Jet Propulsion Laboratory
The Jet Propulsion Laboratory is a federally funded research and development center and NASA field center in La Cañada Flintridge, United States, though it is referred to as residing in Pasadena, because it has a Pasadena ZIP Code. Founded in the 1930s, the JPL is owned by NASA and managed by the nearby California Institute of Technology for NASA; the laboratory's primary function is the construction and operation of planetary robotic spacecraft, though it conducts Earth-orbit and astronomy missions. It is responsible for operating NASA's Deep Space Network. Among the laboratory's major active projects are the Mars Science Laboratory mission, the Mars Reconnaissance Orbiter, the Juno spacecraft orbiting Jupiter, the NuSTAR X-ray telescope, the SMAP satellite for earth surface soil moisture monitoring, the Spitzer Space Telescope, it is responsible for managing the JPL Small-Body Database, provides physical data and lists of publications for all known small Solar System bodies. The JPL's Space Flight Operations Facility and Twenty-Five-Foot Space Simulator are designated National Historic Landmarks.
JPL traces its beginnings to 1936 in the Guggenheim Aeronautical Laboratory at the California Institute of Technology when the first set of rocket experiments were carried out in the Arroyo Seco. Caltech graduate students Frank Malina, Qian Xuesen, Weld Arnold, Apollo M. O. Smith, along with Jack Parsons and Edward S. Forman, tested a small, alcohol-fueled motor to gather data for Malina's graduate thesis. Malina's thesis advisor was engineer/aerodynamicist Theodore von Kármán, who arranged for U. S. Army financial support for this "GALCIT Rocket Project" in 1939. In 1941, Parsons, Martin Summerfield, pilot Homer Bushey demonstrated the first jet-assisted takeoff rockets to the Army. In 1943, von Kármán, Malina and Forman established the Aerojet Corporation to manufacture JATO rockets; the project took on the name Jet Propulsion Laboratory in November 1943, formally becoming an Army facility operated under contract by the university. During JPL's Army years, the laboratory developed two deployed weapon systems, the MGM-5 Corporal and MGM-29 Sergeant intermediate-range ballistic missiles.
These missiles were the first US ballistic missiles developed at JPL. It developed a number of other weapons system prototypes, such as the Loki anti-aircraft missile system, the forerunner of the Aerobee sounding rocket. At various times, it carried out rocket testing at the White Sands Proving Ground, Edwards Air Force Base, Goldstone, California. In 1954, JPL teamed up with Wernher von Braun's engineers at the Army Ballistic Missile Agency's Redstone Arsenal in Huntsville, Alabama, to propose orbiting a satellite during the International Geophysical Year; the team lost that proposal to Project Vanguard, instead embarked on a classified project to demonstrate ablative re-entry technology using a Jupiter-C rocket. They carried out three successful sub-orbital flights in 1956 and 1957. Using a spare Juno I, the two organizations launched the United States' first satellite, Explorer 1, on January 31, 1958. JPL was transferred to NASA in December 1958, becoming the agency's primary planetary spacecraft center.
JPL engineers designed and operated Ranger and Surveyor missions to the Moon that prepared the way for Apollo. JPL led the way in interplanetary exploration with the Mariner missions to Venus and Mercury. In 1998, JPL opened the Near-Earth Object Program Office for NASA; as of 2013, it has found 95% of asteroids that are a kilometer or more in diameter that cross Earth's orbit. JPL was early to employ female mathematicians. In the 1940s and 1950s, using mechanical calculators, women in an all-female computations group performed trajectory calculations. In 1961, JPL hired Dana Ulery as the first female engineer to work alongside male engineers as part of the Ranger and Mariner mission tracking teams. JPL has been recognized four times by the Space Foundation: with the Douglas S. Morrow Public Outreach Award, given annually to an individual or organization that has made significant contributions to public awareness of space programs, in 1998; when it was founded, JPL's site was west of a rocky flood-plain – the Arroyo Seco riverbed – above the Devil's Gate dam in the northwestern panhandle of the city of Pasadena.
While the first few buildings were constructed in land bought from the city of Pasadena, subsequent buildings were constructed in neighboring unincorporated land that became part of La Cañada Flintridge. Nowadays, most of the 177 acres of the U. S. federal government-owned NASA property that makes up the JPL campus is located in La Cañada Flintridge. Despite this, JPL still uses a Pasadena address as its official mailing address; the city of La Cañada Flintridge was incorporated in 1976, well after JPL attained international recognition as a Pasadena institution. There has been occasional rivalry between the two cities over the issue of which one should be mentioned in the media as the home of the laboratory. There are 6,000 full-time Caltech employees, a few thousand additional contractors working on any given day. NASA has a resident office at the facility staffed by federal managers who oversee JPL's activities and work for NASA. There are some Caltech graduate students, college student interns and co-op students.
The JPL Education Office serves educators and students by providi
The kilometre, or kilometer is a unit of length in the metric system, equal to one thousand metres. It is now the measurement unit used for expressing distances between geographical places on land in most of the world. K is used in some English-speaking countries as an alternative for the word kilometre in colloquial writing and speech. A slang term for the kilometre in the US and UK military is klick. There are two common pronunciations for the word; the former follows a pattern in English whereby metric units are pronounced with the stress on the first syllable and the pronunciation of the actual base unit does not change irrespective of the prefix. It is preferred by the British Broadcasting Corporation and the Australian Broadcasting Corporation. Many scientists and other users in countries where the metric system is not used, use the pronunciation with stress on the second syllable; the latter pronunciation follows the stress pattern used for the names of measuring instruments. The problem with this reasoning, however, is that the word meter in those usages refers to a measuring device, not a unit of length.
The contrast is more obvious in countries using the British rather than American spelling of the word metre. When Australia introduced the metric system in 1975, the first pronunciation was declared official by the government's Metric Conversion Board. However, the Australian prime minister at the time, Gough Whitlam, insisted that the second pronunciation was the correct one because of the Greek origins of the two parts of the word. By the 8 May 1790 decree, the Constituent assembly ordered the French Academy of Sciences to develop a new measurement system. In August 1793, the French National Convention decreed the metre as the sole length measurement system in the French Republic; the first name of the kilometre was "Millaire". Although the metre was formally defined in 1799, the myriametre was preferred to the "kilometre" for everyday use; the term "myriamètre" appeared a number of times in the text of Develey's book Physique d'Emile: ou, Principes de la science de la nature, while the term kilometre only appeared in an appendix.
French maps published in 1835 had scales showing myriametres and "lieues de Poste". The Dutch gave it the local name of the mijl, it was only in 1867 that the term "kilometer" became the only official unit of measure in the Netherlands to represent 1000 metres. Two German textbooks dated 1842 and 1848 give a snapshot of the use of the kilometre across Europe - the kilometre was in use in the Netherlands and in Italy and the myriametre was in use in France. In 1935, the International Committee for Weights and Measures abolished the prefix "myria-" and with it the "myriametre", leaving the kilometre as the recognised unit of length for measurements of that magnitude. In the United Kingdom, road signs show distances in miles and location marker posts that are used for reference purposes by road engineers and emergency services show distance references in unspecified units which are kilometre-based; the advent of the mobile phone has been instrumental in the British Department for Transport authorising the use of driver location signs to convey the distance reference information of location marker posts to road users should they need to contact the emergency services.
In the US, the National Highway System Designation Act of 1995 prohibits the use of federal-aid highway funds to convert existing signs or purchase new signs with metric units. The Executive Director of the US Federal Highway Administration, Jeffrey Paniati, wrote in a 2008 memo: "Section 205 of the National Highway System Designation Act of 1995 prohibited us from requiring any State DOT to use the metric system during project development activities. Although the State DOT's had the option of using metric measurements or dual units, all of them abandoned metric measurements and reverted to sole use of inch-pound values." The Manual on Uniform Traffic Control Devices since 2000 is published in both metric and American Customary Units. Some sporting disciplines feature 1000 m races in major events, but in other disciplines though world records are catalogued, the one kilometre event remains a minority event; the world records for various sporting disciplines are: Conversion of units, for comparison with other units of length Cubic metre Metric prefix Mileage Odometer Orders of magnitude Square kilometre Media related to Distance indicators at Wikimedia Commons
Odysseus known by the Latin variant Ulysses, is a legendary Greek king of Ithaca and the hero of Homer's epic poem the Odyssey. Odysseus plays a key role in Homer's Iliad and other works in that same epic cycle. Son of Laërtes and Anticlea, husband of Penelope and father of Telemachus and Acusilaus. Odysseus is renowned for his intellectual brilliance and versatility, is thus known by the epithet Odysseus the Cunning, he is most famous for his nostos or “homecoming”, which took him ten eventful years after the decade-long Trojan War. In Greek the name was used in various versions. Vase inscriptions have the two groups of Olyseus, Olysseus or Ōlysseus, Olyteus or Olytteus. From an early source from Magna Graecia dates the form Oulixēs, while a grammarian has Oulixeus. In Latin the figure was known as Ulyssēs; some have supposed that "there may have been two separate figures, one called something like Odysseus, the other something like Ulixes, who were combined into one complex personality." However, the change between d and l is common in some Indo-European and Greek names, the Latin form is supposed to be derived from the Etruscan Uthuze, which accounts for some of the phonetic innovations.
The etymology of the name is unknown. Ancient authors linked the name to the Greek verbs odussomai “to be wroth against, to hate”, to oduromai “to lament, bewail”, or to ollumi “to perish, to be lost”. Homer relates it to various forms of this verb in puns. In Book 19 of the Odyssey, where Odysseus' early childhood is recounted, Euryclea asks the boy's grandfather Autolycus to name him. Euryclea seems to suggest a name like Polyaretos, "for he has much been prayed for" but Autolycus "apparently in a sardonic mood" decided to give the child another name commemorative of "his own experience in life": "Since I have been angered with many, both men and women, let the name of the child be Odysseus". Odysseus receives the patronymic epithet Laertiades, "son of Laërtes". In the Iliad and Odyssey there are several further epithets used to describe Odysseus, it has been suggested that the name is of non-Greek origin not Indo-European, with an unknown etymology. Robert S. P. Beekes has suggested a Pre-Greek origin.
In Etruscan religion the name of Odysseus were adopted under the name Uthuze, interpreted as a parallel borrowing from a preceding Minoan form of the name. Little is given of Odysseus' background other than that according to Pseudo-Apollodorus, his paternal grandfather or step-grandfather is Arcesius, son of Cephalus and grandson of Aeolus, while his maternal grandfather is the thief Autolycus, son of Hermes and Chione. Hence, Odysseus was the great-grandson of the Olympian god Hermes. According to the Iliad and Odyssey, his father is Laertes and his mother Anticlea, although there was a non-Homeric tradition that Sisyphus was his true father; the rumour went. Odysseus is said to have a younger sister, who went to Same to be married and is mentioned by the swineherd Eumaeus, whom she grew up alongside, in book 15 of the Odyssey; the majority of sources for Odysseus' pre-war exploits—principally the mythographers Pseudo-Apollodorus and Hyginus—postdate Homer by many centuries. Two stories in particular are well known: When Helen is abducted, Menelaus calls upon the other suitors to honour their oaths and help him to retrieve her, an attempt that leads to the Trojan War.
Odysseus tries to avoid it by feigning lunacy, as an oracle had prophesied a long-delayed return home for him if he went. He starts sowing his fields with salt. Palamedes, at the behest of Menelaus' brother Agamemnon, seeks to disprove Odysseus' madness and places Telemachus, Odysseus' infant son, in front of the plow. Odysseus veers the plow away from his son. Odysseus holds a grudge against Palamedes during the war for dragging him away from his home. Odysseus and other envoys of Agamemnon travel to Scyros to recruit Achilles because of a prophecy that Troy could not be taken without him. By most accounts, Achilles' mother, disguises the youth as a woman to hide him from the recruiters because an oracle had predicted that Achilles would either live a long uneventful life or achieve everlasting glory while dying young. Odysseus cleverly discovers which among the women before him is Achilles when the youth is the only one of them to show interest in examining the weapons hidden among an array of adornment gifts for the daughters of their host.
Odysseus arranges further for the sounding of a battle horn, which prompts Achilles to clutch a weapon and show his trained disposition. With his disguise foiled, he joins Agamemnon's call to arms among the Hellenes. Odysseus is one of the most influential Greek champions during the Trojan War. Along with Nestor and Idomeneus he is one of advisors, he always champions the Achaean cause when others question Agamemnon's command
An asteroid family is a population of asteroids that share similar proper orbital elements, such as semimajor axis and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions. An asteroid family is a more specific term than asteroid group whose members, while sharing some broad orbital characteristics, may be otherwise unrelated to each other. Large prominent families contain several hundred recognized asteroids. Small, compact families may have only about ten identified members. About 33% to 35% of asteroids in the main belt are family members. There are about 20 to 30 reliably recognized families, with several tens of less certain groupings. Most asteroid families are found in the main asteroid belt, although several family-like groups such as the Pallas family, Hungaria family, the Phocaea family lie at smaller semi-major axis or larger inclination than the main belt. One family has been identified associated with the dwarf planet Haumea; some studies have tried to find evidence of collisional families among the trojan asteroids, but at present the evidence is inconclusive.
The families are thought to form as a result of collisions between asteroids. In many or most cases the parent body was shattered, but there are several families which resulted from a large cratering event which did not disrupt the parent body; such cratering families consist of a single large body and a swarm of asteroids that are much smaller. Some families have complex internal structures which are not satisfactorily explained at the moment, but may be due to several collisions in the same region at different times. Due to the method of origin, all the members have matching compositions for most families. Notable exceptions are those families. Asteroid families are thought to have lifetimes of the order of a billion years, depending on various factors; this is shorter than the Solar System's age, so few if any are relics of the early Solar System. Decay of families occurs both because of slow dissipation of the orbits due to perturbations from Jupiter or other large bodies, because of collisions between asteroids which grind them down to small bodies.
Such small asteroids become subject to perturbations such as the Yarkovsky effect that can push them towards orbital resonances with Jupiter over time. Once there, they are rapidly ejected from the asteroid belt. Tentative age estimates have been obtained for some families, ranging from hundreds of millions of years to less than several million years as for the compact Karin family. Old families are thought to contain few small members, this is the basis of the age determinations, it is supposed that many old families have lost all the smaller and medium-sized members, leaving only a few of the largest intact. A suggested example of such old family remains are 113 Amalthea pair. Further evidence for a large number of past families comes from analysis of chemical ratios in iron meteorites; these show that there must have once been at least 50 to 100 parent bodies large enough to be differentiated, that have since been shattered to expose their cores and produce the actual meteorites. When the orbital elements of main belt asteroids are plotted, a number of distinct concentrations are seen against the rather uniform distribution of non-family background asteroids.
These concentrations are the asteroid families. Interlopers are asteroids classified as family members based on their so-called proper orbital elements but having spectroscopic properties distinct from the bulk of the family, suggesting that they, contrary to the true family members, did not originate from the same parent body that once fragmented upon a collisional impact. Speaking and their membership are identified by analysing the proper orbital elements rather than the current osculating orbital elements, which fluctuate on timescales of tens of thousands of years; the proper elements are related constants of motion that remain constant for times of at least tens of millions of years, longer. The Japanese astronomer Kiyotsugu Hirayama pioneered the estimation of proper elements for asteroids, first identified several of the most prominent families in 1918. In his honor, asteroid families are sometimes called Hirayama families; this applies to the five prominent groupings discovered by him.
Present day computer-assisted searches have identified more than a hundred asteroid families. The most prominent algorithms have been the hierarchical clustering method, which looks for groupings with small nearest-neighbour distances in orbital element space, wavelet analysis, which builds a density-of-asteroids map in orbital element space, looks for density peaks; the boundaries of the families are somewhat vague because at the edges they blend into the background density of asteroids in the main belt. For this reason the number of members among discovered asteroids is only known and membership is uncertain for asteroids near the edges. Additionally, some interlopers from the heterogeneous background asteroid population are expected in the central regions of a family. Since the true family members caused by the collision are expected to have similar compositions, most such interlopers can in principle be recognised by spectral properties which do not matc
A minor-planet moon is an astronomical object that orbits a minor planet as its natural satellite. As of February 2019, there are 352 minor planets suspected to have moons. Discoveries of minor-planet moons are important because the determination of their orbits provides estimates on the mass and density of the primary, allowing insights of their physical properties, not otherwise possible; the first modern era mention of the possibility of an asteroid satellite was in connection with an occultation of the bright star Gamma Ceti by the asteroid 6 Hebe in 1977. The observer, amateur astronomer Paul D. Maley, detected an unmistakable 0.5 second disappearance of this naked eye star from a site near Victoria, Texas. Many hours several observations were reported in Mexico attributed to the occultation by 6 Hebe itself. Although not confirmed, this documents the first formally documented case of a suspected companion of an asteroid. In addition to the terms satellite and moon, the term "binary" is sometimes used for minor planets with moons, "triple" for minor planets with two moons.
If one object is much bigger it can be referred to as the primary and its companion as secondary. The term double asteroid is sometimes used for systems in which the asteroid and its moon are the same size, while binary tends to be used independently from the relative sizes of the components; when binary minor planets are similar in size, the Minor Planet Center refers to them as "binary companions" instead of referring to the smaller body as a satellite. A good example of a true binary is the 90 Antiope system, identified in August 2000. Small satellites are referred to as moonlets. Prior to the era of the Hubble Space Telescope and space probes reaching the outer Solar System, attempts to detect satellites around asteroids were limited to optical observations from Earth. For example, in 1978, stellar occultation observations were claimed as evidence of a satellite for the asteroid 532 Herculina; however more-detailed imaging by the Hubble Telescope did not reveal a satellite, the current consensus is that Herculina does not have a significant satellite.
There were other similar reports of asteroids having companions in the following years. A letter in Sky & Telescope magazine at this time pointed to simultaneous impact craters on Earth, suggesting that these craters were caused by pairs of gravitationally bound objects. In 1993, the first asteroid moon was confirmed when the Galileo probe discovered the small Dactyl orbiting 243 Ida in the asteroid belt; the second was discovered around 45 Eugenia in 1998. In 2001, 617 Patroclus and its same-sized companion Menoetius became the first known binary asteroids in the Jupiter trojans; the first trans-Neptunian binary after Pluto–Charon, 1998 WW31, was optically resolved in 2002. Triple or trinary minor planets, are known since 2005, when the asteroid 87 Sylvia was discovered to have two satellites, making it the first known triple system; this was followed by the discovery of a second moon orbiting 45 Eugenia. In 2005, the dwarf planet Haumea was discovered to have two moons, making it the second trans-Neptunian object after Pluto known to have more than one moon.
Additionally, 216 Kleopatra and 93 Minerva were discovered to be trinary asteroids in 2008 and 2009 respectively. Since the first few triple minor planets were discovered, more continue to be discovered at a rate of about one a year. Most discovered were two moons orbiting large near-earth asteroid 3122 Florence, bringing the number of known trinary systems in the Solar System up to 14; the following table lists all satellites of triple systems chronologically by their discovery date, starting with Charon, discovered in 1978. The data about the populations of binary objects are still patchy. In addition to the inevitable observational bias the frequency appears to be different among different categories of objects. Among asteroids, an estimated 2% would have satellites. Among trans-Neptunian objects, an estimated 11% are thought to be binary or multiple objects, the majority of the large TNOs have at least one satellite, including all four IAU-listed dwarf planets. More than 50 binaries are known in each of the main groupings: near-Earth asteroids, belt asteroids, trans-Neptunian objects, not including numerous claims based on light-curve variation.
Two binaries have been found so far among centaurs with semi-major axes smaller than Neptune. Both are double ring systems around 2060 Chiron and 10199 Chariklo, discovered in 1994–2011 and 2013 respectively; the origin of minor-planet moons is not known with certainty, a variety of theories exist. A accepted theory is that minor-planet moons are formed from debris knocked off of the primary by an impact. Other pairings may be formed. Formation by collision is constrained by the angular momentum of the components, i.e. by the masses and their separation. Close binaries fit this model. Distant binaries however, with components of comparable size, are unlikely to have followed this scenario, unless considerable mass has been lost in the event; the distances of the components for the known binaries vary from a few hundreds of kilometres to more than 3000 km for the asteroids. Among TNOs, the known separations vary from 3,000 to 50,000 km. What is "typical" for a binary system tends to depend on its location in the Solar System (presumably because of different modes
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 a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, greater than 1 is a hyperbola; the term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is used for the isolated two-body problem, but extensions exist for objects following a Klemperer 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. The eccentricity may take the following values: circular orbit: e = 0 elliptic orbit: 0 < e < 1 parabolic trajectory: e = 1 hyperbolic trajectory: e > 1 The eccentricity e is given by e = 1 + 2 E L 2 m red α 2 where E is the total orbital energy, L is the angular momentum, mred is the reduced mass, α the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics: F = α r 2 or in the case of a gravitational force: e = 1 + 2 ε h 2 μ 2 where ε is the specific orbital energy, μ the standard gravitational parameter based on the total mass, h the specific relative angular momentum.
For values of e from 0 to 1 the orbit's shape is an elongated ellipse. 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 hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, one must calculate the inverse sine to find the projection angle of 11.86 degrees. Next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity; the word "eccentricity" comes from Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros "out of the center", from ἐκ- ek-, "out of" + κέντρον kentron "center".
"Eccentric" first appeared in English in 1551, with the definition "a circle in which the earth, sun. Etc. deviates from its center". By five years in 1556, an adjectival form of the word had developed; the eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector: e = | e | where: e is the eccentricity vector. For elliptical orbits it can 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: ra is the radius at apoapsis. Rp is the radius at periapsis; the eccentricity of an elliptical orbit can be used to obtain the ratio of the periapsis to the apoapsis: r p r a = 1 − e 1 + e For Earth, orbital eccentricity ≈ 0.0167, apoapsis= aphelion and periapsis= perihelion relative to sun. For Earth's annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈ 1.034 relative to center point of path. The eccentricity of the Earth's orbit is about 0.0167.
The term apsis refers to an extreme point in the orbit of an object. It denotes either the respective distance of the bodies; the word comes via Latin from Greek, there denoting a whole orbit, is cognate with apse. Except for the theoretical possibility of one common circular orbit for two bodies of equal mass at diametral positions, there are two apsides for any elliptic orbit, named with the prefixes peri- and ap-/apo-, added in reference to the body being orbited. All periodic orbits are, according to Newton's Laws of motion, ellipses: either the two individual ellipses of both bodies, with the center of mass of this two-body system at the one common focus of the ellipses, or the orbital ellipses, with one body taken as fixed at one focus, the other body orbiting this focus. All these ellipses share a straight line, the line of apsides, that contains their major axes, the foci, the vertices, thus the periapsis and the apoapsis; the major axis of the orbital ellipse is the distance of the apsides, when taken as points on the orbit, or their sum, when taken as distances.
The major axes of the individual ellipses around the barycenter the contributions to the major axis of the orbital ellipses are inverse proportional to the masses of the bodies, i.e. a bigger mass implies a smaller axis/contribution. Only when one mass is sufficiently larger than the other, the individual ellipse of the smaller body around the barycenter comprises the individual ellipse of the larger body as shown in the second figure. For remarkable asymmetry, the barycenter of the two bodies may lie well within the bigger body, e.g. the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If the smaller mass is negligible compared to the larger the orbital parameters are independent of the smaller mass. For general orbits, the terms periapsis and apoapsis are used. Pericenter and apocenter are equivalent alternatives, referring explicitly to the respective points on the orbits, whereas periapsis and apoapsis may refer to the smallest and largest distances of the orbiter and its host.
For a body orbiting the Sun, the point of least distance is the perihelion, the point of greatest distance is the aphelion. The terms become apastron when discussing orbits around other stars. For any satellite of Earth, including the Moon, the point of least distance is the perigee and greatest distance the apogee, from Ancient Greek Γῆ, "land" or "earth". For objects in lunar orbit, the point of least distance is sometimes called the pericynthion and the greatest distance the apocynthion. Perilune and apolune are used. In orbital mechanics, the apsides technically refer to the distance measured between the barycenters of the central body and orbiting body. However, in the case of a spacecraft, the terms are used to refer to the orbital altitude of the spacecraft above the surface of the central body; these formulae characterize the pericenter and apocenter of an orbit: Pericenter Maximum speed, v per = μ a, at minimum distance, r per = a. Apocenter Minimum speed, v ap = μ a, at maximum distance, r ap = a.
While, in accordance with Kepler's laws of planetary motion and the conservation of energy, these two quantities are constant for a given orbit: Specific relative angular momentum h = μ a Specific orbital energy ε = − μ 2 a where: a is the semi-major axis: a = r per + r ap 2 μ is the standard gravitational parameter e is the eccentricity, defined as e = r ap − r per r ap + r per = 1 − 2 r ap r per + 1 Note t