1.
Orbit
–
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

2.
Apsis
–
An apsis is an extreme point in an objects orbit. The word comes via Latin from Greek and is cognate with apse, for elliptic orbits about a larger body, there are two apsides, named with the prefixes peri- and ap-, or apo- added to a reference to the thing being orbited. For a body orbiting the Sun, the point of least distance is the perihelion, the terms become periastron and apastron when discussing orbits around other stars. For any satellite of Earth including the Moon the point of least distance is the perigee, for objects in Lunar orbit, the point of least distance is the pericynthion and the greatest distance the apocynthion. For any orbits around a center of mass, there are the terms pericenter and apocenter, periapsis and apoapsis are equivalent alternatives. A straight line connecting the pericenter and apocenter is the line of apsides and this is the major axis of the ellipse, its greatest diameter. For a two-body system the center of mass of the lies on this line at one of the two foci of the ellipse. When one body is larger than the other it may be taken to be at this focus. Historically, in systems, apsides were measured from the center of the Earth. In orbital mechanics, the apsis technically refers to the distance measured between the centers of mass of the central and orbiting body. However, in the case of spacecraft, the family of terms are used to refer to the orbital altitude of the spacecraft from the surface of the central body. The arithmetic mean of the two limiting distances is the length of the axis a. The geometric mean of the two distances is the length of the semi-minor axis b, the geometric mean of the two limiting speeds is −2 ε = μ a which is the speed of a body in a circular orbit whose radius is a. The words pericenter and apocenter are often seen, although periapsis/apoapsis are preferred in technical usage, various related terms are used for other celestial objects. The -gee, -helion and -astron and -galacticon forms are used in the astronomical literature when referring to the Earth, Sun, stars. The suffix -jove is occasionally used for Jupiter, while -saturnium has very rarely used in the last 50 years for Saturn. The -gee form is used as a generic closest approach to planet term instead of specifically applying to the Earth. During the Apollo program, the terms pericynthion and apocynthion were used when referring to the Moon, regarding black holes, the term peri/apomelasma was used by physicist Geoffrey A. Landis in 1998 before peri/aponigricon appeared in the scientific literature in 2002

3.
Lagrangian point
–
The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centrifugal force required to orbit with them. There are five points, labeled L1 to L5, all in the orbital plane of the two large bodies. The first three are on the line connecting the two bodies, the last two, L4 and L5, each form an equilateral triangle with the two large bodies. The two latter points are stable, which implies that objects can orbit around them in a coordinate system tied to the two large bodies. Several planets have satellites near their L4 and L5 points with respect to the Sun, the three collinear Lagrange points were discovered by Leonhard Euler a few years before Lagrange discovered the remaining two. In 1772, Joseph-Louis Lagrange published an Essay on the three-body problem, in the first chapter he considered the general three-body problem. From that, in the chapter, he demonstrated two special constant-pattern solutions, the collinear and the equilateral, for any three masses, with circular orbits. The five Lagrangian points are labeled and defined as follows, The L1 point lies on the line defined by the two large masses M1 and M2, and between them. It is the most intuitively understood of the Lagrangian points, the one where the attraction of M2 partially cancels M1s gravitational attraction. Explanation An object that orbits the Sun more closely than Earth would normally have an orbital period than Earth. If the object is directly between Earth and the Sun, then Earths gravity counteracts some of the Suns pull on the object, the closer to Earth the object is, the greater this effect is. At the L1 point, the period of the object becomes exactly equal to Earths orbital period. L1 is about 1.5 million kilometers from Earth, the L2 point lies on the line through the two large masses, beyond the smaller of the two. Here, the forces of the two large masses balance the centrifugal effect on a body at L2. Explanation On the opposite side of Earth from the Sun, the period of an object would normally be greater than that of Earth. The extra pull of Earths gravity decreases the orbital period of the object, like L1, L2 is about 1.5 million kilometers from Earth. The L3 point lies on the line defined by the two masses, beyond the larger of the two. Explanation L3 in the Sun–Earth system exists on the side of the Sun

4.
Geosynchronous orbit
–
A geosynchronous orbit is an orbit about the Earth of a satellite with an orbital period that matches the rotation of the Earth on its axis of approximately 23 hours 56 minutes and 4 seconds. Over the course of a day, the position in the sky traces out a path, typically in a figure-8 form, whose precise characteristics depend on the orbits inclination. Satellites are typically launched in an eastward direction, a special case of geosynchronous orbit is the geostationary orbit, which is a circular geosynchronous orbit at zero inclination. A satellite in a geostationary orbit appears stationary, always at the point in the sky. Popularly or loosely, the term geosynchronous may be used to mean geostationary, specifically, geosynchronous Earth orbit may be a synonym for geosynchronous equatorial orbit, or geostationary Earth orbit. A semi-synchronous orbit has a period of ½ sidereal day. Relative to the Earths surface it has twice this period, examples include the Molniya orbit and the orbits of the satellites in the Global Positioning System. Circular Earth geosynchronous orbits have a radius of 42,164 km, all Earth geosynchronous orbits, whether circular or elliptical, have the same semi-major axis.4418 km3/s2. In the special case of an orbit, the ground track of a satellite is a single point on the equator. A geostationary equatorial orbit is a geosynchronous orbit in the plane of the Earths equator with a radius of approximately 42,164 km. A satellite in such an orbit is at an altitude of approximately 35,786 km above sea level. It maintains the position relative to the Earths surface. The theoretical basis for this phenomenon of the sky goes back to Newtons theory of motion. In that theory, the existence of a satellite is made possible because the Earth rotates. Such orbits are useful for telecommunications satellites, a perfectly stable geostationary orbit is an ideal that can only be approximated. Elliptical geosynchronous orbits can be and are designed for satellites in order to keep the satellite within view of its assigned ground stations or receivers. A satellite in a geosynchronous orbit appears to oscillate in the sky from the viewpoint of a ground station. Satellites in highly elliptical orbits must be tracked by ground stations

5.
Earth's orbit
–
Earths orbit is the path through which the Earth travels around the Sun. The average distance between the Earth and the Sun is 149.60 million kilometers, and a complete orbit occurs every 365.256 days, Earths orbit has an eccentricity of 0.0167. Earths orbital motion gives an apparent movement of the Sun with respect to other stars at a rate of about 1° per day eastward as seen from Earth. Earths orbital speed averages about 30 km/s, which is fast enough to cover the planets diameter in seven minutes, viewed from a vantage point above the north poles of both the Sun and the Earth, the Earth would appear to revolve in a counterclockwise direction about the Sun. From the same point, both the Earth and the Sun would appear to rotate in a counterclockwise direction about their respective axes. Heliocentrism is the model that first placed the Sun at the center of the Solar System and put the planets, including Earth. Historically, heliocentrism is opposed to geocentrism, which placed the Earth at the center, aristarchus of Samos already proposed a heliocentric model in the 3rd century BC. This Copernican revolution resolved the issue of planetary motion by arguing that such motion was only perceived. Although Copernicuss groundbreaking book. had been over a century earlier, because of Earths axial tilt, the inclination of the Suns trajectory in the sky varies over the course of the year. For an observer at a northern latitude, when the pole is tilted toward the Sun the day lasts longer. This results in average temperatures, as additional solar radiation reaches the surface. When the north pole is tilted away from the Sun, the reverse is true, above the Arctic Circle and below the Antarctic Circle, an extreme case is reached in which there is no daylight at all for part of the year. This is called a polar night and this variation in the weather results in the seasons. The solstices and equinoxes divide the year up into four equal parts. In the northern winter solstice occurs on or about December 21, summer solstice is near June 21, spring equinox is around March 20. In modern times, Earths perihelion occurs around January 3, the changing Earth–Sun distance results in an increase of about 6. 9% in total solar energy reaching the Earth at perihelion relative to aphelion. The Hill sphere of the Earth is about 1,500,000 kilometers in radius and this is the maximal distance at which the Earths gravitational influence is stronger than the more distant Sun and planets. Objects orbiting the Earth must be within this radius, otherwise they can become unbound by the perturbation of the Sun

6.
Horseshoe orbit
–
A horseshoe orbit is a type of co-orbital motion of a small orbiting body relative to a larger orbiting body. The orbital period of the body is very nearly the same as for the larger body. The loop is not closed but will drift forward or backward slightly each time, when the object approaches the larger body closely at either end of its trajectory, its apparent direction changes. Over an entire cycle the center traces the outline of a horseshoe, asteroids in horseshoe orbits with respect to Earth include 54509 YORP,2002 AA29,2010 SO16,2015 SO2 and possibly 2001 GO2. A broader definition includes 3753 Cruithne, which can be said to be in a compound and/or transition orbit, saturns moons Epimetheus and Janus occupy horseshoe orbits with respect to each other. The following explanation relates to an asteroid which is in such an orbit around the Sun, the asteroid is in almost the same solar orbit as Earth. Both take approximately one year to orbit the Sun and it is also necessary to grasp two rules of orbit dynamics, A body closer to the Sun completes an orbit more quickly than a body further away. If a body accelerates along its orbit, its orbit moves outwards from the Sun, if it decelerates, the orbital radius decreases. The horseshoe orbit arises because the attraction of the Earth changes the shape of the elliptical orbit of the asteroid. The shape changes are small but result in significant changes relative to the Earth. The horseshoe becomes apparent only when mapping the movement of the relative to both the Sun and the Earth. The asteroid always orbits the Sun in the same direction, however, it goes through a cycle of catching up with the Earth and falling behind, so that its movement relative to both the Sun and the Earth traces a shape like the outline of a horseshoe. Starting at point A, on the ring between L5 and Earth, the satellite is orbiting faster than the Earth and is on its way toward passing between the Earth and the Sun. But Earths gravity exerts an outward accelerating force, pulling the satellite into an orbit which decreases its angular speed. When the satellite gets to point B, it is traveling at the speed as Earth. Earths gravity is still accelerating the satellite along the orbital path, eventually, at Point C, the satellite reaches a high and slow enough orbit such that it starts to lag behind Earth. It then spends the next century or more appearing to drift backwards around the orbit when viewed relative to the Earth and its orbit around the Sun still takes only slightly more than one Earth year. Given enough time, the Earth and the satellite will be on opposite sides of the Sun, eventually the satellite comes around to point D where Earths gravity is now reducing the satellites orbital velocity

7.
Orbit of the Moon
–
Not to be confused with Lunar orbit. The Moon orbits Earth in the direction and completes one revolution relative to the stars in approximately 27.323 days. Earth and the Moon orbit about their barycentre, which lies about 4,600 km from Earths center, on average, the Moon is at a distance of about 385,000 km from Earths centre, which corresponds to about 60 Earth radii. With a mean velocity of 1.022 km/s, the Moon appears to move relative to the stars each hour by an amount roughly equal to its angular diameter. The Moon differs from most satellites of planets in that its orbit is close to the plane of the ecliptic. The plane of the orbit is inclined to the ecliptic by about 5°. The properties of the orbit described in this section are approximations, the Moons orbit around Earth has many irregularities, whose study has a long history. The orbit of the Moon is distinctly elliptical, with an eccentricity of 0.0549. The non-circular form of the lunar orbit causes variations in the Moons angular speed and apparent size as it moves towards, the mean angular movement relative to an imaginary observer at the barycentre is 13. 176° per day to the east. The Moons elongation is its angular distance east of the Sun at any time, at new moon, it is zero and the Moon is said to be in conjunction. At full moon, the elongation is 180° and it is said to be in opposition, in both cases, the Moon is in syzygy, that is, the Sun, Moon and Earth are nearly aligned. When elongation is either 90° or 270°, the Moon is said to be in quadrature, the orientation of the orbit is not fixed in space, but rotates over time. This orbital precession is also called apsidal precession and is the rotation of the Moons orbit within the orbital plane, the Moons apsidal precession is distinct from, and should not be confused with its axial precession. The mean inclination of the orbit to the ecliptic plane is 5. 145°. The rotational axis of the Moon is also not perpendicular to its plane, so the lunar equator is not in the plane of its orbit. Therefore, the angle between the ecliptic and the equator is always 1. 543°, even though the rotational axis of the Moon is not fixed with respect to the stars. The period from moonrise to moonrise at the poles is quite close to the sidereal period, when the sun is the furthest below the horizon, the moon will be full when it is at its highest point. The nodes are points at which the Moons orbit crosses the ecliptic, the Moon crosses the same node every 27.2122 days, an interval called the draconic or draconitic month

8.
Molniya orbit
–
A Molniya orbit is a type of highly elliptical orbit with an inclination of 63.4 degrees, an argument of perigee of −90 degrees and an orbital period of one half of a sidereal day. Molniya orbits are named after a series of Soviet/Russian Molniya communications satellites which have been using this type of orbit since the mid-1960s.4 degrees north, to get a continuous high elevation coverage of the Northern Hemisphere, at least three Molniya spacecraft are needed. The reason that the inclination should have the value 63. 4° is that then the argument of perigee is not perturbed by the J2 term of the field of the Earth. Much of the area of the former Soviet Union, and Russia in particular, is located at high latitudes, to broadcast to these latitudes from a geostationary orbit would require considerable power due to the low elevation angles. A satellite in a Molniya orbit is better suited to communications in these regions because it looks directly down on them, an additional advantage is that considerably less launch energy is needed to place a spacecraft into a Molniya orbit than into a geostationary orbit. It is necessary to have at least three spacecraft if permanent high elevation coverage is needed for an area like the whole of Russia where some parts are as far south as 45° N. If three spacecraft are used, each spacecraft is active for periods of eight hours per orbit centered at apogee as illustrated in figure 9. The Earth completes half a rotation in 12 hours, so the apogees of successive Molniya orbits will alternate between one half of the hemisphere and the other half. For example if the apogee longitudes are 90° E and 90° W, said next spacecraft has the visibility displayed in figure 3 and the switch-over can take place. Note that the two spacecraft at the time of switch-over are separated about 1500 km, so that the stations only have to move the antennas a few degrees to acquire the new spacecraft. To avoid this expenditure of fuel, the Molniya orbit uses an inclination of 63. 4° and that this is the case follows from equation of the article Orbital perturbation analysis as the factor then is zero. The reason why the orbital period shall be half a day is that the geometry relative to the ground stations should repeat every 24 hours. In fact, the precise ideal orbital period resulting in a ground track repeating every 24 hours is not precisely half a sidereal day, but rather half a synodic day. For a Molniya orbit, the inclination is selected such that Δ ω as given by the formula above is zero but Δ Ω, as given by the other equation, will be −0. 0742° per orbit. The rotational period of the Earth relative to the node will therefore be only 86,129 seconds,35 seconds less than the day which is 86,164 seconds. The primary use of the Molniya orbit was for the satellite series of the same name. After two launch failures in 1964, the first successful satellite to use this orbit was Molniya 1-01 launched on April 23,1965. The early Molniya-1 satellites were used for military communications starting in 1968

9.
Geostationary orbit
–
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

10.
Orbital eccentricity
–
The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is an orbit, values between 0 and 1 form an elliptical orbit,1 is a parabolic escape orbit. The term derives its name from the parameters of conic sections and it is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the galaxy. In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit, the eccentricity of this Kepler orbit is a non-negative number that defines its shape. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola, radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits have zero angular momentum and hence eccentricity equal to one, keeping the energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity. From Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros out of the center, from ἐκ- ek-, eccentric first appeared in English in 1551, with the definition a circle in which the earth, sun. Five years later, in 1556, a form of the word was added. The eccentricity of an orbit can be calculated from the state vectors as the magnitude of the eccentricity vector, e = | e | where. For elliptical orbits it can also be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p =1 −2 r a r p +1 where, rp is the radius at periapsis. For Earths annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈1.034 relative to center point of path, the eccentricity of the Earths orbit is currently about 0.0167, the Earths orbit is nearly circular. Venus and Neptune have even lower eccentricity, over hundreds of thousands of years, the eccentricity of the Earths orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets. The table lists the values for all planets and dwarf planets, Mercury has the greatest orbital eccentricity of any planet in the Solar System. Such eccentricity is sufficient for Mercury to receive twice as much solar irradiation at perihelion compared to aphelion, before its demotion from planet status in 2006, Pluto was considered to be the planet with the most eccentric orbit

11.
Tundra orbit
–
A Tundra orbit is a highly elliptical geosynchronous orbit with a high inclination and an orbital period of one sidereal day. A satellite placed in this orbit spends most of its time over an area of the Earth. The ground track of a satellite in an orbit is a closed figure eight. These orbits are similar to Molniya orbits, which have the same inclination. The only current known user of Tundra orbits is the EKS satellite, until 2016, Sirius Satellite Radio, now part of Sirius XM Holdings operated a constellation of three satellites in Tundra orbits for satellite radio. The RAAN and mean anomaly of each satellite was offset by 120° so that when one satellite moved out of position, the three satellites were launched in 2000 and moved into circular disposal orbits in 2016, Sirius XM now broadcasts only from geostationary satellites. Tundra and Molniya orbits are used to high latitude users with higher elevation angles than a geostationary orbit. An argument of perigee of 270° places apogee at the northernmost point of the orbit, an argument of perigee of 90° would likewise serve the high southern latitudes. An argument of perigee of 0° or 180° would cause the satellite to dwell over the equator, the Tundra and Molniya orbits use a sin−1 √4/5 ≈63. 4° inclination to null the secular perturbation of the argument of perigee caused by the Earths equatorial bulge. With any inclination other than 63. 4° or its supplement,116. 6°, the argument of perigee would change steadily over time, and apogee would occur either before or after the highest latitude is reached

12.
Lissajous orbit
–
Lyapunov orbits around a Lagrangian point are curved paths that lie entirely in the plane of the two primary bodies. In contrast, Lissajous orbits include components in this plane and perpendicular to it, halo orbits also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are not. In practice, any orbits around Lagrangian points L1, L2, or L3 are dynamically unstable, as a result, spacecraft in these Lagrangian point orbits must use their propulsion systems to perform orbital station-keeping. These orbits can however be destabilized by other nearby massive objects, several missions have used Lissajous orbits, ACE at Sun–Earth L1, SOHO at Sun-Earth L1, DSCOVR at Sun–Earth L1, WMAP at Sun–Earth L2, and also the Genesis mission collecting solar particles at L1. On 14 May 2009, the European Space Agency launched into space the Herschel and Planck observatories, eSAs current Gaia mission also uses a Lissajous orbit at Sun–Earth L2. In 2011, NASA transferred two of its THEMIS spacecraft from Earth orbit to Lunar orbit by way of Earth-Moon L1 and L2 Lissajous orbits. In the 2005 science fiction novel Sunstorm by Arthur C. Clarke and Stephen Baxter, the shield is described to have been in a Lissajous orbit at L1. In the story a group of wealthy and powerful people shelter opposite the shield at L2 so as to be protected from the storm by the shield, the Earth. Koon, W. S. M. W. Lo, J. E. Marsden, dynamical Systems, the Three-Body Problem, and Space Mission Design