite to track eastward during part of its orbit. This phenomenon allows for ground tracks which cross over themselves, as in the geosynchronous, a satellite whose orbital period is an integer fraction of a day will follow roughly the same ground track every day. This ground track is shifted east or west depending on the longitude of the ascending node, which can vary over time due to perturbations of the orbit. If the period of the satellite is slightly longer than a fraction of a day, the ground track will shift west over time, if it is slightly shorter. For orbital periods longer than the Earths rotational period, an increase in orbital period corresponds to a stretching out of the ground track. A satellite whose orbital period is equal to the period of the Earth is said to be in a geosynchronous orbit. Its ground track will have a figure eight shape over a location on the Earth. It will track eastward when it is on the part of its orbit closest to perigee, a special case of the geosynchronous orbit, the geostationary orbit, has an eccentrity of zero, and an inclination of zero in the Earth-Centered, Earth-Fixed coordinate system

17.
Heliocentric orbit
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A heliocentric orbit is an orbit around the barycenter of the Solar System, which is usually located within or very near the surface of the Sun. All planets, comets, and asteroids in the Solar System are in such orbits, the moons of planets in the Solar System, by contrast, are not in heliocentric orbits as they orbit their respective planet. A similar phenomenon allows the detection of exoplanets by way of the radial velocity method, the helio- prefix is derived from the Greek word helios, meaning sun, and also Helios, the personification of the Sun in Greek mythology. The first spacecraft to be put in an orbit is Luna 1. A trans-Mars injection is an orbit in which a propulsive maneuver is used to set a spacecraft on a trajectory, also known as Mars transfer orbit. Every two years, low-energy transfer windows open up which allow movement between planets with the lowest possible delta-v requirements, transfer injections can place spacecraft into either a Hohmann transfer orbit or bi-elliptic transfer orbit. Trans-Mars injections can be either a single maneuver burn, such as used by the NASA MAVEN orbiter, or a series of perigee kicks. Earths orbit Geocentric orbit Heliocentrism Astrodynamics Low-energy transfer List of artificial objects in heliocentric orbit List of orbits

18.
Hohmann transfer orbit
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In orbital mechanics, the Hohmann transfer orbit /ˈhoʊ. mʌn/ is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The orbital maneuver to perform the Hohmann transfer uses two engine impulses, one to move a spacecraft onto the orbit and a second to move off it. This maneuver was named after Walter Hohmann, the German scientist who published a description of it in his 1925 book Die Erreichbarkeit der Himmelskörper, Hohmann was influenced in part by the German science fiction author Kurd Lasswitz and his 1897 book Two Planets. The diagram shows a Hohmann transfer orbit to bring a spacecraft from a circular orbit into a higher one. It is one half of an orbit that touches both the lower circular orbit the spacecraft wishes to leave and the higher circular orbit that it wishes to reach. The transfer is initiated by firing the engine in order to accelerate it so that it will follow the elliptical orbit. When the spacecraft has reached its orbit, its orbital speed must be increased again in order to change the elliptic orbit to the larger circular one. The engine is fired again at the lower distance to slow the spacecraft into the lower circular orbit. The Hohmann transfer orbit is based on two instantaneous velocity changes, extra fuel is required to compensate for the fact that the bursts take time, this is minimized by using high thrust engines to minimize the duration of the bursts. Low thrust engines can perform an approximation of a Hohmann transfer orbit and this requires a change in velocity that is up to 141% greater than the two impulse transfer orbit, and takes longer to complete. Typically μ is given in units of m3/s2, as such be sure to use meters not kilometers for r 1 and r 2, the total Δ v is then, Δ v t o t a l = Δ v 1 + Δ v 2. In application to traveling from one body to another it is crucial to start maneuver at the time when the two bodies are properly aligned. In the smaller circular orbit the speed is 7.73 km/s, in the elliptical orbit in between the speed varies from 10.15 km/s at the perigee to 1.61 km/s at the apogee. The Δv for the two burns are thus 10.15 −7.73 =2.42 and 3.07 −1.61 =1.46 km/s, together 3.88 km/s. It is interesting to note that this is greater than the Δv required for an orbit,10.93 −7.73 =3.20 km/s. Applying a Δv at the LEO of only 0.78 km/s more would give the rocket the escape speed, as the example above demonstrates, the Δv required to perform a Hohmann transfer between two circular orbits is not the greatest when the destination radius is infinite. The Δv required is greatest when the radius of the orbit is 15.58 times that of the smaller orbit. This number is the root of x3 − 15x2 − 9x −1 =0

19.
International Berthing and Docking Mechanism
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The International Berthing and Docking Mechanism is the European androgynous low impact docking mechanism that is capable of docking and berthing large and small spacecraft. The development of the IBDM is under ESA contract with QinetiQ Space as prime contractor, the IBDM development was initiated as a joint development programme with NASA JSC. The first application of the IBDM was intended to be the ISS Crew Return Vehicle, in the original Agency to Agency agreement, it was decided to develop an Engineering Development Unit to demonstrate the feasibility of the system and the associated technologies. NASA JSC were responsible for the system and avionics designs and ESA for the mechanical design, however, since the cancellation of the CRV program, the two Agencies have independently progressed with the docking system development. The IBDM is now designed to be compatible with the International Docking System Standard and is compatible with the future ISS International Docking Adapters on the US side of the ISS. The European Space Agency has now started a cooperation with SNC to provide the IBDM for attaching this new vehicle to the ISS in the future, the IBDM provides both docking and berthing capability. The docking mechanism comprises a Soft Capture Mechanism, and a mating system called the Hard Capture System. The IBDM avionics runs in hot redundancy, the SCS utilizes active control using 6 servo-actuated legs from RUAG Space which are coordinated to control the SCS ring in its 6 degrees of freedom. The leg forces are measured to modify the compliance of the SCS ring to facilitate alignment of the platform during capture. A large range of mass properties can be handled. The HCS uses structural hook mechanisms to close the sealed mated interface, QinetiQ Space has developed several generations of latches and hooks to come to the final hook design. SENER will be responsible for the development and qualification of the HCS subsystem. The key feature of IBDM is that it is a computer controlled mechanism having in the following SAFE advantages, Smooth. Low impact berthing means that the SCS mating forces are smaller than the IDSS requirement, autonomous, the IBDM comprises autonomous fast switch-over from primary to redundant lane in case of a single failure and from redundant lane to safe mode in case of two failures. This switch-over is performed at IBDM level and does not require the vehicle avionics to be in the loop, effective, a very high capture success rate, enabled by an agile force-sensing controlled capture mode. As a result, IBDM can cope with the range of initial conditions specified in the IDSS. SAFE, the IBDM comprises a backup or safe mode in which the Steward platform behaves like an electro-magnetic damper, the American company Sierra Nevada Corporation is developing the Dream Chaser, which is a small reusable spacecraft that is selected to transport cargo and/or crew to the ISS. The European Space Agency has started a cooperation with SNC to potentially provide the IBDM for attaching this new vehicle to the ISS in the future, the IBDM will be mounted to the unpressurised cargo module, which will be ejected before reentry

20.
Interplanetary Transport Network
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The Interplanetary Transport Network is a collection of gravitationally determined pathways through the Solar System that require very little energy for an object to follow. The ITN makes particular use of Lagrange points as locations where trajectories through space are redirected using little or no energy and these points have the peculiar property of allowing objects to orbit around them, despite lacking an object to orbit. While they use energy, the transport can take a very long time. The key to discovering the Interplanetary Transport Network was the investigation of the nature of the winding paths near the Earth-Sun. They were first investigated by Jules-Henri Poincaré in the 1890s and he noticed that the paths leading to and from any of those points would almost always settle, for a time, on an orbit about that point. There are in fact a number of paths taking one to the point and away from it. When plotted, they form a tube with the orbit about the Lagrange point at one end, the derivation of these paths traces back to mathematicians Charles C. Hiten, Japans first lunar probe, was moved into orbit using similar insight into the nature of paths between the Earth and the Moon. They referred to it as an Interplanetary Superhighway As it turns out and this makes sense, since the orbit is unstable, which implies one will eventually end up on one of the outbound paths after spending no energy at all. However, with careful calculation, one can pick which outbound path one wants and this turned out to be useful, as many of these paths lead to some interesting points in space, such as the Earths Moon or between the Galilean moons of Jupiter. As a result, for the cost of reaching the Earth–Sun L2 point, but the trip from earth to Mars or other distant location would likely take thousands of years. The transfers are so low-energy that they travel to almost any point in the Solar System possible. On the downside, these transfers are very slow, for trips from earth to other planets, they are not useful for manned or unmanned probes, as the trip would take many generations. The network is also relevant to understanding Solar System dynamics, Comet Shoemaker–Levy 9 followed such a trajectory on its path with Jupiter. In a more recent example, the Chinese spacecraft Change 2 used the ITN to travel from lunar orbit to the Earth-Sun L2 point, then on to fly by the asteroid 4179 Toutatis. In addition to orbits around Lagrange points, the dynamics that arise from the gravitational pull of more than one mass yield interesting trajectories. For example, the gravity environment of the Sun–Earth–Moon system allows spacecraft to travel distances on very little fuel. Launched in 1978, the ISEE-3 spacecraft was sent on a mission to orbit around one of the Lagrange points, the spacecraft was able to maneuver around the Earths neighborhood using little fuel by taking advantage of the unique gravity environment

21.
Mass ratio
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In aerospace engineering, mass ratio is a measure of the efficiency of a rocket. It describes how much more massive the vehicle is with propellant than without, that is, typical multistage rockets have mass ratios in the range from 8 to 20. The Space Shuttle, for example, has a mass ratio around 16 and this equation indicates that a Δv of n times the exhaust velocity requires a mass ratio of e n. For instance, for a vehicle to achieve a Δ v of 2.5 times its exhaust velocity would require a ratio of e 2.5. Rocket fuel Propellant mass fraction Payload fraction Zubrin, Robert, entering Space, Creating a Spacefaring Civilization

22.
Minimum orbit intersection distance
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Minimum orbit intersection distance is a measure used in astronomy to assess potential close approaches and collision risks between astronomical objects. It is defined as the distance between the closest points of the orbits of two bodies. Of greatest interest is the risk of a collision with Earth, Earth MOID is often listed on comet and asteroid databases such as the JPL Small-Body Database. MOID values are defined with respect to other bodies as well, Jupiter MOID, Venus MOID. An object is classified as a hazardous object – that is, posing a possible risk to Earth – if, among other conditions. A low MOID does not mean that a collision is inevitable as the planets frequently perturb the orbit of small bodies. It is also necessary that the two bodies reach that point in their orbits at the time before the smaller body is perturbed into a different orbit with a different MOID value. Two Objects gravitationally locked in orbital resonance may never approach one another, numerical integrations become increasingly divergent as trajectories are projected further forward in time, especially beyond times where the smaller body is repeatedly perturbed by other planets. MOID has the convenience that it is obtained directly from the elements of the body. The only object that has ever been rated at 4 on the Torino Scale and this is not the smallest Earth MOID in the catalogues, many bodies with a small Earth MOID are not classed as PHOs because the objects are less than roughly 140 meters in diameter. Earth MOID values are more practical for asteroids less than 140 meters in diameter as those asteroids are very dim. It is even smaller at the more precise JPL Small Body Database

23.
Nodal precession
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Nodal precession is the precession of the orbital plane of a satellite around the rotation axis of an astronomical body such as Earth. This precession is due to the nature of a spinning body. The following discussion relates to low orbit of artificial satellites which have no describable effect on the motion of the Earth. The nodal precession of more massive, natural satellites such as the Moon is more complex, around a spherical body, an orbital plane would remain fixed in space around the central body. However, most bodies rotate, which causes an equatorial bulge and this bulge creates a gravitational effect that causes orbits to precess around the rotational axis of the central body. The direction of precession is opposite the direction of revolution, for a typical prograde orbit around Earth, the longitude of the ascending node decreases, i. e. node precesses westward. If the orbit is retrograde, this increases the longitude of the ascending node and this nodal progression enables Sun-synchronous orbits to maintain approximately constant angle relative to the Sun. A non-rotating body of planetary scale or larger would be pulled by gravity into a sphere, the centrifugal force deforms the body so that it has an equatorial bulge. Because of the bulge the gravitational force on the satellite is not directly toward the center of the central body, whichever hemisphere the satellite is in it is preferentially pulled slightly toward the equator. This creates a torque on the orbit and this torque does not reduce the inclination, rather, it causes a torque-induced gyroscopic precession, which causes the orbital nodes to drift with time. The rate of precession depends on the inclination of the plane to the equatorial plane. For a satellite in an orbit around Earth, the precession is westward. The apparent motion of the sun is approximately +1° per day, so apparent motion of the sun relative to the plane is about 2. 8° per day. For retrograde orbits ω is negative, so the precession becomes positive, in this case it is possible to make the precession approximately match the apparent motion of the sun, resulting in a sun-synchronous orbit

24.
Orbit phasing
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In astrodynamics, orbit phasing is the adjustment of the time-position of spacecraft along its orbit, usually described as adjusting the orbiting spacecrafts true anomaly. Orbital phasing is primarily used in scenarios where a spacecraft in a given orbit must be moved to a different location within the same orbit. The change in position within the orbit is defined as the phase angle, ϕ. To gain or lose time, the spacecraft must be subjected to a simple two-impulse Hohmann transfer which takes the spacecraft away from. The first impulse to change the orbit is performed at a specific point in the original orbit. The impulse creates a new orbit called the “phasing orbit” and is larger or smaller than the original orbit resulting in a different period time than the original orbit. The difference in time between the original and phasing orbits will be equal to the time converted from the phase angle. When complete, the spacecraft will be in the final position within the original obit. To find some of the orbital parameters, first one must find the required period time of the phasing orbit using the following equation. Total change of velocity required for the maneuver is equal to two times ∆V. Orbit phasing can also be referenced as co-orbital rendezvous like an approach to a space station in a docking maneuver. Orbital maneuver Docking maneuver Hohmann transfer orbit General Curtis, Howard D, sellers, Jerry Jon, Marion, Jerry B. Understanding Space An Introduction to Astronautics, http, //arc. aiaa. org/doi/pdf/10. 2514/2.6921 Minimum-Time Orbital Phasing Maneuvers - AIAA, CD Hall -2003 Phasing Maneuver

25.
Orbit
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In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet about a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating path around a body, to a close approximation, planets and satellites follow elliptical orbits, with the central mass being orbited at a focal point of the ellipse, as described by Keplers laws of planetary motion. For ease of calculation, in most situations orbital motion is adequately approximated by Newtonian Mechanics, historically, the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and it assumed the heavens were fixed apart from the motion of the spheres, and was developed without any understanding of gravity. After the planets motions were accurately measured, theoretical mechanisms such as deferent. Originally geocentric it was modified by Copernicus to place the sun at the centre to help simplify the model, the model was further challenged during the 16th century, as comets were observed traversing the spheres. The basis for the understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. Second, he found that the speed of each planet is not constant, as had previously been thought. Third, Kepler found a relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter,5. 23/11.862, is equal to that for Venus,0. 7233/0.6152. Idealised orbits meeting these rules are known as Kepler orbits, isaac Newton demonstrated that Keplers laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections. Newton showed that, for a pair of bodies, the sizes are in inverse proportion to their masses. Where one body is more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body. Lagrange developed a new approach to Newtonian mechanics emphasizing energy more than force, in a dramatic vindication of classical mechanics, in 1846 le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus. This led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits, in relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions but the differences are measurable. Essentially all the evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy

26.
Orbital maneuver
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In spaceflight, an orbital maneuver is the use of propulsion systems to change the orbit of a spacecraft. For spacecraft far from Earth an orbital maneuver is called a deep-space maneuver, the rest of the flight, especially in a transfer orbit, is called coasting. The applied change in speed of each maneuver is referred to as delta-v, the total delta-v for all and each maneuver is estimated for a mission and is called a delta-v budget. With a good approximation of the delta-v budget designers can estimate the fuel to payload requirements of the using the rocket equation. An impulsive maneuver is the model of a maneuver as an instantaneous change in the spacecrafts velocity as illustrated in figure 1. It is the case of a burn to generate a particular amount of delta-v. Applying a low thrust over a period of time is referred to as a non-impulsive maneuver. Another term is finite burn, where the finite is used to mean non-zero, or practically, again. For a few missions, such as those including a space rendezvous. Calculating a finite burn requires a model of the spacecraft. The most important of details include, mass, center of mass, moment of inertia, thruster positions, thrust vectors, thrust curves, specific impulse, thrust centroid offsets, and fuel consumption. In astronautics, the Oberth effect is where the use of an engine when travelling at high speed generates much more useful energy than one at low speed. Oberth effect occurs because the propellant has more energy and it turns out that the vehicle is able to employ this kinetic energy to generate more mechanical power. It is named after Hermann Oberth, the Austro-Hungarian-born, German physicist and a founder of modern rocketry, since the Oberth maneuver happens in a very limited time, to generate a high impulse the engine necessarily needs to achieve high thrust. Thus the Oberth effect is far less useful for low-thrust engines, gravity assistance can be used to accelerate, decelerate and/or re-direct the path of a spacecraft. The assist is provided by the motion of the body as it pulls on the spacecraft. The technique was first proposed as a mid-course manoeuvre in 1961, orbit insertion is a general term for a maneuver that is more than a small correction. It may be used for a maneuver to change a transfer orbit or an ascent orbit into a stable one, but also to change a stable orbit into a descent, descent orbit insertion

27.
Orbital Mechanics for Engineering Students
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Orbital Mechanics for Engineering Students is an aerospace engineering textbook by Howard D. Curtis, in its third edition as of 2013. The book provides an introduction to orbital mechanics, while assuming an undergraduate-level background in physics, rigid body dynamics, differential equations, the text focuses primarily on orbital mechanics, but also includes material on rigid body dynamics, rocket vehicle dynamics, and attitude control. Control theory and spacecraft systems are less thoroughly covered. The textbook includes exercises at the end of each chapter, and supplemental material is available online, including MATLAB code for orbital mechanics projects

28.
Orbital station-keeping
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In astrodynamics, the orbital maneuvers made by thruster burns that are needed to keep a spacecraft in a particular assigned orbit are called orbital station-keeping. The deviation of Earths gravity field from that of a homogeneous sphere, for spacecraft in low orbits the effects of atmospheric drag must often be compensated for. Solar radiation pressure will in general perturb the eccentricity, see Orbital perturbation analysis, for some missions this must be actively counter-acted with manoeuvres. For geostationary spacecraft the eccentricity must be sufficiently small for a spacecraft to be tracked with a non-steerable antenna. Also for Earth observation spacecraft for which a very repetitive orbit with a ground track is desirable. A large part of compensation can be done by using a frozen orbit design. For a spacecraft in a low orbit the atmospheric drag is sufficiently strong to cause a re-entry before the intended end of mission if orbit raising manoeuvres are not executed from time to time. An example of this is the International Space Station, which has an altitude above Earths surface of between 330 and 410 km. Due to atmospheric drag the space station is constantly losing orbital energy, in order to compensate for this loss, which would eventually lead to a re-entry of the station, it has from time to time been re-boosted to a higher orbit. The chosen orbital altitude is a trade-off between the delta-v needed to counter-act the air drag and the delta-v needed to send payloads, the upper limitation of orbit altitude is due to the constraints imposed by the Soyuz spacecraft. On 25 April 2008, the Automated Transfer Vehicle Jules Verne raised the orbit of the ISS for the first time, thereby proving its ability to replace the Soyuz at this task. For Earth observation spacecraft typically operated in an altitude above the Earth surface of about 700 –800 km the air-drag is very faint and these manoeuvres will be very small, typically in the order of a few mm/s of delta-v. If a frozen orbit design is used very small orbit raising manoeuvres are sufficient to also control the eccentricity vector. To maintain a fixed ground track it is necessary to make out-of-plane manoeuvres to compensate for the inclination change caused by Sun/Moon gravitation. These are executed as thruster burns orthogonal to the orbital plane.85 degrees per year, the delta-v needed to compensate for this perturbation keeping the inclination to the equatorial plane amounts to in the order 45 m/s per year. This part of the GEO station-keeping is called North-South control, the East-West control is the control of the orbital period and the eccentricity vector performed by making thruster burns tangential to the orbit. These burns are then designed to keep the orbital period perfectly synchronous with the Earth rotation, perturbation of the orbital period results from the imperfect rotational symmetry of the Earth relative the North/South axis, sometimes called the ellipticity of the Earth equator. The eccentricity is perturbed by the radiation pressure

29.
Parking orbit
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A parking orbit is a temporary orbit used during the launch of a satellite or other space probe. A launch vehicle boosts into the orbit, then coasts for a while. The alternative to an orbit is direct injection, where the rocket fires continuously until its fuel is exhausted. There are several reasons why a parking orbit may be used, geostationary spacecraft require an orbit in the plane of the equator. Getting there requires a transfer orbit with an apogee directly above the equator. Unless the launch site itself is close to the equator. Instead, the craft is placed with a stage in an inclined parking orbit. When the craft crosses the equator, the stage is fired to raise the spacecrafts apogee to geostationary altitude. Finally, a burn is required to raise the perigee to the same altitude. In order to reach the Moon or a planet at a desired time, using a preliminary parking orbit before final injection can widen this window from seconds or minutes, to several hours. For the Apollo programs manned lunar missions, a parking orbit allowed time for spacecraft checkout while still close to home, use of a parking orbit requires a rocket upper stage to perform the injection burn while under zero g conditions. Often, the upper stage which performs the parking orbit injection is used for the final injection burn. During the parking orbit coast, the propellants will drift away from the bottom of the tank and this must be dealt with through the use of tank diaphragms, or ullage rockets to settle the propellant back to the bottom of the tank. A reaction control system is needed to orient the stage properly for the final burn, cryogenic propellants must be stored in well-insulated tanks, to prevent excessive boiloff during coast. Battery life and other consumables must be sufficient for the duration of the parking coast, the Centaur and Agena families of upper stages were designed for such restarts and have often been used in this manner. The last Agena flew in 1987, but Centaur is still in production, the Briz-M stage often performs the same role for Russian rockets. The Apollo program used parking orbits, for all the mentioned above except those that pertain to geostationary orbits. When the Space Shuttle orbiter launched interplanetary probes such as Galileo, the Ariane 5 does not use parking orbits

30.
Payload fraction
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In aerospace engineering, payload fraction is a common term used to characterize the efficiency of a particular design. Payload fraction is calculated by dividing the weight of the payload by the weight of aircraft. Fuel represents an amount of the overall takeoff weight. For this reason the useful load fraction calculates a similar number, propeller-driven airliners had useful load fractions on the order of 25-35%. Modern jet airliners have considerably higher useful load fractions, on the order of 45-55%, for spacecraft the payload fraction is often less than 1%, while the useful load fraction is perhaps 90%. In this case the useful load fraction is not a useful term, for this reason the related term propellant mass fraction, is used instead. However, if the latter is large, the payload can only be small, note, the above table may incorrectly include the mass of the empty upper stage or stages

31.
Photonic laser thruster
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Because of the recycling of energy, the photonic laser thruster is more energy efficient than other laser-pushed sail concepts. However, in this research Bae discovered that photonic laser thruster was stable against movements of laser mirrors, initial proposed uses include high-precision and high-speed maneuver of small spacecraft, such as formation flying, orbit adjustments, and drag compensation. It can be used for beaming thrust from a heavy tanker vehicle to a more expensive, lightweight mission vehicle. Recently in 2015 under another NASA program, Y. K, Bae Corporation demonstrated a photonic laser thruster with a thrust of 3.5 mN for the first time in history. In this demonstration, the laser power of the photonic laser thruster was greater than 500 kW. The use of light for propulsion has been researched since the beginning of the 20th century, Photon propulsion has been discussed for decades as a propulsion that could enable interstellar flight. In the traditional photonic propulsion, such as laser- or microwave-pushed lightsails, the photonic thruster utilized this approach of recycling the reflected light, but with the addition of an active material amplifying the beam. In August 2015, under another NASA program he demonstrated additional 100-fold improvement, in addition, a small 1U CubeSat satellite was propelled and stopped in simulated zero-gravity. The laser power of the photon beam exceeded 500 kW that is 10 times stronger than typical Directed Energy Laser Weapons. The limitations posed by the equation can be overcome, if the energy source is not carried by the spacecraft. In the Beamed Laser Propulsion concept, the photons are beamed from the source to the spacecraft as coherent light. Robert L. Forward pioneered interstellar propulsion concepts including photon propulsion, specifically, Forward introduced beamed laser propulsion, aiming at the goal of achieving roundtrip manned interstellar travel. However, at speeds, owing to the favorable Doppler-shift energy transfer. Photons transfer their energy to the spacecraft by redshifting upon reflection, thus the higher the spacecraft speed, the higher the efficiency. The figure shows the transfer efficiency from photons to the spacecrafts kinetic energy as a function of β=v/c in photon propulsion. As the spacecraft velocity approaches the light velocity the efficiency of photon propulsion approaches 100%, the lower solid curve in the figure represents the efficiency of conventional photon rocket or sail with photon recycling. The upper solid line represents schematically an example the efficiency of a recycling photon rocket, at low β, the recycling rocket can have a high thrust amplification factor, however as β approaches 1, the amplification factor converges to 1 and the overhead of recycling is unneeded. Therefore, these rockets are projected to bridge the efficiency gap, the simplest recycling scheme is a Herriot cell with multi-bouncing laser beams between two high reflectance mirrors that do not form a resonant optical cavity as illustrated in Figure 4