G l o s s a r yAcceleration -- Rate at which velocity changes (negative acceleration--slowing down--is also known as deceleration). Acceleration is a vector quantity. Angle of attack--in the theory of airplane wings, the angle between the wing profile (roughly, measured along its bottom) and the wing's motion relative to the surrounding air. Anomaly -- in orbital motion, one of the angles which gauges the motion of a planet or satellite around its orbit, increasing by 360^{o} every revolution. The true anomaly f equals the polar angle f in polar coordinates with origin at the center of the motion (e.g. Sun or Earth). The mean anomaly is a related angle which increases in direct proportion to the time elapsed (the true anomaly does not--the motion is faster near the center). The eccentric anomaly is an auxiliary angle used in relating true anomaly (which is observed) and mean anomaly (which is calculated). Aphelion -- the point in a planet's orbit furthest from the Sun (Helios is Greek for Sun). See perihelion, apogee. Apogee -- the point in a satellite's orbit furthest away from Earth (see perigee, aphelion). Apparent motion -- The observed motion of a heavenly body across the celestial sphere, assuming the Earth is at the sphere's center and is standing still. Atlas -- An early liquid-fueled rocket, used by US astronauts and still in use for unmanned launches. Because of its lightweight construction it uses no staging, but only drops two of its engines. Azimuth and elevation -- Two angles which give the direction of a surveyor's telescope (theodolite). Azimuth is the rotation angle of the telescope around a vertical axis, measured (counterclockwise from above) from due north, a direction whose azimuth is zero degrees. Elevation is the angle the telescope is lifted above the horizontal plane. Ballistic pendulum -- A device often used for measuring the energy of motion of a bullet, adapted by Goddard to measure the thrust of small rockets with various nozzles. For a bullet is is a heavy block of wood or sand-filled box, hanging by a string; the bullet is weighed, then fired into the pendulum, and the distance the pendulum rises allows the bullet's velocity to be deduced. Binomial Theorem--A formula first derived by Newton, giving (1+z)^{ a}, the result of raising 1 + z to an arbitrary power a, as a sequence of form
where the terms A_{i} (i = 1,2,3...) are given by the formula and where a can be positive, negative, fractional or whole. When the magnitude of z is less than 1, the higher powers get smaller and smaller and the formula can be made as precise as one wishes by including enough of them (for z of small magnitude, 1-2 terms are sufficient), although the result is never exact. For magnitudes of z equal to 1 or more, the formula only holds for values of a which are positive whole numbers. In that case, for any z, the result is exact and the sum of terms with powers ofz does not go on arbitrarily but ends with z^{ a}. Calendar -- A system of marking days of the year, usually devised in a way to give each date a fixed place in the cycle of seasons. Calorie -- Unit used in measuring the energy of heat or chemical energy. A "small" calorie is the heat needed to warm up one gram of water by 1 degree centigrade and equals about 4.18 joule. A "kilocalorie" or "big calorie" equals 1000 calories and is the unit usually used in describing the energy content of food. Cartesian coordinates -- A system of uniquely marking the position of a point on a plane [or in 3-dimensional space] -- by 2 [3] numbers (its "cartesian coordinates") giving its distances from 2 [3] mutually perpendicular lines ("cartesian axes"). The distances and the axes to which they are parallel are usually marked (x,y) in a plane and (x,y,z) in space; the "origin" is the point at which the axes intersect. Celestial coordinates -- see "right ascension and declination." Celestial pole -- One of the two points in the sky around which the celestial sphere seems to rotate. Celestial sphere -- An immense sphere surrounding Earth, to which the fixed stars seen at night appear to be attached. Although strictly speaking such a sphere does not exist, it is often used as a convenient tool for mapping the position of stars and other heavenly bodies. In a similar way, although it is clear that the apparent rotation of the celestial sphere is really due to the Earth rotating around its axis, that rotation is often used for convenient description of apparent motions such as the rising and setting of stars. Center of gravity -- (CG), also known (more precisely) as center of mass. In a distributed mass, an appropriately defined "average location" of its parts. If the mass is a rigid (=undeforming) body subject to the earth's gravity, then if it is supported at the CG, it will stay balanced and not tilt to any side. Centrifugal force -- A force which must be included in the calculation of equilibria between forces in a rotating frame of reference (e.g. rotating carrousel, rotating space station, rotating Earth). In the rotating frame, the forces on a body of mass m are in equilibrium (as evidenced by the body staying at the same place) only if all forces acting on it, plus a "centrifugal force" mv^{ 2}/R directed away from the center of rotation, add up to zero. See Coriolis force. Centripetal acceleration -- The acceleration associated with motion around a circle, directed to the center of the circle. Centripetal force -- The force making a motion is a circle possible, always directed to the center of the circle. To make a (small) object of mass m move with velocity v around a circle of radius R, a centripetal force of magnitude mv^{ 2}/R must be applied. Component of vector--When a vector is resolved into a sum of vectors in specified directions, each of those vector is the component of the given vector in the specified direction. Conic Sections -- The family of curves generated by planes intersecting with a cone. Several cases are distinguished, depending on the angle between the plane and the axis of the cone. Precise definitions exist for each, but in general terms, when the plane is:
--Moderately inclined to the axis, the curve is an ellipse. --Parallel to one of the straight lines which generate the cone, the curve is a parabola. --Even more steeply inclined, the curve is a hyperbola. Constellation -- A named grouping of fixed stars, e.g. Orion or the Big Dipper. Copernican System -- A theory of planetary motions, proposed by Copernicus, according to which all planets move in circular orbits areound the Sun, the ones closer to the Sun moving faster, with the Earth itself a planet orbiting between Venus and Mars. Coriolis force -- A force which must be included in the calculation of motion in a rotating frame of reference, if the body moves in such a way that its rotation velocity changes. In general, it tends to preserve that part of its velocity. The Coriolis force is responsible for the swirling of hurricanes and large weather systems--for air flowing into a region of low pressure, counterclockwise north of the equator, clockwise south of the equator (reverse directions for air flowing out of a high pressure region). See centrifugal force. Declination -- See "right ascension and declination" De Laval nozzle -- A device for efficiently converting the energy of a hot gas to kinetic energy of motion, originally used in some steam turbines and now used in practically all rockets. By constricting the outflow of the gas until it reaches the velocity of sound and then letting it expand again, an extremely fast jet is produced. Drag--the air resistance encountered by a moving object. Drag is one of the four forces sensed by an airplane, the others being lift, thrust and weight. Eccentricity -- Number between 0 and 1, gauging the elongation of elliptic orbit. The eccentricity e of the orbital ellipse is one of the "orbital elements" characterizing it. Ecliptic -- A line around the middle of the celestial sphere, connecting the points occupied by the Sun over the year. The moon and the visible planets also appear to move very close to that line, which cuts the celestial equator at an angle of about 23.5^{o} . See plane of the ecliptic. Ellipse -- A closed curve resembling a flattened circle (the shadow of a circle tilted towards the light is an ellipse). May be defined:
Energy -- Ability to perform work, i.e. to advance against resistance, for instance lift a body against gravity, or drag it against friction. Epicycle -- A circle around a point which (in the simplest form of Ptolemy's system) moved steadily around the celestial sphere. Greek astronomers proposed that planets moved along epicycles around the Sun or around other points which circled around the sky; later additional corrections were added. The theory of epicycles was the earliest explanation for the irregular apparent motion of the planets--prograde (forward), then retrograde Equatorial axis -- Among the two mutually perpendicular axes of a telescope, the one that points at the celestial pole. To keep a star in view, the telescope must be rotated around this axis at the same rate as the Earth turns. Equilibrium (of forces) -- A situation when more than one force acts on a body, but because the sum of forces is zero, no motion results. Equinox -- the time of the year (around March 21 and September 23) when the position of the Sun in the sky (following the ecliptic) crosses the celestial equator. To a good approximation, the length of the day and night are then equal, and the Sun rises exactly in the east and sets exactly in the west. . Equinox is viewed as the beginning of spring and fall. Explorer 1 -- The first US artificial satellite, launched 31 January 1958 by a 4-stage modified military rocket. Provided the earliest observations of the Earth's radiation belt. Firmament -- The celestial sphere and the collection of stars whose position is fixed on it. First point in Aries -- Another name for the position on the celestial sphere of the vernal equinox. It is called so because in ancient time that point was in Aries, a constellation of the zodiac. It is currently moving from Pisces to Aquarius. Fly-by maneuver (or swing-by maneuver) -- The encounter between a moving spacecraft and a moving planet or moon, affecting the spacecraft's motion like an elastic collision (in which no energy is lost to heat). Depending on the details of the encounter, the spacecraft can gain or lose appreciable amounts of energy, and appreciable changes in the direction of its motion can result. Force -- In mechanics, the cause of motion. It is a vector quantity, in the direction of the acceleration it causes. g -- The symbol used for the acceleration due to gravity. At the Earth's surface it averages 9.81 meters/second^{2}, directed towards the Earth's center. In common talk, "g forces" are stresses due to acceleration, e.g. on astronauts or payloads. In the same vein, "zero g" is the condition when no acceleration is sensed, because gravity is already fully employed supplying the centripetal force which holds the object in its orbit (or alternatively from the rotating frame of reference, because gravity is fully balanced by the centrifugal force). Geodesy -- The study of the shape of the Earth, e.g. its deviations from an exact sphere. Gnomon -- The part of a sundial which casts the shadow, usually a rod or fin pointed at the celestial pole. Gregorian calendar -- Introduced in 1582 by Pope Gregory the 13th, this calendar modifies the Julian calendar for greater precision, decreeing that century years such as 1900 are not leap years, except if the number of centuries is divisible by 4 (e.g. 2000). Ice ages -- Times in the geological past when great glaciers extended far into Europe, Asia and America. Iteration--The repetition of a process of calculation again and again, each time improving the accuracy of the result. For an example of iteration (with "Kepler's Equation") see here Jet Propulsion Lab -- An outgrowth of the Guggenheim Aeronautical Laboratory of Caltech, in Pasadena (near Los Angeles, California). JPL was the center of US rocket development in World War II and was founded by Theodore Von Karman and Frank Malina. Today it is the focus of NASA's exploration of the planets and of distant space. Joule -- (pronounced like "jewel"). Unit of energy: the ability to overcome one Newton along 1 meter (assuming g = 10 meter/sec^{2}, it is also the energy required to lift 1 kg by 0.1 meters). Named for James Prescott Joule, one of the first to measure the "rate of exchange" between mechanical energy and heat. Julian Calendar -- Introduced in 46 BC by the Roman ruler Julius Ceasar, this calendar assumes a year of 365.25 days, and uses a cycle in which 3 "ordinary" years of 365 days are followed by a "leap year" with 366 days. Leap years are the years whose number is divisible by 4. Kepler's laws --
Comments: Kilowatt-hour -- (KWH). The amount of energy supplied by one kilowatt (1000 watt) for 1 hour (3600 seconds), equal to 3 600 000 joule. Electric bills are usually figured by the number of KWHs consumed. Kinetic energy -- Energy stored in the motion of a mechanical system--e.g. by a rolling car, or a turning flywheel. Lagrangian points -- In a system of two large bodies (Sun-Earth or Earth-Moon), these are the points where a small third body will keep a fixed position relative to the other two. Named for French astronomer Louis Lagrange (1736-1813) who first studied them and who showed there existed 5 such points. In the Sun-Earth system only two are important, both on the Earth-Sun line--the L1 point 236 Earth radii sunward of Earth, and the L2 point at a similar distance on the night side. The L1 point is a good "early warning" outpost intercepting shocks and particles emitted by the Sun and its vicinity has been occupied by several spacecraft. Altogether five Lagrangian points exist in the Earth-Sun or Earth-Moon system. Latitude and longitude -- Two angles which specify a location on Earth. If a line is drawn from the Earth's center to the given location, then latitude is the angle between that line and its projection on the plane of the Earth's equator (latitude also equals 90^{o}- q, where the "co-latitude" q is the angle between the line and the axis of the Earth). To define longitude, imagine a large number of planes ("meridional planes") all of which contain the axis of the Earth. Assuming the equator is a circle, divide it into 360 degrees and fractions of degrees: then each meridional plane can be labeled by the angle at its intersection of the equator, and the longitude of a point is the angle f marking the meridional plane on which it sits. Longitude is similar to the angle f of 3-dimensional polar coordinates or to right ascension, but is measured from a zero longitude chosen as the longitude of the Greenwich observatory near London, Great Britain. Law of areas -- Another name for Kepler's 2nd law. Lift--the lifting force on a flying object (in particular, a wing or an aircraft), due to its motion relative to the surrounding air. Lift is one of the four forces sensed by an airplane, the others being drag, thrust and weight. Liquid fueled rockets -- Rockets in which a liquid fuel (kerosene, liquid hydrogen) is combined in a combustion chamber with a liquid oxidizer (usually liquid oxygen, also fuming nitric acid or hydrogen peroxide). Very efficient and controllable, such rockets are generally used in spaceflight. Unlike solid fueled rockets, they can be shut off by remote command, simply by closing off their fuel line. Magnetosphere -- The outermost environment of Earth, dominated by the Earth's magnetic field. The magnetosphere is the site of the radiation belt and many intricate phenomena. See solar wind. Mass -- The mass of a body can be loosely defined as the amount of matter it contains. That is expressed in two ways:
Metonic Calendar -- Named for the Athenian astronomer Meton, it is based on the moon, counting each cycle of the phases of the Moon as one month. Days are kept approximately in step with the seasons by including 7 leap years of 13 months in each cycle of 19 years. Used by the Chinese and the Jews. Milankovich theory -- Theory by which ice ages were caused by slow changes of the motion of the Earth in space, including the coupling between the 26 000 year cycle of the precession of the equinoxes and the annual variation of the Earth-Sun distance. Muslim Calendar -- Based on a year of 12 months, each corresponding to one cycle of the Moon, but without the Metonic correction. Its months migrate through the seasons. Newton -- Unit of force, the force which, when applied to one kilogram mass, causes an acceleration of 1 meter/sec^{2}. Newton's laws of motion -- Three laws which form the foundation of classical mechanics, i.e. of the theory of ordinary motions (not motions on an atomic scale, covered by quantum mechanics, and not at velocities close to that of light, covered by relativity). The laws introduce the concepts of force and mass and state (in modern terms)
Newton's laws (2) and (3) in Mach's formulation reduce to:" When two small bodies act on each other, they accelerate in opposite directions and the ratio of their accelerations is always the same." Orbit -- The path of a body in space, generally under the influence of gravity. Orbital elements -- Variables which characterize the motion of an orbiting body. For a planet or satellite in an elliptic orbit, 6 orbital elements exist: the semi-major axis gives its size, eccentricity its shape and mean anomaly its position along the orbit, at the given time. The three other elements are three angles which give the orientation in space of its orbital plane, e.g. that plane's inclination (to the plane of the Earth's equator or the ecliptic,depending on choice of coordinates). Orbital period -- The length of time required for a body to complete one full (closed) orbit. Perigee -- the point of a satellite's orbit closest to Earth (see perihelion, apogee). Perihelion -- The point in a planet's orbit when it is closest to the Sun (Helios is Greek for Sun). See aphelion, perigee Plane of the ecliptic -- (also called "the ecliptic" for short) The orbital plane of the Earth around the Sun. The line of the ecliptic on the celestial sphere is formed by the intersection of the plane of the ecliptic with that sphere. The reason the major planets and Moon appear in the sky close to the ecliptic is that the solar system is flat, and its orbital planes are very close to each other. We observe their motion (very nearly) edge-on. Planets -- Celestial bodies such as the Earth which orbit the Sun (and by extension, similar orbiters around distant stars). Counting from the Sun outwards, planets visible to the eye are Mercury, Venus, (Earth), Mars, Jupiter and Saturn. The telescope also sees the more distant Uranus, Neptune and Pluto, as well as smaller asteroids (most of them inside the Jupiter orbit) and Kuiper objects (in the outer solar system). See also retrograde motion Polar Coordinates -- An alternative system of marking a point on a plane by its radial distance (r) from an "origin" and a polar angle (f). Polar coordinates in 3-dimensional space use (r) and two polar angles (q,f) giving the direction from the origin to the point. Polaris (Pole Star, North Star) -- A fairly bright star, the last star in the tail (or handle) of the constellation of the Little Dipper (Ursa Minor). Currently located within a fraction of a degree from the celestial north pole, the point around which the celestial sphere appears to rotate. In the northern hemisphere, the direction towards Polaris is very nearly due north. Potential energy -- Energy stored in the set-up of a mechanical system--e.g. by a weight able to descend (in the presence of gravity), or by a compressed spring. Power -- The rate at which energy is supplied. See watt. Precession -- A modern term, derived from the precession of the equinoxes and meaning a motion around a cone of the rotation axis of a spinning body. Precession of the Equinoxes -- A slow motion of the axis of the Earth around a cone, one cycle in about 26000 years. As a result, the celestial pole moves around a circle in the sky, and in ancient times, for instance, was quite far from Polaris. Discovered by Hipparchus around 130 BC as a slow shift of the vernal equinox around the ecliptic (i.e. around the zodiac). Propeller pitch--the angle at which the propeller blade (or part of it) "bites" into the air, its angle of attack. Ptolemy's System -- The explanation given by ancient Greek astronomers to the motion of planets around the sky, described in a book by the Greek Ptolemy, around 150 AD. It regarded Earth as the center of the universe and assumed the motion of planets was a superposition of circular motions (see epicycles). Pythagoras, theorem of -- A proved assertion in geometry, that in a right-angled triangle which has sides of length (a, b, c), if c is the long side facing the right angle, then a^{2} + b^{2} = c^{2} Reaction force -- The added force implied by the lack of motion (equilibrium) when an applied force exists (e.g. gravity). Re-entry (atmospheric re-entry) -- The return of a spacecraft from orbit to Earth, in which the kinetic energy of the orbital motion is converted into heat. Since that heat is sufficient to melt the spacecraft, if the spacecraft is to land intact, the heat must be safely dissipated. Heat-resistant shields of various types are used, and the reentry is at a shallow angle, to stretch out the process. Retrograde motion -- Temporary reversal of the apparent motion of a planet along the ecliptic. Caused because (by Kepler's 3rd law) a planet moves faster the closer it is to the Sun, so that (for instance) Jupiter appears to move backward when the faster-moving Earth overtakes it. Right angle -- The angle formed when two straight lines intersect and the 4 angles at their crossing are all equal. When measured in degrees it equals 90^{o}. Right ascension and declination -- Two angles marking the position of a star on the celestial sphere. Imagine a line from the observer to the star, and draw its projection (like a shadow) onto the celestial equator. Declination d is the angle between the line and its projection (d = 90^{o} - q, where q is the angle to the direction to the celestial pole); it is negative south of the equator. RA is the angle between the projection and the direction to the vernal equinox or first point in Aries. Rocket -- A device shooting out a fast jet of gas, in order to produce a force in the opposite direction. See center of gravity, also Newton's laws of motion in Mach's formulation. Rotation axis of the Earth -- The imaginary line around which the Earth turns. Its inclination of about 23.5^{o} to the ecliptic is the reason for the seasons of the year. Saturn V -- The biggest rocket built to date, weighing 2700 tons fully loaded. It was used to launch NASA's Moon mission and the Skylab space station. Second law of thermodynamics -- A fundamental law of energy exchange, one of whose formulations is "no process is possible whose only net effect is the flow of heat from a cold body to a hot one." A consequence of this is that in any system only part of the heat energy can be converted to other forms; the rest of the heat flows to lower temperature. Semimajor axis -- a property of an ellipse, equal to half its greatest width, as measured along the line connecting its two foci. The semi-major axis of an orbital ellipse is one of the "orbital elements" characterizing it, and is directly related to the energy of the motion. Solar wind -- A fast outflow of hot gas in all directions from the upper atmosphere of the Sun ("solar corona"), which is too hot to allow the Sun's gravity to hold on to its gas. Its composition matches that of the Sun's atmosphere (mostly hydrogen) and its typical velocity is 400 km/sec, covering the distance from Sun to Earth in 4-5 days. The solar wind confines the Earth's magnetic field inside a cavity known as the magnetosphere and supplies energy to phenomena in the magnetosphere such as polar aurora ("northern lights") and magnetic storms. Solid fueled rockets -- Rockets which burn a solid mixture of fuel and oxidizer, and have no separation between combustion chamber and fuel reservoir. Gunpowder is such a mixture and was the earliest rocket fuel. They are somewhat less efficient than the best liquid fuel rockets, but are preferred for military use because they need no lengthy preparation and are easily stored in ready-to-fly condition. They are also used in auxiliary rockets that help heavily loaded liquid-fuel rockets (Space Shuttle, Delta) lift off and go through the first stage of their flight. Solstice -- The time of the year when the Sun's position is the sky is most distant from the celestial equator. To a good approximation, north of the equator the day (around June 21) and the night (around December 21) are at their longest at the summer and winter solstices, and that is when those seasons are assumed to begin (the dates themselves, however, are known as midsummer day and midwinter day, respectively). Summer north of the equator coincides with winter south of it (and vice versa), and solstice names are also interchanged there. Sputnik ("satellite") -- The first artificial Earth satellite, orbited by the Soviet Union on October 7, 1957, using Korolev's R-7 rocket. Staging of a rocket -- The placing of smaller rockets on top of larger ones, increasing the lifting ability of the combined set-up. Sundial -- A device for telling time of day by the shadow which sunlight produces on the instrument. See gnomon. Sweepback--the angle by which the wing of an airplane is swept back, measured from the direction perpendicular to the fuselage. Synchronous orbit -- The circular orbit above the equator at a distance of 6.6 Earth radii, in which a spacecraft has an orbital period of 24 hours. Such satellites stay above the same spot on Earth and are therefore ideally suited for transmitting communications and broadcasts. Thrust--the force acting on a rocket or an airplane, produced by the action of its motor and pulling it forward. In an airplane, thrust is one of the four forces sensed by an airplane, the others being lift, drag and weight V2 -- Abbreviation of "Vergeltungwaffe 2" (vengeance weapon 2), a 12-ton German rocket carrying a 1-ton explosive charge, used in World War II, starting in 1944. The V2 had a range of around 200 miles, used a liquid-fuel rocket and was the first large military rocket. Vector -- A quantity having both magnitude and direction, e.g. displacement, velocity, acceleration and force. Vectors are added when, for instance, one moves in a frame that itself is moving too (e.g. swims across a flowing river). Vectors are added like arrows, end to end, and the sum (for two) is the vector from the tail of the first vector to the tip of the second. Vector resolution--The representation of a given vector as the sum of vectors in given directions. See componenet Velocity -- Rate of position change, a vector quantity. Vernal equinox -- The spring equinox. The term is also used for the point occupied by the Sun at that time, one of the two intersections on the celestial spher, between the ecliptic and the celestial equator. Also known as first point in Aries. Watt -- Unit of power, the rate at which energy is supplied. One watt is the power which supplies 1 joule per second, 1 kilowatt = 1000 watts. A grown human climbing stairs (e.g.) supplies about 100 watt; 1 horsepower = 736 watt. Named for James Watt, inventor of the modern steam engine. Weight -- The force exerted on mass by gravity. X-1 -- A rocket-powered research airplane, the first to fly faster than sound, on 14 October 1947. Zodiac -- Twelve constellations dividing the ecliptic into approximately equal parts. Each month the Sun is in a different constellation of the zodiac. |