Las Cruces, New Mexico
Las Cruces is the seat of Doña Ana County, New Mexico, United States. As of the 2010 census the population was 97,618, in 2017 the estimated population was 101,712, making it the second largest city in the state, after Albuquerque. Las Cruces is the largest city in southern New Mexico; the Las Cruces metropolitan area had an estimated population of 213,849 in 2017. It is the principal city of a metropolitan statistical area which encompasses all of Doña Ana County and is part of the larger El Paso–Las Cruces combined statistical area. Las Cruces is the economic and geographic center of the Mesilla Valley, the agricultural region on the floodplain of the Rio Grande which extends from Hatch to the west side of El Paso, Texas. Las Cruces is the home of New Mexico's only land-grant university; the city's major employer is the federal government on nearby White Sands Test Facility and White Sands Missile Range. The Organ Mountains, 10 miles to the east, are dominant in the city's landscape, along with the Doña Ana Mountains, Robledo Mountains, Picacho Peak.
Las Cruces lies 225 miles south of Albuquerque, 48 miles northwest of El Paso, Texas and 46 miles north of the Mexican border at Santa Teresa. Spaceport America, which has corporate offices in Las Cruces, operates from 55 miles to the north, has completed several successful manned, suborbital flights; the city is the headquarters for Virgin Galactic, the world's first company to offer sub-orbital spaceflights. The area where Las Cruces rose was inhabited by the Manso people, with the Mescalero Apache living nearby; the area was colonized by the Spanish beginning in 1598, when Juan de Oñate claimed all territory north of the Rio Grande for New Spain and became the first governor of the Spanish territory of New Mexico. The area remained under New Spain's control until September 28, 1821, when the first Mexican Empire claimed ownership; the area was claimed by the Republic of Texas during this time until the end of the Mexican–American War in 1846–48. The Treaty of Guadalupe Hidalgo in 1848 established the United States as owner of this territory, Las Cruces was founded in 1849 when the US Army laid out the town plans.
Mesilla became the leading settlement of the area, with more than 2,000 residents in 1860, more than twice what Las Cruces had. When the Atchison and Santa Fe Railway reached the area, the landowners of Mesilla refused to sell it the rights-of-way, instead residents of Las Cruces donated the rights-of-way and land for a depot in Las Cruces; the first train reached Las Cruces in 1881. Las Cruces was not affected as by the train as some other villages, as it was not a terminus or a crossroads, but the population did grow to 2,300 in the 1880s. Las Cruces was incorporated as a town in 1907. Pat Garrett is best known for his involvement in the Lincoln County War, but he worked in Las Cruces on a famous case, the disappearance of Albert Jennings Fountain in 1896. New Mexico State University was founded in 1888, it has grown as Las Cruces has grown. Growth of Las Cruces has been attributed to the university, government jobs, recent retirees; the establishment of White Sands Missile Range in 1944 and White Sands Test Facility in 1963 has been integral to population growth.
Las Cruces is the nearest city to each, they provide Las Cruces' work force many high-paying, government jobs. In recent years, the influx of retirees from out of state has increased Las Cruces' population. In the 1960s Las Cruces undertook a large urban renewal project, intended to convert the old downtown into a modern city center; as part of this, St. Genevieve's Catholic Church, built in 1859, was razed to make way for a downtown pedestrian mall; the original covered walkways are now being removed in favor of a more traditional main street thoroughfare. The exact origin of the city's name is unknown. In the 18th century, a party consisting of a priest, colonel, captain, 4 trappers and 4 choir boys were attacked at the nearby Rio Grande. Multiple crosses were erected in their honor, providing for the name of El Pueblo del Jardin de Las Cruces, which evolved and shortened to Las Cruces. A group of about 40 travelers coming along the Camino Real de Tierra Adentro died nearby, resulting in a similar group of crosses.
Crosses on a hillside marking the graves of bandits echo an old tale of the valley of "Los Hermanos". The name may be a mistranslation of the Spanish for "crossing" or "crossroads", as cruce, the singular form of "crossroad", is masculine and the phrase would be Los Cruces; the Las Cruces Bowling Alley Massacre occurred in Las Cruces on February 10, 1990. The approximate elevation of Las Cruces is 3,908 feet above sea level. According to the United States Census Bureau, the city has a total area of 76.6 square miles, of which 76.5 square miles is land and 0.2 square miles, or 0.18%, is water. Las Cruces is the center of the Organ Caldera, its major eruption was 32 Ma. Doña Ana County lies within the Chihuahuan Desert ecoregion, the vegetation surrounding the built portions of the city are typical of this setting; the Rio Grande bisects the Mesilla Valley and passes west of Las Cruces proper, supplying irrigation water for the intensive agriculture surrounding the city. However, the Rio Grande fills its b
Colorado Springs, Colorado
Colorado Springs is a home rule municipality, the largest city by area in Colorado as well as the county seat and the most populous municipality of El Paso County, United States. Colorado Springs is located in the east central portion of the state, it is situated on Fountain Creek and is located 60 miles south of the Colorado State Capitol in Denver. At 6,035 feet the city stands over 1 mile above sea level, though some areas of the city are higher and lower. Colorado Springs is situated near the base of Pikes Peak, which rises 14,115 feet above sea level on the eastern edge of the Southern Rocky Mountains; the city is home to 24 national governing bodies of sport, including the United States Olympic Committee, the United States Olympic Training Center, USA Hockey. The city had an estimated population of 465,101 in 2016, a metro population of 712,000, ranking as the second most populous city in the state of Colorado, behind Denver, the 42nd most populous city in the United States; the Colorado Springs, CO Metropolitan Statistical Area had an estimated population of 712,327 in 2016.
The city is included in the Front Range Urban Corridor, an oblong region of urban population along the Front Range of the Rocky Mountains in Colorado and Wyoming following the path of Interstate 25 in both states. The city covers 194.9 square miles. In 2018, Colorado Springs received several accolades: U. S. News named Colorado Springs the number one most desirable place to live in the United States, number two on their list of the 125 Best Places to Live in the USA; the Metropolitan Policy Program at Brookings found that Colorado Springs was the fastest growing city for Millennials. Thumbtack's annual Small Business Friendliness Survey found Colorado Springs to be the number four most business friendly city in the country; the Ute and Cheyenne peoples were the first recorded inhabiting the area which would become Colorado Springs. Part of the territory included in the United States' 1803 Louisiana Purchase, the current city area was designated part of the 1854 Kansas Territory. In 1859, after the first local settlement was established, it became part of the Jefferson Territory on October 24 and of El Paso County on November 28.
Colorado City at the Front Range confluence of Fountain and Camp creeks was "formally organized on August 13, 1859" during the Pike's Peak Gold Rush. It served as the capital of the Colorado Territory from November 5, 1861, until August 14, 1862, when the capital was moved to Denver. In 1871 the Colorado Springs Company laid out the towns of La Font and Fountain Colony and downstream of Colorado City. Within a year, Fountain Colony would be renamed "Colorado Springs", was incorporated; the El Paso County seat shifted from Colorado City in 1873 to the Town of Colorado Springs. On December 1, 1880, Colorado Springs expanded northward with two annexations; the second period of annexations was during 1889–90, included Seavey's Addition, West Colorado Springs, East End, another North End addition. In 1891 the Broadmoor Land Company built the Broadmoor suburb, which included the Broadmoor Casino, by December 12, 1895, the city had "four Mining Exchanges and 275 mining brokers." By 1898, the city was designated into quadrants by the north-south Cascade Avenue and the east-west Washington/Pike's Peak avenues.
From 1899 to 1901 Tesla Experimental Station operated on Knob Hill, aircraft flights to the Broadmoor's neighboring fields began in 1919. Alexander Airport north of the city opened in 1925, in 1927 the original Colorado Springs Municipal Airport land was purchased east of the city. In World War II the United States Army Air Forces leased land adjacent to the municipal airfield, naming it "Peterson Field" in December 1942; this was only one of several military presences around Colorado Springs during the war. In November 1950, Ent Air Force Base was selected as the Cold War headquarters for Air Defense Command; the former WWII Army Air Base, Peterson Field, inactivated at the end of the war, was re-opened in 1951 as a U. S. Air Force base; the 1950s through 1970s saw a continued expansion of the military presence in the area, with the establishment of NORAD's headquarters in the city, as well as the ADCOM headquarters. Between 1965 and 1968, the University of Colorado Colorado Springs, Pikes Peak Community College and Colorado Technical University were established in or near the city.
In 1977 most of the former Ent AFB became a US Olympic training center. The Libertarian Party was founded within the city in the 1970s. On October 1, 1981, the Broadmoor Addition, Cheyenne Canon, Ivywild and Stratton Meadows were annexed after the Colorado Supreme Court "overturned a district court decision that voided the annexation". Further annexations expanding the city include the Nielson Addition and Vineyard Commerce Park Annexation in September 2008; the city lies in a high desert with the Southern Rocky Mountains to the west, the Palmer Divide to the north, high plains further east, high desert lands to the south when leaving Fountain and approaching Pueblo. According to the United States Census Bureau, the city has a total area of 194.6 square miles, of which 194.6 square miles is land and 0.35 square miles, or 0.19%, is water. Colorado Springs has many features of a modern urban area, such as parks, bike trails, urban open-area spaces. However, it is not exempt from problems that plague cities that experience tremendous growth, such as overcrowded roads and highways, crime and government budget issues.
Many of the problems are indirec
In astronomy, a light curve is a graph of light intensity of a celestial object or region, as a function of time. The light is in a particular frequency interval or band. Light curves can be periodic, as in the case of eclipsing binaries, Cepheid variables, other periodic variables, transiting extrasolar planets, or aperiodic, like the light curve of a nova, a cataclysmic variable star, a supernova or a microlensing event or binary as observed during occultation events; the study of the light curve, together with other observations, can yield considerable information about the physical process that produces it or constrain the physical theories about it. Graphs of the apparent magnitude of a variable star over time are used to visualise and analyse their behaviour. Although the categorisation of variable star types is done from their spectral properties, the amplitudes and regularity of their brightness changes are still important factors; some types such as Cepheids have regular light curves with the same period and shape in each cycle.
Others such as Mira variables have somewhat less regular light curves with large amplitudes of several magnitudes, while the semiregular variables are less regular still and have smaller amplitudes. The shapes of variable star light curves give valuable information about the underlying physical processes producing the brightness changes. For eclipsing variables, the shape of the light curve indicates the degree of totality, the relative sizes of the stars, their relative surface brightnesses, it may show the eccentricity of the orbit and distortions in the shape of the two stars. For pulsating stars, the amplitude or period of the pulsations can be related to the luminosity of the star, the light curve shape can be an indicator of the pulsation mode. Light curves from supernovae can be indicative of the type of supernova. Although supernova types are defined on the basis of their spectra, each has typical light curve shapes. Type I supernovae have light curves with a sharp maximum and decline, while Type II supernovae have less sharp maxima.
Light curves are helpful for classification of faint supernovae and for the determination of sub-types. For example, the type II-P have similar spectra to the type II-L but are distinguished by a light curve where the decline flattens out for several weeks or months before resuming its fade. In planetary science, a light curve can be used to derive the rotation period of a minor planet, moon, or comet nucleus. From the Earth there is no way to resolve a small object in the Solar System in the most powerful of telescopes, since the apparent angular size of the object is smaller than one pixel in the detector. Thus, astronomers measure the amount of light produced by an object as a function of time; the time separation of peaks in the light curve gives an estimate of the rotational period of the object. The difference between the maximum and minimum brightnesses can be due to the shape of the object, or to bright and dark areas on its surface. For example, an asymmetrical asteroid's light curve has more pronounced peaks, while a more spherical object's light curve will be flatter.
This allows astronomers to infer information about the spin of asteroids. The Asteroid Lightcurve Database of the Collaborative Asteroid Lightcurve Link uses a numeric code to assess the quality of a period solution for minor planet light curves, its quality code parameter "U" ranges from 0 to 3: U = 0 → Result proven incorrect U = 1 → Result based on fragmentary light curve, may be wrong. U = 2 → Result based on less than full coverage. Period may be wrong by ambiguous. U = 3 → Secure result within the precision given. No ambiguity. U = n.a. → Not available. Incomplete or inconclusive result. A trailing plus sign or minus sign is used to indicate a better or worse quality than the unsigned value; the occultation light curve is characterised as binary, where the light from the star is terminated instantaneously, remains constant for the duration, is reinstated instantaneously. The duration is equivalent to the length of a chord across the occulting body. Circumstances where the transitions are not instantaneous are.
When the occulted body is large, e.g. a star like Antares the transitions are gradual. When the occulting body has an atmosphere, e.g. the moon TitanThe observations are recorded using video equipment and the disappearance and reappearance timed using a GPS disciplined Video Time Inserter. Occultation light curves are archived at the VizieR service. Light curve inversion is a mathematical technique used to model the surfaces of rotating objects from their brightness variations; this can be used to image starspots or asteroid surface albedos. Microlensing is a process where small and low-mass astronomical objects cause a brief small increase in the brightness of a more distant object; this is caused by the small relativistic effect as larger gravitational lenses, but allows the detection and analysis of otherwise-invisible stellar and planetary mass objects. The properties of these objects can be inferred from the shape of the lensing light curve. For example, PA-99-N2 is a microlensing event that may have been due to a star in the Andromeda galaxy that has an exoplanet.
The AAVSO online light curve generator can plot light curves for thousands of variable stars The Open Astronomy
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
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 Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process, it is by far the most important source of energy for life on Earth. Its diameter is about 1.39 million kilometers, or 109 times that of Earth, its mass is about 330,000 times that of Earth. It accounts for about 99.86% of the total mass of the Solar System. Three quarters of the Sun's mass consists of hydrogen; the Sun is a G-type main-sequence star based on its spectral class. As such, it is informally and not accurately referred to as a yellow dwarf, it formed 4.6 billion years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into an orbiting disk that became the Solar System; the central mass became so hot and dense that it initiated nuclear fusion in its core. It is thought that all stars form by this process.
The Sun is middle-aged. It fuses about 600 million tons of hydrogen into helium every second, converting 4 million tons of matter into energy every second as a result; this energy, which can take between 10,000 and 170,000 years to escape from its core, is the source of the Sun's light and heat. In about 5 billion years, when hydrogen fusion in its core has diminished to the point at which the Sun is no longer in hydrostatic equilibrium, its core will undergo a marked increase in density and temperature while its outer layers expand to become a red giant, it is calculated that the Sun will become sufficiently large to engulf the current orbits of Mercury and Venus, render Earth uninhabitable. After this, it will shed its outer layers and become a dense type of cooling star known as a white dwarf, no longer produce energy by fusion, but still glow and give off heat from its previous fusion; the enormous effect of the Sun on Earth has been recognized since prehistoric times, the Sun has been regarded by some cultures as a deity.
The synodic rotation of Earth and its orbit around the Sun are the basis of solar calendars, one of, the predominant calendar in use today. The English proper name Sun may be related to south. Cognates to English sun appear in other Germanic languages, including Old Frisian sunne, Old Saxon sunna, Middle Dutch sonne, modern Dutch zon, Old High German sunna, modern German Sonne, Old Norse sunna, Gothic sunnō. All Germanic terms for the Sun stem from Proto-Germanic *sunnōn; the Latin name for the Sun, Sol, is not used in everyday English. Sol is used by planetary astronomers to refer to the duration of a solar day on another planet, such as Mars; the related word solar is the usual adjectival term used for the Sun, in terms such as solar day, solar eclipse, Solar System. A mean Earth solar day is 24 hours, whereas a mean Martian'sol' is 24 hours, 39 minutes, 35.244 seconds. The English weekday name Sunday stems from Old English and is a result of a Germanic interpretation of Latin dies solis, itself a translation of the Greek ἡμέρα ἡλίου.
The Sun is a G-type main-sequence star. The Sun has an absolute magnitude of +4.83, estimated to be brighter than about 85% of the stars in the Milky Way, most of which are red dwarfs. The Sun is heavy-element-rich, star; the formation of the Sun may have been triggered by shockwaves from more nearby supernovae. This is suggested by a high abundance of heavy elements in the Solar System, such as gold and uranium, relative to the abundances of these elements in so-called Population II, heavy-element-poor, stars; the heavy elements could most plausibly have been produced by endothermic nuclear reactions during a supernova, or by transmutation through neutron absorption within a massive second-generation star. The Sun is by far the brightest object in the Earth's sky, with an apparent magnitude of −26.74. This is about 13 billion times brighter than the next brightest star, which has an apparent magnitude of −1.46. The mean distance of the Sun's center to Earth's center is 1 astronomical unit, though the distance varies as Earth moves from perihelion in January to aphelion in July.
At this average distance, light travels from the Sun's horizon to Earth's horizon in about 8 minutes and 19 seconds, while light from the closest points of the Sun and Earth takes about two seconds less. The energy of this sunlight supports all life on Earth by photosynthesis, drives Earth's climate and weather; the Sun does not have a definite boundary, but its density decreases exponentially with increasing height above the photosphere. For the purpose of measurement, the Sun's radius is considered to be the distance from its center to the edge of the photosphere, the apparent visible surface of the Sun. By this measure, the Sun is a near-perfect sphere with an oblateness estimated at about 9 millionths, which means that its polar diameter differs from its equatorial diameter by only 10 kilometres; the tidal effect of the planets is weak and does not affect the shape of the Sun. The Sun rotates faster at its equator than at its poles; this differential rotation is caused by convective motion
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