Planets dictionary definition | Planets defined See also astrology ; astronomy ; cosmology ; earth ; mars ; moon . aphelion the point in the orbit of a heavenly body where it is farthest from the sun. See also perihelion. apocynthion apolune. apogee the farthest point in an orbit from the body being orbited. apolune the farthest point from the moon in a lunar orbit, as that of a spacecraft. Also called apocynthion. areography the study of the physical features of the planet Mars. celidography Archaic. a description of the surface markings of the sun or a planet. —celidographer, n. exobiology the branch of biology that studies life beyond the earth’s atmosphere, as on other planets. —exobiologist, n. meridian the highest point a planet or other orbiting heavenly body reaches in its orbit. —meridian, meridional, adj. occultation the process of one heavenly body disappearing behind another as viewed by an observer. pericynthion perilune. perigee the closest point in an orbit to the body being orbited.

perihelion the point in the orbit of a heavenly body where it is nearest the sun. Also called perihelium. See also aphelion. perihelium perihelion. perilune the closest point to the moon in a lunar orbit, as that of a spacecraft. Also called pericynthion. planetarium 1. a representation of the planetary system, particularly one in which the movements of the planets are simulated by projectors. 2. a room or building housing such an apparatus. planetoid Astronomy. any of thousands of small celestial bodies that revolve about the sun in orbits chiefly between those of Mars and Jupiter ranging in diameter from one mile to 480 miles. Also called asteroids, minor planets. —planetoidal, adj. zenography the study and description of Jupiter. —zenographical, adj. planets » more... They'd trained together on one of the Council's neutral planets and ended up rivals in everything. I didn't believe the planets died without the dhjan and his lifemate until I saw what happened to Anshan.

The Council disallowed lasers or other advanced weapons, instead opting for the traditional weapons of their ancestors, and the only weapons some planets with their crude civilizations in the nearby galaxies used. The Brains set up the Planetary Council-- the alien version of the United Nations-- several generations before to mediate between the warring planets within the Five Galaxies. When he's running around destroying planets, I cannot help him. Planets - definition of planets by The Free Dictionary Planets - definition of planets by The Free Dictionary 1. a representation of the planetary system, particularly one in which the movements of the planets are simulated by projectors. 2. a room or building housing such an apparatus. the study and description of Jupiter. — zenographical, adj. planets The eight major bodies, apart from Earth, which move around the Sun: Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. It is an astrological convention to also include the Sun and the Moon when speaking of the planets, making ten astrological planets in all. Translations Want to thank TFD for its existence? Tell a friend about us , add a link to this page, or visit the webmaster's page for free fun content .

Link to this page: epicyclic gear train References in classic literature ? As Queequeg's Ramadan, or Fasting and Humiliation, was to continue all day, I did not choose to disturb him till towards night-fall; for I cherish the greatest respect towards everybody's religious obligations, never mind how comical, and could not find it in my heart to undervalue even a congregation of ants worshipping a toad-stool; or those other creatures in certain parts of our earth, who with a degree of footmanism quite unprecedented in other planets, bow down before the torso of a deceased landed proprietor merely on account of the inordinate possessions yet owned and rented in his name.

View in context Jeremiah, and Billings and Buddha walk together, side by side, right behind a crowd from planets not in our astronomy; next come a dozen or two from Jupiter and other worlds; next come Daniel, and Sakka and Confucius; next a lot from systems outside of ours; next come Ezekiel, and Mahomet, Zoroaster, and a knife-grinder from ancient Egypt; then there is a long string, and after them, away down toward the bottom, come Shakespeare and Homer, and a shoemaker named Marais, from the back settlements of France.

View in context For if, in its perihelion, it should approach within a certain degree of the sun (as by their calculations they have reason to dread) it will receive a degree of heat ten thousand times more intense than that of red hot glowing iron, and in its absence from the sun, carry a blazing tail ten hundred thousand and fourteen miles long, through which, if the earth should pass at the distance of one hundred thousand miles from the nucleus, or main body of the comet, it must in its passage be set on fire, and reduced to ashes: that the sun, daily spending its rays without any nutriment to supply them, will at last be wholly consumed and annihilated; which must be attended with the destruction of this earth, and of all the planets that receive their light from it. Orbit | Article about orbit by The Free Dictionary Orbit | Article about orbit by The Free Dictionary Related to orbit: Priceline orbit, in astronomy, path in space described by a body revolving about a second body where the motion of the orbiting bodies is dominated by their mutual gravitational attraction. Within the solar system, planets, dwarf planets, asteroids, and comets orbit the sun and satellites orbit the planets and other bodies.

Planetary Orbits From earliest times, astronomers assumed that the orbits in which the planets moved were circular; yet the numerous catalogs of measurements compiled especially during the 16th cent. did not fit this theory. At the beginning of the 17th cent., Johannes Kepler stated three laws of planetary motion that explained the observed data: the orbit of each planet is an ellipse with the sun at one focus; the speed of a planet varies in such a way that an imaginary line drawn from the planet to the sun sweeps out equal areas in equal amounts of time; and the ratio of the squares of the periods of revolution of any two planets is equal to the ratio of the cubes of their average distances from the sun. The orbits of the solar planets, while elliptical, are almost circular; on the other hand, the orbits of many of the extrasolar planets discovered during the 1990s are highly elliptical. After the laws of planetary motion were established, astronomers developed the means of determining the size, shape, and relative position in space of a planet's orbit. The size and shape of an orbit are specified by its semimajor axis and by its eccentricity.

The semimajor axis is a length equal to half the greatest diameter of the orbit. The eccentricity is the distance of the sun from the center of the orbit divided by the length of the orbit's semimajor axis; this value is a measure of how elliptical the orbit is. The position of the orbit in space, relative to the earth, is determined by three factors: (1) the inclination inclination, in astronomy, the angle of intersection between two planes, one of which is an orbital plane. The inclination of the plane of the moon's orbit is 5°9' with respect to the plane of the ecliptic (the plane of the earth's orbit around the sun). ..... Click the link for more information. , or tilt, of the plane of the planet's orbit to the plane of the earth's orbit (the ecliptic); (2) the longitude of the planet's ascending node (the point where the planet cuts the ecliptic moving from south to north); and (3) the longitude of the planet's perihelion point (point at which it is nearest the sun; see apsis apsis (pl.

apsides), point in the orbit of a body where the body is neither approaching nor receding from another body about which it revolves. Any elliptical orbit has two apsides. ..... Click the link for more information. ). These quantities, which determine the size, shape, and position of a planet's orbit, are known as the orbital elements. If only the sun influenced the planet in its orbit, then by knowing the orbital elements plus its position at some particular time, one could calculate its position at any later time. However, the gravitational attractions of bodies other than the sun cause perturbations perturbation , in astronomy and physics, small force or other influence that modifies the otherwise simple motion of some object. The term is also used for the effect produced by the perturbation, e.g., a change in the object's energy or path of motion. ..... Click the link for more information. in the planet's motions that can make the orbit shift, or precess, in space or can cause the planet to wobble slightly. Once these perturbations have been calculated one can closely determine its position for any future date over long periods of time.

Modern methods for computing the orbit of a planet or other body have been refined from methods developed by Newton Newton, Sir Isaac, 1642–1727, English mathematician and natural philosopher (physicist), who is considered by many the greatest scientist that ever lived. Early Life and Work ..... Click the link for more information. , Laplace Laplace, Pierre Simon, marquis de , 1749–1827, French astronomer and mathematician. At 18 he went to Paris, proved his gift for mathematical analysis to Jean le Rond d'Alembert, and was made professor of mathematics in the École militaire of Paris. ..... Click the link for more information. , and Gauss Gauss, Carl Friedrich , born Johann Friederich Carl Gauss, 1777–1855, German mathematician, physicist, and astronomer. Gauss was educated at the Caroline College, Brunswick, and the Univ. ..... Click the link for more information. , in which all the needed quantities are acquired from three separate observations of the planet's apparent position.

Nonplanetary Orbits The laws of planetary orbits also apply to the orbits of comets, natural satellites, artificial satellites, and space probes. The orbits of comets are very elongated; some are long ellipses, some are nearly parabolic (see parabola parabola , plane curve consisting of all points equidistant from a given fixed point (focus) and a given fixed line (directrix). It is the conic section cut by a plane parallel to one of the elements of the cone. ..... Click the link for more information. ), and some may be hyperbolic. When the orbit of a newly discovered comet is calculated, it is first assumed to be a parabola and then corrected to its actual shape when more measured positions are obtained. Natural satellites that are close to their primaries tend to have nearly circular orbits in the same plane as that of the planet's equator, while more distant satellites may have quite eccentric orbits with large inclinations to the planet's equatorial plane. Because of the moon's proximity to the earth and its large relative mass, the earth-moon system is sometimes considered a double planet.

It is the center of the earth-moon system, rather than the center of the earth itself, that describes an elliptical orbit around the sun in accordance with Kepler's laws Kepler's laws, three mathematical statements formulated by the German astronomer Johannes Kepler that accurately describe the revolutions of the planets around the sun. Kepler's laws opened the way for the development of celestial mechanics, i.e. ..... Click the link for more information. . All of the planets and most of the satellites in the solar system move in the same direction in their orbits, counterclockwise as viewed from the north celestial pole; some satellites, probably captured asteroids, have retrograde motion retrograde motion, in astronomy, real or apparent movement of a planet, dwarf planet, moon, asteroid, or comet from east to west relative to the fixed stars. The most common direction of motion in the solar system, both for orbital revolution and axial rotation, is from west to ..... Click the link for more information. , i.e., they revolve in a clockwise direction. orbit (or -bit) The path followed by a celestial object or an artificial satellite or spaceprobe that is moving in a gravitational field.

For a single object moving freely in the gravitational field of a massive body the orbit is a conic section , in actuality either elliptical or hyperbolic. Closed (repeated) orbits are elliptical, most planetary orbits being almost circular. A hyperbolic orbit results in the object escaping from the vicinity of a massive body. See also Kepler's laws ; orbital elements . Orbit (religion, spiritualism, and occult) An orbit is the path in space that one heavenly body makes in its movement around another heavenly body. The Moon, for example, makes an orbit around Earth, while Earth and the other planets make orbits around the Sun. The technical name for the orbiting body is satellite. The orbited body is called a primary. Because primaries are also in motion, the orbits described by satellites are elliptical rather than circular. Satellites form stable orbits by counterbalancing two forces—their movement away from the primary and the force of gravity drawing them back toward the primary. In other words, in the absence of gravity a satellite would move in a straight line, which would soon take it away from its primary; in the absence of satellite motion, gravity would draw a satellite and its primary together until they collided. Sources: Robinson, J.

Hedley, and James Muirden. Astronomy Data Book. 2d ed. New York: John Wiley & Sons, 1979. Smoluchowski, Roman. The Solar System: The Sun, Planets, and Life. New York: Scientific American Books, 1983. orbit Orbits | Article about orbits by The Free Dictionary Orbits | Article about orbits by The Free Dictionary Related to orbits: Priceline orbit, in astronomy, path in space described by a body revolving about a second body where the motion of the orbiting bodies is dominated by their mutual gravitational attraction. Within the solar system, planets, dwarf planets, asteroids, and comets orbit the sun and satellites orbit the planets and other bodies. Planetary Orbits From earliest times, astronomers assumed that the orbits in which the planets moved were circular; yet the numerous catalogs of measurements compiled especially during the 16th cent. did not fit this theory.

At the beginning of the 17th cent., Johannes Kepler stated three laws of planetary motion that explained the observed data: the orbit of each planet is an ellipse with the sun at one focus; the speed of a planet varies in such a way that an imaginary line drawn from the planet to the sun sweeps out equal areas in equal amounts of time; and the ratio of the squares of the periods of revolution of any two planets is equal to the ratio of the cubes of their average distances from the sun. The orbits of the solar planets, while elliptical, are almost circular; on the other hand, the orbits of many of the extrasolar planets discovered during the 1990s are highly elliptical. After the laws of planetary motion were established, astronomers developed the means of determining the size, shape, and relative position in space of a planet's orbit. The size and shape of an orbit are specified by its semimajor axis and by its eccentricity. The semimajor axis is a length equal to half the greatest diameter of the orbit. The eccentricity is the distance of the sun from the center of the orbit divided by the length of the orbit's semimajor axis; this value is a measure of how elliptical the orbit is.

The position of the orbit in space, relative to the earth, is determined by three factors: (1) the inclination inclination, in astronomy, the angle of intersection between two planes, one of which is an orbital plane. The inclination of the plane of the moon's orbit is 5°9' with respect to the plane of the ecliptic (the plane of the earth's orbit around the sun). ..... Click the link for more information. , or tilt, of the plane of the planet's orbit to the plane of the earth's orbit (the ecliptic); (2) the longitude of the planet's ascending node (the point where the planet cuts the ecliptic moving from south to north); and (3) the longitude of the planet's perihelion point (point at which it is nearest the sun; see apsis apsis (pl. apsides), point in the orbit of a body where the body is neither approaching nor receding from another body about which it revolves. Any elliptical orbit has two apsides. ..... Click the link for more information. ). These quantities, which determine the size, shape, and position of a planet's orbit, are known as the orbital elements.

If only the sun influenced the planet in its orbit, then by knowing the orbital elements plus its position at some particular time, one could calculate its position at any later time. However, the gravitational attractions of bodies other than the sun cause perturbations perturbation , in astronomy and physics, small force or other influence that modifies the otherwise simple motion of some object. The term is also used for the effect produced by the perturbation, e.g., a change in the object's energy or path of motion. ..... Click the link for more information. in the planet's motions that can make the orbit shift, or precess, in space or can cause the planet to wobble slightly. Once these perturbations have been calculated one can closely determine its position for any future date over long periods of time. Modern methods for computing the orbit of a planet or other body have been refined from methods developed by Newton Newton, Sir Isaac, 1642–1727, English mathematician and natural philosopher (physicist), who is considered by many the greatest scientist that ever lived. Early Life and Work ..... Click the link for more information.

, Laplace Laplace, Pierre Simon, marquis de , 1749–1827, French astronomer and mathematician. At 18 he went to Paris, proved his gift for mathematical analysis to Jean le Rond d'Alembert, and was made professor of mathematics in the École militaire of Paris. ..... Click the link for more information. , and Gauss Gauss, Carl Friedrich , born Johann Friederich Carl Gauss, 1777–1855, German mathematician, physicist, and astronomer. Gauss was educated at the Caroline College, Brunswick, and the Univ. ..... Click the link for more information. , in which all the needed quantities are acquired from three separate observations of the planet's apparent position. Nonplanetary Orbits The laws of planetary orbits also apply to the orbits of comets, natural satellites, artificial satellites, and space probes. The orbits of comets are very elongated; some are long ellipses, some are nearly parabolic (see parabola parabola , plane curve consisting of all points equidistant from a given fixed point (focus) and a given fixed line (directrix).

It is the conic section cut by a plane parallel to one of the elements of the cone. ..... Click the link for more information. ), and some may be hyperbolic. When the orbit of a newly discovered comet is calculated, it is first assumed to be a parabola and then corrected to its actual shape when more measured positions are obtained. Natural satellites that are close to their primaries tend to have nearly circular orbits in the same plane as that of the planet's equator, while more distant satellites may have quite eccentric orbits with large inclinations to the planet's equatorial plane. Because of the moon's proximity to the earth and its large relative mass, the earth-moon system is sometimes considered a double planet. It is the center of the earth-moon system, rather than the center of the earth itself, that describes an elliptical orbit around the sun in accordance with Kepler's laws Kepler's laws, three mathematical statements formulated by the German astronomer Johannes Kepler that accurately describe the revolutions of the planets around the sun. Kepler's laws opened the way for the development of celestial mechanics, i.e. ..... Click the link for more information. .

All of the planets and most of the satellites in the solar system move in the same direction in their orbits, counterclockwise as viewed from the north celestial pole; some satellites, probably captured asteroids, have retrograde motion retrograde motion, in astronomy, real or apparent movement of a planet, dwarf planet, moon, asteroid, or comet from east to west relative to the fixed stars. The most common direction of motion in the solar system, both for orbital revolution and axial rotation, is from west to ..... Click the link for more information. , i.e., they revolve in a clockwise direction. orbit (or -bit) The path followed by a celestial object or an artificial satellite or spaceprobe that is moving in a gravitational field. For a single object moving freely in the gravitational field of a massive body the orbit is a conic section , in actuality either elliptical or hyperbolic. Closed (repeated) orbits are elliptical, most planetary orbits being almost circular. A hyperbolic orbit results in the object escaping from the vicinity of a massive body. See also Kepler's laws ; orbital elements .

Orbit (religion, spiritualism, and occult) An orbit is the path in space that one heavenly body makes in its movement around another heavenly body. The Moon, for example, makes an orbit around Earth, while Earth and the other planets make orbits around the Sun. The technical name for the orbiting body is satellite. The orbited body is called a primary. Because primaries are also in motion, the orbits described by satellites are elliptical rather than circular. Satellites form stable orbits by counterbalancing two forces—their movement away from the primary and the force of gravity drawing them back toward the primary. In other words, in the absence of gravity a satellite would move in a straight line, which would soon take it away from its primary; in the absence of satellite motion, gravity would draw a satellite and its primary together until they collided. Sources: Robinson, J. Hedley, and James Muirden. Astronomy Data Book. 2d ed. New York: John Wiley & Sons, 1979. Smoluchowski, Roman. The Solar System: The Sun, Planets, and Life. New York: Scientific American Books, 1983.

orbit Astronomy Definition, Prefix, Suffix, Ologies and Isms, Astronomy Information and Meaning the branch of astronomy that studies meteors. aerolitics the branch of astronomy that studies aerolites, or stony meteors. albedo the ratio between the light reflected from a surface and the total light falling upon that surface, as the albedo of the moon. aphelion the point in the orbit of a heavenly body where it is farthest from the sun. Cf. perihelion. apolune in an orbit around a moon, the point furthest from the moon. Cf. perilune. areology the astronomical studies of the planet Mars. — areologist, n. — areologic, areological, adj. asterism Rare. a constellation or small group of unrelated stars. — asterismal, adj. astrogation the art of navigating in space. Cf. astronavigation. — astrogator, n. astrogeny, astrogony the theory of the evolution of heavenly bodies. astrogeology a geological specialty that studies celestial bodies. astrognosy the branch of astronomy that studies the fixed stars. astrography a scientific analysis and mapping of the stars and planets.

— astrographic, adj. astrolatry the worship of the heavenly bodies. Also called Sabaism . — astrolater, n. astromancy 1. a form of divination involving studying the stars. 2. Rare. astrology. Also called sideromancy. — astromancer, n. — astromantic, adj. astrometry the branch of astronomy that studies the dimensions of heavenly bodies, especially the measurements made to determine the positions and orbits of various stars. — astrometric, astrometrical, adj. astronautics the science of space travel, concerned with both the construction and the operation of vehicles that travel through interplanetary or interstellar space. Also called cosmonautics . — astronautic, astronautical, adj. — astronaut, n . astronavigation a type of navigation involving observations of the apparent positions of heavenly bodies. Also called celestial navigation, celo-navigation . — astronavigator, n. astronomy the science that studies the stars and other features of the material universe beyond the earth’s atmosphere. — astronomer, n . — astronomical, adj. astrophile a person strongly attracted to knowledge about the stars. — astrophilic, adj.

astrophotography a form of photography used to record astronomical phenomena. astrophysics the branch of astronomy concerned with the origin, and the chemical and physical nature of heavenly bodies. — astrophysicist, n . celestial navigation astronavigation. Also called celo-navigation . chromatoscopy the study of stars through a telescope in which the star appears as a ring of light, in order to observe the star’s scintillation. — chromatoscope, n. Copernicanism the fundamental theoretical basis of modern astronomy, first demonstrated in the early 16th century by Copernicus, who showed that the earth and the other planets orbit around the sun. Cf. Ptolemaism . cosmolabe Obsolete, an instrument, like an astrolabe, used for astronomical observations. cosmonautics astronautics. —cosmonaut. n. — cosmonautical, adj. heliodon an instrument used in astronomy to show the apparent movement of the sun. heliometer an instrument originally designed for measuring the sun’s diameter, now used for measuring the angular distance between stars. heliometry the practice of measuring the angular distance between stars by means of a heliometer.

— heliometric, heliometrical, adj. interlunation the period between the old moon and the new when the moon is invisible each month. — interlunar, adj. meridian an imaginary great circle in the sphere of the heavens, passing through the poles and the zenith and nadir of any point and intersecting the equator at right angles. See also 178. GEOGRAPHY. — meridian, meridional, adj. metagalaxy the entire system of galaxies, including the Milky Way. — metagalactic, adj. nutation the periodic oscillation that can be observed in the precession of the earth’s axis and the precession of the equinoxes. See also 133. EARTH. — nutational, adj. obliquity the inclination of the earth’s equator or the angle between the plane of the earth’s orbit and the plane of the equator (23°27’). Also called obliquity of the ecliptic . See also 133. EARTH. — obliquitous, adj. occultation the process of one heavenly body disappearing behind another as viewed by an observer.

paraselene a false moon, in reality a bright spot or a luminous ring surrounding the moon. perihelion the point in the orbit of a heavenly body where it is nearest the sun. Also spelled perihelium. Cf. aphelion. perihelium in orbit around a moon, the point nearest the moon. Cf. apolune. phantasmatography Rare. a work or treatise on astronomy or celestial bodies. planetarium 1. a representation of the planetary system, particularly one in which the movements of the planets are simulated by projectors. 2. a room or building housing such an apparatus. planetology the branch of astronomy that studies the planets. — planetologist, n . — planetologic, planetological, adj. planisphere a map showing half or more of the sphere of the heavens, indicating which part is visible at what hour from a given location. — planispheric, planispherical, adj. Ptolemaism the complicated demonstration of Ptolemynd-century geographer and astronomer, that the earth is the fixed center of the universe around which the sun and the other planets revolve; now discredited. Cf. Copemicanism .

Ptolemaist a supporter of the Ptolemaic explanation of planetary motions. radioastronomy the branch of astronomy that studies radio frequencies emitted by the sun, planets, and other celestial bodies. Sabaism astrolatry. Sabianism, Sabaeanism, Sabeanism the religion of the Sabians, a group sometimes associated with worship of the sun, moon, and stars. See also 349. RELIGION . schematism the combination or configuration of the aspects of the planets and other heavenly bodies. selenography the scientific analysis and mapping of the moon’s physical features. — selenographer, selenographist, n. — selenographic, selenographical, adj. selenology the branch of astronomy that studies the moon. — selenologist, n . — selenologic, selenological, adj. sideromancy a form of divination involving observations of the stars. Also called astromancy . — sideromancer, n. — sideromantic, adj. siderophobia an abnormal fear of the stars. uranianism Obsolete, astronomy.

uranography the branch of astronomy that deals with the description of the heavens by constructing maps and charts, especially of the fixed stars. Also called uranology . — uranographer, uranographist, n . — uranographic, uranographical, adj. uranology conservation of energy & angular momentum in a comet orbit conservation of energy and angular momentum for a comet orbiting the sun The goal of this page is to guide the reader through a spreadsheet exercise that shows that the total energy (kinetic and gravitational) and the orbital angular momentum of a comet orbiting the sun are the same at each position in the comet's orbit. Kepler's three laws of planetary motion are seen to apply to comet orbits as well. (browser issues: Mozilla 1.5x & IExplorer 6.x & Netscape 7.x display this page properly; Netscape 4.x is a disaster; don't use it!) 1) obtaining comet data The Ephemeris Generator at NASA-JPL is a flexible method of generating position-vs-time data for any comet (or any other solar system body, for that matter).

The ephemeris consists of (a) the comet-sun distance, (b) the rate at which the comet-sun distance changes with time, and (c) the comet's orbital speed with respect to the sun.

A short guide to use the Ephemeris Generator follows: Step 1: Modify current settings as desired: Target Body for a comet, use the "Select Small Body" portion; you must know the comet name and input it using one of the following example formats: 2P/Encke or 2P or Encke or 1990 XXI; limit the search to "Comets Only" in the box, and then click on the "Search" button; the generator then returns a list of possible comets; select the appropriate one; then click on the "Use Selected Asteroid/Comet" button Observer Location for generating position-vs-time data for a comet orbit around the sun, the observer location is irrelevant, although if you are interested in observing the comet from your geographic location, it can't hurt to input your latitude and longitude Time Span the start time will be today's date; you will want to know the orbital period of the comet if you want to insure your ephemeris covers a complete revolution of the comet about the sun; for Output Interval you will have to experiment; if you select a time interval that is too small, your ephemeris will be huge; if you select a time interval that is too

 large, you may miss key positions in the comet orbit perihelion, especially if the orbit is highly eccentric; click on "Use Specified Settings" when finished IMPORTANT NOTE: the accuracy of the ephemeris is NOT affected by the time step you insert; the model produces the same results no matter whether the time step is 1 minute or 10 days; the only difference is the number of values returned Output Quantities and Format The following are important for generating a comet orbit; click in their boxes 19.

Heliocentric range and range-rate (this is distance from sun and radial velocity relative to sun) 22. Speed wrt sun and observer (this is the object's speed relative to the sun and and to the observer) Uncheck the other boxes (unless you are interested in observing the comet from your geographic location); when finished, click on "Use Selected Settings" Step 2. Select desired options: if you are interested in importing the results into an Excel spreadsheet, click in the "Use CSV (spreadsheet) format " box; also check the "Include Body Information Page" Step 3. Request the ephemeris: click on the "Generate Ephermis" box The ephemeris will be returned in html table format. To save the file in spreadsheet-ready format, 1) select Save As... (or Save Page As...) 2) change the file extension to .csv in the File Name box 3) make sure that All Files is selected in Save as type box.

The three crucial pieces of data that will allow you to generate position-vs-time data for the comet are a) the column labeled r (the distance of the comet from the sun; the units returned are au) b) the column labeled rdot (the radial velocity of the comet relative to the sun = dr/dt ; i.e., the component of the comet's orbital velocity along the sun-comet line); this will be labeled vr below; the units returned are km/s c) the column labeled VmagSn (the orbital speed of the comet relative to the sun); this quantity will be labeled v below; the units returned are km/s A sample ephemeris for comet Encke (for a time span of 4 years at 30-day intervals) can be found here 2) elliptical orbits: semimajor axis and eccentricity Kepler's first law is commonly stated as "A planet's orbit about the sun is an ellipse with the sun located at one of the foci." A comet's orbit can be either an ellipse or a hyperbola. An elliptical orbit can be characterized by two parameters: the semimajor axis a and the eccentricity e.

The semimajor axis is one-half of the longest axis ( = major axis) of the ellipse. The eccentricity parameter characterizes the shape of the ellipse. An ellipse with an eccentricity of 0 is a circle; in this case, the two foci of the ellipse are coincident at the center of the circle. (The two foci are always located on the major axis of the ellipse. One definition of an ellipse is that for any point P on the ellipse, the sum of the distance from P to one focus and the distance from P to the other focus is the same and equal to the length of the major axis: PF1 + PF2 = 2a.) The eccentricity is defined as the ratio of the distance between the two foci to the length of the major axis: e = F1F2 /(2a) . As the eccentricity approaches 1, the ellipse becomes more elongated. The perihelion distance of the comet (distance from the sun at closest approach) = a (1 - e) ; the aphelion distance of the comet (furthest distance from the sun) = a (1 + e).

Note that the semimajor axis is the arithmetic mean of the perihelion and aphelion distances.

3) kinetic and gravitational energy in orbits a) the comet's kinetic energy (KE) = 1/2 mv2 where m is the mass of the comet the sun's kinetic energy is negligible in comparison b) the gravitational energy (GE) of the comet-sun system is = - G m Msun/r where M is the mass of the sun, G is Newton's Gravitational Constant c) the total energy (TE) is therefore = 1/2 mv2 - G m Msun/r because the mass m of the comet is generally unknown or known inaccurately, it is best to reformat these three energies as energies per (comet) mass: KE/mass = 1/2 v2 ; in order to have the units in standard SI (J/kg), convert the orbit speed from km/s to m/s GE/mass = - GMsun/r ; in order to have units of J/kg, convert the comet-sun distance from au to m it is important to use the most accurate values of quantities available G = 6.6742 x 10-11 m3/kg/s2 Msun = 1.9891 x 1030 kg 1 au = 1.

495 978 707 x 1011 m TE/mass = 1/2 v2 - G Msun/r 4) Is the total energy per mass constant?

Open the .csv file created by the Ephemeris Generator in Part 1 above. The next task is to create columns in the spreadsheet that calculate the KE/mass,. the GE/mass, and the TE/mass according to the above rules. (Familiarity with Excel or similar spreadsheet s is assumed.) You should find that the total energy is constant throughout the comet orbit, if you did the calculations correctly. It may not be precisely constant, as there will be some uncertainty in the data returned and in the values of the constants used; the first 4 or 5 significant digits should be the same for each of the total energy numbers. The total energy will be negative if the comet is bound to the sun, i.e., if it has an elliptical orbit and not a hyperbolic one; the total energy will be positive if the comet is unbound and has a hyperbolic orbit about the sun. The total energy (per mass) should also be equal to - G Msun/(2a) where a is the semimajor axis of the comet orbit. A calculation of the quantity TE/mass = - G Msun/(2a) should agree well with the values calculated in the previous section.

5) angular momentum in orbits: how to determine the tangential speed and the angular speed The angular momentum of the comet is L = m r vt where vt is the tangential component of the orbit velocity (vt is perpendicular to the radial compent of the velocity vr ). Because these two components are perpendicular, they are related to the orbit speed by the Pythagorean theorem: v2 = vr2 + vt2 Therefore, the tangential speed vt can be calculated using this equation and the values of v and vr that were produced by the Ephemeris Generator. Note that the tangential speed can also be written as vt = r dÎ¸/dt, where Î¸ is the position angle of the comet with respect to some defined direction. The quantity dÎ¸/dt is called angular speed and can be calculated by using the equation in the previous sentence along with the values of vt and r . The units of angular speed will be radians/s if tangential speed and the comet-sun distance incorporate the same distance units (e.g., kilometers). Angular momentum is another quantity that remains constant in an orbit as Kepler knew. His second law states that the line joining a planet to the sun sweeps out equal amounts of area in equal times.

This is true for any orbiting body including comets. Kepler's second law is equivalent to saying that the area swept out by the comet-sun line per unit time is constant. Because the area swept out by the line joining the comet to the sun is that of a triangle, with "height" equal to the comet-sun distance and with "base" equal to the distance the comet moves tangentially during the time interval, the area swept out per time interval is = 1/2 (base) (height)/(time interval) = 1/2 (r) (r ÎÎ¸) /Ît = 1/2 r vt Note that the area swept out per time by the comet-sun line is just one-half the angular momentum per mass. 6) Is the angular momentum per mass constant? Generate columns in the spreadsheet to calculate vt , dÎ¸/dt, and the angular momentum per mass (or, alternatively, the area swept out by the comet-sun line per time). Once again, the first 4 significant digits of the angular momentum should be constant with time if you have done the calculation correctly. A sample spreadsheet with energy and angular momentum calculations for comet Encke is here .

7) Generating an orbit shape To be able to plot the orbit of the comet around the sun it is best to use polar coordinates: r and Î¸ . Polar coordinate graph paper can be obtained here . The ephemeris has already returned values of r (comet-sun distance) as a function of time. A value for ÎÎ¸ , the angular change in position during a time interval, can be calculated by multiplying the angular speed (dÎ¸/dt) by the time interval over which that angular speed applies. (For this calculation, the ephemeris was recalculated so that the time intervals were 10 days; it is important that the time interval be small enough that the perihelion angular speed is small.) The position angle Î¸ has been defined to be zero at the time of perihelion in both figures 1 and 2 above; this is purely arbitrary, and the Î¸ = 0 position can be set by the user.. Once the angular position changes during each time interval have been calculated, then can be summed, starting at the position defined to be Î¸ = 0 in order to find the angular position at any particular time.

Generate columns in the spreadsheet for ÎÎ¸ and Î¸ as a function of time. The orbit of comet Encke generated in the manner described is shown at the right. The red dots show the position of the comet at monthly intervals. The sun is located at the black dot at the center of the polar plot. Note the labels of 2 au and 4 au radially. Also note that, as expected, the comet moves much more slowly when farthest from the sun (i.e., the red dots are closer together) than when nearest the sun. 8) Is Kepler's 3rd law obeyed? The final calculation is a test of Kepler's third law: P2 = a3 where P is the period of the comet's revolution about the sun (in years) and a is the semimajor axis of the comet orbit (in au). If you prefer to test the law in standard SI units, the equivalent form (due to Newton) of Kepler's third law is G Msun P2 = 4 Ï2 a3

Question: What is the name for the position in the orbit of a heavenly body when it is nearest the sun?
Answer: Perihelion