CHAPTER 15NAVIGATIONALASTRONOMYPRELIMINARYCONSIDERATIONS1500.Definitioning principally with celestial coordinates, time, and theapparentmotions ofcelestial bodies,is thebranch of as-Astronomy predicts the futurepositions andmotionstronomy most important to the navigator.The symbolsof celestial bodies and seeks to understand and explaincommonly recognized in navigational astronomy aregiveninTable1500.their physical properties.Navigational astronomy,deal-Celestial BodiesOSunLower limbMoon0tCenter学Mercury7UpperlimbQVenusONewmoon@EarthCrescentmoonMarsOFirst quarter24JupiterOGibbous moonhSaturnOFullmoonUranusOGibbousmoonyNeptuneOLast quarterePlutoCrescentmoon★Star☆-P Star-planet altitude correction (alti-tude)Miscellaneous SymbolsYears米InterpolationimpracticalMonthsDegreesDays'Minutes of areHoursWSeconds of areMinutes of timed Conjunction· Seconds of time8OppositionRemsins belowhorizonQuadratureRemains above horizon88Ascending nodeUIll Twilight all nigheDescending nodeSigns of the ZodiaeT Aries (vernal equinox)Libra (autumnal equinox)8Taurusm Scorpius口Gemini1SagittariusCancer (summer solstice)Capricornus (wintersolstice)&Leo-AquariusVirgoXPisceeTable1500.Astronomicalsymbols.225
225 CHAPTER 15 NAVIGATIONAL ASTRONOMY PRELIMINARY CONSIDERATIONS 1500. Definition Astronomy predicts the future positions and motions of celestial bodies and seeks to understand and explain their physical properties. Navigational astronomy, dealing principally with celestial coordinates, time, and the apparent motions of celestial bodies, is the branch of astronomy most important to the navigator. The symbols commonly recognized in navigational astronomy are given in Table 1500. Table 1500. Astronomical symbols
226NAVIGATIONALASTRONOMY1501.TheCelestial Sphereserverat some distant point in space.When discussing therisingorsettingofabodvonalocalhorizon,wemustlocateLooking at the sky on a dark night, imagine that celes-the observer at a particularpoint on the earth because thetial bodies are located on the inner surface of a vast, earth-setting sun for one observer may be the rising sun foranother.centered sphere. This model is useful since we are only in-terested in the relativepositions and motions of celestialMotiononthecelestial sphereresultsfromthemotionsbodies on this imaginary surface.Understanding the con-in space of both the celestial body and the earth.Withoutcept of the celestial sphere is most important whenspecial instruments,motionstowardand awayfromthediscussingsightreduction inChapter20earthcannotbediscerned1502.RelativeAndApparentMotion1503.AstronomicalDistancesCelestial bodiesare in constantmotion.There isnoConsiderthecelestial sphere as having an infinite radi-fixed position in spacefrom whichonecan observeabso-usbecausedistancesbetweencelestial bodiesarelutemotion.Sinceall motionisrelative,thepositionoftheremarkablyvast.Thedifficultyofillustratingastronomicalobservermustbenotedwhendiscussingplanetarymotion.distances is indicated by thefact that ifthe earth were rep-Fromtheearthweseeapparentmotionsofcelestialbodiesresented by a circle one inch in diameter,themoon wouldon the celestial sphere.In considering how planetsfollowbeacircleone-fourthinchindiameteratadistanceof30their orbits around the sun, we assume a hypothetical ob-inches, the sun would be a circle ninefeet in diameter atFigure 1501.The celestial sphere
226 NAVIGATIONAL ASTRONOMY 1501. The Celestial Sphere Looking at the sky on a dark night, imagine that celestial bodies are located on the inner surface of a vast, earthcentered sphere. This model is useful since we are only interested in the relative positions and motions of celestial bodies on this imaginary surface. Understanding the concept of the celestial sphere is most important when discussing sight reduction in Chapter 20. 1502. Relative And Apparent Motion Celestial bodies are in constant motion. There is no fixed position in space from which one can observe absolute motion. Since all motion is relative, the position of the observer must be noted when discussing planetary motion. From the earth we see apparent motions of celestial bodies on the celestial sphere. In considering how planets follow their orbits around the sun, we assume a hypothetical observer at some distant point in space. When discussing the rising or setting of a body on a local horizon, we must locate the observer at a particular point on the earth because the setting sun for one observer may be the rising sun for another. Motion on the celestial sphere results from the motions in space of both the celestial body and the earth. Without special instruments, motions toward and away from the earth cannot be discerned. 1503. Astronomical Distances Consider the celestial sphere as having an infinite radius because distances between celestial bodies are remarkably vast. The difficulty of illustrating astronomical distances is indicated by the fact that if the earth were represented by a circle one inch in diameter, the moon would be a circle one-fourth inch in diameter at a distance of 30 inches, the sun would be a circle nine feet in diameter at Figure 1501. The celestial sphere
227NAVIGATIONALASTRONOMYadistanceof nearlyafifth ofa mile,and Plutowould bea1504.Magnitudecircle half an inch in diameter at a distance ofabout sevenThe relativebrightness of celestial bodies is indicatedmiles.Theneareststarwouldbeone-fifththeactual dis-by a scale of stellarmagnitudes.Initially,astronomers di-tancetothemoonvided the stars into 6groups accordingto brightness.TheBecause ofthe size ofcelestialdistances,itis inconve-20 brightest wereclassifiedas of thefirstmagnitude, andnientto measurethem in common units such as themile orthedimmestwereofthesixthmagnitude.Inmoderntimeskilometer.Themeandistanceto our nearest neighbor, thewhenitbecamedesirabletodefinemorepreciselythe limitsmoon, is 238,900miles.For conveniencethisdistance isof magnitude,a first magnitude star was considered 100sometimes expressed in units oftheequatorial radiusofthetimes brighter than one of the sixth magnitude.Since theearth:60.27earthradii.fifthrootof100is2.512.thisnumberisconsideredtheDistances between theplanets are usuallyexpressed inmagnitude ratio.A first magnitude star is 2.512 times asterms of the astronomical unit (AU),the mean distancebright as a second magnitude star, which is 2.512 times asbetween the earth and the sun.This is approximatelybright as a third magnitude star,.A second magnitude is92,960,000miles.Thusthemeandistanceoftheearthfrom2.512x2.512=6.310timesasbrightasafourthmagnitudestar. A first magnitude star is 2.51220 times as bright as athe sun is 1 A.U.The mean distance of Pluto, the outermoststar ofthe 2ist magnitude,the dimmestthat can be seenknownplanetinoursolarsystem,is39.5A.U.Expressed inthrough a 200-inchtelescope.astronomical units,the mean distancefrom theearthto theBrightness is normally tabulated to the nearest 0.1moonis0.00257A.U.magnitude,aboutthesmallestchangethatcanbedetectedDistances to the stars require another leap in units.Aby the unaided eye ofa trained observer.All stars of magcommonly-used unit is the light-year, the distance lightnitude 1.50 or brighter are popularly called firsttravels in one year.Since the speed of light is about 1.86xmagnitude"stars.Thosebetween 1.51and 2.50 are called105milespersecondandthereareabout3.16×107seconds"second magnitude"stars,thosebetween2.51and3.50areper year, the length of one light-year is about 5.88 × 1012called "third magnitude"stars,etc.Sirius, thebrightest star.miles.Theneareststars,AlphaCentaurianditsneighborhasamagnitudeof-1.6.TheonlyotherstarwithanegativeProxima,are 4.3 light-years away.Relativelyfew stars aremagnitude is Canopus, -0.9. At greatest brilliance Venusless than 100 light-years away.The nearest galaxies, thehasamagnitudeofabout-4.4.Mars,Jupiter,andSaturnareClouds of Magellan, are 150,000 to 200,000 light yearssometimes of negative magnitude.The full moon has aaway.Themost distantgalaxies observed byastronomersmagnitudeofabout-12.6,but varies somewhat.The magare severalbillion light years away.nitude of the sun is about -26.7.THEUNIVERSE1505.TheSolarSystemThehierarchies of motions in the universe are caused bytheforce of gravity.As a result ofgravity,bodies attract eachotherinproportiontotheirmassesandtotheinversesquareThe sun, the most conspicuous celestial object in the sky,of thedistancesbetweenthem.This forcecauses theplanetsis the central body ofthe solar system.Associated with it are atto go around the sun in nearly circular,elliptical orbitsleast nine principal planets and thousands of asteroids, com-In eachplanet'sorbit,thepointnearestthesun iscalledets,andmeteors.Someplanets likeearthhave satellitesthe perihelion.The point farthest from the sun is called theaphelion. The line joining perihelion and aphelion is called1506.MotionsOfBodiesOfTheSolarSystemthe line of apsides.In the orbit ofthemoon, the point near-est the earth is called the perigee, and that point farthestAstronomers distinguish between two principal mo-from the earth is called the apogee. Figure 1506 shows thetions of celestial bodies.Rotation is a spinning motionorbit of the earth (with exaggerated eccentricity), and theabout an axis within the body, whereas revolution is theorbit ofthemoon around the earth.motionofabodyinitsorbitaroundanotherbody.Thebodyaroundwhichacelestialobjectrevolvesisknownasthat1507.The Sunbody's primary.For the satellites,the primary is a planet.For the planets and other bodies of the solar system,thepri-Thesundominates our solar system.Itsmass is nearlyamary is the sun.The entire solar system is held together bythousand timesthatofall otherbodiesofthe solarsystemcom-thegravitational force of the sun.The whole system re-bined. Its diameter is about 866,000 miles. Since it is a star, itvolvesaround thecenteroftheMilky Waygalaxy(sectiongenerates its own energy throughthermonuclear reactions,1515), and the Milky Way is in motion relative to its neigh-thereby providing heat and light for the entire solar systemboring galaxies.Pluto
NAVIGATIONAL ASTRONOMY 227 a distance of nearly a fifth of a mile, and Pluto would be a circle half an inch in diameter at a distance of about seven miles. The nearest star would be one-fifth the actual distance to the moon. Because of the size of celestial distances, it is inconvenient to measure them in common units such as the mile or kilometer. The mean distance to our nearest neighbor, the moon, is 238,900 miles. For convenience this distance is sometimes expressed in units of the equatorial radius of the earth: 60.27 earth radii. Distances between the planets are usually expressed in terms of the astronomical unit (AU), the mean distance between the earth and the sun. This is approximately 92,960,000 miles. Thus the mean distance of the earth from the sun is 1 A.U. The mean distance of Pluto, the outermost known planet in our solar system, is 39.5 A.U. Expressed in astronomical units, the mean distance from the earth to the moon is 0.00257 A.U. Distances to the stars require another leap in units. A commonly-used unit is the light-year, the distance light travels in one year. Since the speed of light is about 1.86 × 105 miles per second and there are about 3.16 × 107 seconds per year, the length of one light-year is about 5.88 × 1012 miles. The nearest stars, Alpha Centauri and its neighbor Proxima, are 4.3 light-years away. Relatively few stars are less than 100 light-years away. The nearest galaxies, the Clouds of Magellan, are 150,000 to 200,000 light years away. The most distant galaxies observed by astronomers are several billion light years away. 1504. Magnitude The relative brightness of celestial bodies is indicated by a scale of stellar magnitudes. Initially, astronomers divided the stars into 6 groups according to brightness. The 20 brightest were classified as of the first magnitude, and the dimmest were of the sixth magnitude. In modern times, when it became desirable to define more precisely the limits of magnitude, a first magnitude star was considered 100 times brighter than one of the sixth magnitude. Since the fifth root of 100 is 2.512, this number is considered the magnitude ratio. A first magnitude star is 2.512 times as bright as a second magnitude star, which is 2.512 times as bright as a third magnitude star,. A second magnitude is 2.512 × 2.512 = 6.310 times as bright as a fourth magnitude star. A first magnitude star is 2.51220 times as bright as a star of the 21st magnitude, the dimmest that can be seen through a 200-inch telescope. Brightness is normally tabulated to the nearest 0.1 magnitude, about the smallest change that can be detected by the unaided eye of a trained observer. All stars of magnitude 1.50 or brighter are popularly called “first magnitude” stars. Those between 1.51 and 2.50 are called “second magnitude” stars, those between 2.51 and 3.50 are called “third magnitude” stars, etc. Sirius, the brightest star, has a magnitude of –1.6. The only other star with a negative magnitude is Canopus, –0.9. At greatest brilliance Venus has a magnitude of about –4.4. Mars, Jupiter, and Saturn are sometimes of negative magnitude. The full moon has a magnitude of about –12.6, but varies somewhat. The magnitude of the sun is about –26.7. THE UNIVERSE 1505. The Solar System The sun, the most conspicuous celestial object in the sky, is the central body of the solar system. Associated with it are at least nine principal planets and thousands of asteroids, comets, and meteors. Some planets like earth have satellites. 1506. Motions Of Bodies Of The Solar System Astronomers distinguish between two principal motions of celestial bodies. Rotation is a spinning motion about an axis within the body, whereas revolution is the motion of a body in its orbit around another body. The body around which a celestial object revolves is known as that body’s primary. For the satellites, the primary is a planet. For the planets and other bodies of the solar system, the primary is the sun. The entire solar system is held together by the gravitational force of the sun. The whole system revolves around the center of the Milky Way galaxy (section 1515), and the Milky Way is in motion relative to its neighboring galaxies. The hierarchies of motions in the universe are caused by the force of gravity. As a result of gravity, bodies attract each other in proportion to their masses and to the inverse square of the distances between them. This force causes the planets to go around the sun in nearly circular, elliptical orbits. In each planet’s orbit, the point nearest the sun is called the perihelion. The point farthest from the sun is called the aphelion. The line joining perihelion and aphelion is called the line of apsides. In the orbit of the moon, the point nearest the earth is called the perigee, and that point farthest from the earth is called the apogee. Figure 1506 shows the orbit of the earth (with exaggerated eccentricity), and the orbit of the moon around the earth. 1507. The Sun The sun dominates our solar system. Its mass is nearly a thousand times that of all other bodies of the solar system combined. Its diameter is about 866,000 miles. Since it is a star, it generates its own energy through thermonuclear reactions, thereby providing heat and light for the entire solar system
228NAVIGATIONALASTRONOMYThe distance from the earth to the sun varies fromphotosphere.91,300,000 atperihelion to94,500,000milesat aphelion.The sun is continuously emitting charged particles,When the earth is at perihelion, which always occurs earlywhich form the solar wind. As the solar wind sweeps pastin January,the sun appears largest, 32.6'in diameter.Sixthe earth, these particles interact with the earth's magneticfield. If the solar wind is particularly strong, the interactionmonths later at aphelion, the sun's apparent diameter is aminimumof31.5'.can producemagnetic storms which adverselyaffectradioObservations of the sun's surface (called the photo-signals on the earth. At such times the auroras are particu-sphere) reveal small dark areas called sunspots. These arelarlybrilliantandwidespread.areas of intensemagneticfields inwhichrelativelycool gas (atThe sun is moving approximately in the direction of7000°F.)appears dark in contrast to the surrounding hotter gasVega at about 12 miles per second, or about two-thirds as(10,000°F.).Sunspots vary in sizefrom perhaps 50,000 milesfast as the earth moves in its orbit around the sun.This is inindiameter to the smallest spots thatcan bedetected (afewadditionto thegeneral motion ofthe sunaround the centerhundred miles in diameter).They generally appear in groups.of ourgalaxy.Large sunspots canbe seen withoutatelescope if the eyes areprotected, as by the shade glasses ofa sextant1508.PlanetsSurrounding the photosphere is an outer corona ofThe principal bodies orbiting the sun are called planets.very hot but tenuous gas. This can only be seen during aneclipse of the sun, when the moon blocks the light of theNineprincipal planets areknown:Mercury,Venus,Earth,(April)PERIHELION(Januory)LINEOF APSIDIAPHELUION(uuly)(Odober)Figure1506.Orbits of the earth and mo0n
228 NAVIGATIONAL ASTRONOMY The distance from the earth to the sun varies from 91,300,000 at perihelion to 94,500,000 miles at aphelion. When the earth is at perihelion, which always occurs early in January, the sun appears largest, 32.6' in diameter. Six months later at aphelion, the sun’s apparent diameter is a minimum of 31.5'. Observations of the sun’s surface (called the photosphere) reveal small dark areas called sunspots. These are areas of intense magnetic fields in which relatively cool gas (at 7000°F.) appears dark in contrast to the surrounding hotter gas (10,000°F.). Sunspots vary in size from perhaps 50,000 miles in diameter to the smallest spots that can be detected (a few hundred miles in diameter). They generally appear in groups. Large sunspots can be seen without a telescope if the eyes are protected, as by the shade glasses of a sextant. Surrounding the photosphere is an outer corona of very hot but tenuous gas. This can only be seen during an eclipse of the sun, when the moon blocks the light of the photosphere. The sun is continuously emitting charged particles, which form the solar wind. As the solar wind sweeps past the earth, these particles interact with the earth’s magnetic field. If the solar wind is particularly strong, the interaction can produce magnetic storms which adversely affect radio signals on the earth. At such times the auroras are particularly brilliant and widespread. The sun is moving approximately in the direction of Vega at about 12 miles per second, or about two-thirds as fast as the earth moves in its orbit around the sun. This is in addition to the general motion of the sun around the center of our galaxy. 1508. Planets The principal bodies orbiting the sun are called planets. Nine principal planets are known: Mercury, Venus, Earth, Figure 1506. Orbits of the earth and moon
229NAVIGATIONALASTRONOMYFigure1507.Wholesolardiskand anenlargementoftheFigure1509.Oblatespheroidorellipsoidof revolutiongreatspotgroupofApril7,1947.Courtesy of Mt. Wilson and Palomar Observatories.Mars,Jupiter,Saturn,Uranus,Neptune,andPluto.fThe orbits of manythousands of tinyminorplanets orasteroids lie chieflybetween the orbits of Mars and Jupiter.these,onlyfourarecommonlyusedforcelestial navigationThese are all too faint to be seen with thenaked eyeVenus,Mars, Jupiter,and SaturnExceptfor Pluto,the orbits of the planets lie in nearly1509.TheEarththe same plane as the earth's orbit.Therefore, as seen fromthe earth, theplanets areconfined toa stripof the celestialIn common with other planets, theearth rotates on itssphere called the ecliptic.axis and revolves in its orbit around the sun.These motionsThetwo planets with orbits smaller than that of theeartharetheprincipal sourceofthedailyapparentmotions ofare called inferiorplanets, and those with orbits largerthanothercelestialbodies.Theearth'srotationalsocausesadethat of the earth are called superior planets. The four planetsflection of waterand air currents totheright in the Northernnearestthesunaresometimescalledtheinnerplanets,andtheHemisphereandtotheleft inthe SouthernHemisphere.Be-others the outer planets.Jupiter, Saturn, Uranus, and Neptunecause of the earth's rotation, high tides on the open sea lagare so much larger than the others that they are sometimesbehind the meridian transit of themoon.classed as major planets. Uranus is barely visible to the unaid-Formostnavigationalpurposes,theearthcanbeconedeye,NeptuneandPlutoarenotvisiblewithoutatelescopesidered a sphere.However, like the other planets, the earthPlanets can be identified in the sky because, unlike theis approximatelyan oblate spheroid,or ellipsoid of revo-stars.thevdonottwinkle.Thestarsaresodistantthattheylution, flattened at thepoles and bulged at the equator. Seearevirtuallypointsources of light.Therefore thetiny streamFigure1509.Therefore, the polar diameter is less than theoflightfromastariseasilyscatteredbynormalmotionsofequatorial diameter, and the meridians are slightly ellipti-air in the atmospherecausing theaffectoftwinkling.Thena-cal, rather than circular.The dimensions of the earth areked-eyeplanets.however,areclose enoughto presentrecomputed from timetotime,asadditional andmorepre-perceptible disks. The broader stream of light from a planetcisemeasurementsbecomeavailable.Sincetheearthis notis noteasily disrupted unless theplanet is low on the horizonexactly an ellipsoid, results differ slightly when equallyor the air is especially turbulent.precise and extensivemeasurements are made on different
NAVIGATIONAL ASTRONOMY 229 Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. Of these, only four are commonly used for celestial navigation: Venus, Mars, Jupiter, and Saturn. Except for Pluto, the orbits of the planets lie in nearly the same plane as the earth’s orbit. Therefore, as seen from the earth, the planets are confined to a strip of the celestial sphere called the ecliptic. The two planets with orbits smaller than that of the earth are called inferior planets, and those with orbits larger than that of the earth are called superior planets. The four planets nearest the sun are sometimes called the inner planets, and the others the outer planets. Jupiter, Saturn, Uranus, and Neptune are so much larger than the others that they are sometimes classed as major planets. Uranus is barely visible to the unaided eye; Neptune and Pluto are not visible without a telescope. Planets can be identified in the sky because, unlike the stars, they do not twinkle. The stars are so distant that they are virtually point sources of light. Therefore the tiny stream of light from a star is easily scattered by normal motions of air in the atmosphere causing the affect of twinkling. The naked-eye planets, however, are close enough to present perceptible disks. The broader stream of light from a planet is not easily disrupted unless the planet is low on the horizon or the air is especially turbulent. The orbits of many thousands of tiny minor planets or asteroids lie chiefly between the orbits of Mars and Jupiter. These are all too faint to be seen with the naked eye. 1509. The Earth In common with other planets, the earth rotates on its axis and revolves in its orbit around the sun. These motions are the principal source of the daily apparent motions of other celestial bodies. The earth’s rotation also causes a deflection of water and air currents to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. Because of the earth’s rotation, high tides on the open sea lag behind the meridian transit of the moon. For most navigational purposes, the earth can be considered a sphere. However, like the other planets, the earth is approximately an oblate spheroid, or ellipsoid of revolution, flattened at the poles and bulged at the equator. See Figure 1509. Therefore, the polar diameter is less than the equatorial diameter, and the meridians are slightly elliptical, rather than circular. The dimensions of the earth are recomputed from time to time, as additional and more precise measurements become available. Since the earth is not exactly an ellipsoid, results differ slightly when equally precise and extensive measurements are made on different Figure 1507. Whole solar disk and an enlargement of the great spot group of April 7, 1947. Courtesy of Mt. Wilson and Palomar Observatories. Figure 1509. Oblate spheroid or ellipsoid of revolution