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LUNAR RADIATION AND TEMPERATURES By EDISON and SETH B. NICHOLSON ABSTRACT Methods of observing.—The vacuum thermocouple attached to the 100-inch tele- scope was used as in measuring stellar radiation. A microscope cover-glass was used to separate the reflected light from the planetary heat. A fluorite screen and water-cell were used for special purposes. Reduction of the measurements.—Comparison stars, whose radiometric magnitudes we have already determined, were used to reduce the galvanometer deflections to abso- lute intensities. These are expressed in terms of the radiometric magnitude of the plane- tary heat in a solid angle of i sq. sec. of arc. The relation of radiometric magnitude to absolute temperature is given by the equation log r= 2.612 — 0.i (wr —Awr) . An expression applicable to the screens used and to the conditions of observing is de- rived from this equation. Limiting measurable temperature.—Temperatures below ioo° K are measured with difficulty, since the value of mf for that temperature is 12.47 mag.; and it is probably not feasible to detect planetary radiation from a celestial body whose temperature is below 70o K. Reflection of solar radiation between 8 and 14 ¡jl.—Even if the moon reflected all the solar radiation in this region, it would add only, per cent to the planetary heat and affect the computed temperature by only i°. With the fluorite screen the emissivity between 8 and 10 ß is áhown to be the same as between 8 and 14 ¿4, which indicates that the silicates, if present in the lunar crust, cannot be detected by the selective emis- sivity between 8 and 10 ju as in laboratory tests, probably because they are in a finely divided or porous state for which the emissivity would be more like that of a black body. Distribution of radiation over the disk.—From drift-curves it is found that the distri- bution of planetary heat over the disk at full moon does not follow the formula E = a cos 6, derived from the Lommel-Seeliger law, but more nearly the formula E = a cos3/2 6 . This is explained by the rough surface. From the water-cell drift-curve it appears that the general trend of reflected light at full moon is uniform, but that at the limb in the E.-W. direction the intensity is 60 per cent greater than that of the neighboring maria. Temperature of the subsolar point.—The measures indicate that at full moon, when the subsolar point is nearly central on the disk, its temperature is 407o K, but that at quarter-phase, when it is on the limb, they show a temperature of 358o K. The directive effect of the rough surface on the planetary heat probably accounts for this difference. Temperatures during a lunar eclipse.—Measurements made near the limb on June 14, 1927, show that the temperature fell from 3420 to 175o K during the first par- tial phase, continued to drop to 156o K during totality, and rose again abruptly to nearly the original temperature during the last partial phase. From these data it is estimated that less than 0.1 cal cm-3 min-1 is conducted into the moon from the surface. Distribution of planetary heat and reflected light about the subsolar point.—With spe- cial equipment the night-to-night values of the reflected light transmitted by the cover- 1 Contributions from the Mount Wilson Observatory, Carnegie Institution of Washing- ton, No. 392. 102

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1930ApJ 11. . 102P o -21 -2-1o o -3-1 12 3 glass andoftheplanetaryheateliminatedbyitweredeterminedforsubsolarpoint pared withthetheoreticaltemperatureof374K. planetary heataboutthesubsolarpointmeansphericalrateofemissionisfoundto light overthehemisphereaboutsubsolarpointis0.85mag.fainterandplan- as itpassedovertheearthwardsideofmoon.Themeansphericaldistribution in thesequantities. and theoreticalrateoflunaremissiongivesasetcorrectionstotheatmosphericab- stant, wefindthemeansphericalrateoflunaremissiontobe1.61calcmmin'and tribution-curve, thelightreflectedfromsubsolarpointisestimatedtobe0.24cal be 1.93calcmminandthecorrespondingtemperature391K,whichistocom- the computedblack-bodytemperaturetobe374K.Fromdistribution-curveof cm min;andcombiningthiswiththeamountconductedsolarcon- low thatconsiderableobservingwillbenecessarytoestablishagoodvalue. laws ofLambert,LommelandSeeliger,Eulercannotbemadetofittheobserva- sorption constants,derivedontheassumptionthatentiredifferenceisduetoerrors etary heat0.15mag.fainterthanthecorrespondingintensitiesatfullmoon. in thecaseofplanetMercury.Toseparatetheseradiationsa of wave-length0.3to5/x,andthelow-temperatureradiationcalled light which,whenitreachesus,isconfinedpracticallytothelimits flected lightis0.093. be —13.3,andofthewholelunarradiation—14.8.Theradiometricalbedo,ofre- was derived,whereiand0aretheanglesofincidencereflection,respectively.The the beamformula reflected lightaboutthesubsolarpointanddrift-curvemadewithwater-cellin heat transmittedbetween0.3and8/xisnearlynegligibleexcept mission bandbetween8and14m-Thesmallamountofplanetary which reachesusprincipallythroughthegreatwater-vaportrans- tional material. with thelatter. enter intotheresultsverymuchlesswithformerscreenthan since anyerrorsinthespectralreflectioncoeflicientsforplanet microscope cover-glass0.165mmthickissuperiortoawater-cell, “planetary heat/’whichisemittedbythewarmedsurfaceand cell, fluoritescreen,*rock-saltwindow,and theatmosphereare © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 1 1 o Atmospheric absorption.—Adiscussionofthediscrepancybetweenobserved Reflection ofsolarradiationfromthelunarsurface.—Fromdistribution-curve Radiometric albedo.—Theradiometricmagnitudeofthereflectedlightisfoundto SmithsonianPhysicalTables(7thed.),p.305,1921. The radiationfromaplanetconsistsoftwoparts:reflectedsun- * SmithsonianMiscellaneousCollections,68,No.8,1917. The transmission-curvesofthemicroscopecover-glass, water- The theoreticallunartemperature.—Fromthewater-cellmeasurementsanddis- Mt.WilsonContr.,No.336;AstrophysicalJournal,66,43, 1927. Temperature ofthedarkside.—Thiswasfoundtobe120K.Thetemperatureisso LUNAR RADIATIONANDTEMPERATURES103 TRANSMISSION COEFFICIENTS :6 Se2 Er =K°3fT~() a 0.46 cos0+sm0 3 mm 3 1 Smithsonian Institution,3,171,1913. of steam16.7mlongatnormalatmosphericpressure. 0.7 cmofprécipitablewaterasrecommendedby Fowle,withdetails hood oficmprécipitablewater,whichisequivalenttoacolumn of watervaporbetween2.7and20¡xforamountsintheneighbor- no greatercontributiontoourknowledgeofplanetarytemperatures over arange900percentgreaterthanthatobserved.Probably glass, 0.165thick;(d)fluorite4mm;and(e)rocksalt2mm. shaded curve);(b)watervapor0.082cmprécipitablewater;(c)microscopecover- observer onMountWilsonandacelestialobjectinthezenithis0.7 0.082 cmofprécipitablewater,whereastheamountbetweenan mission coefficientsweredeterminedcoveredtherange0.001to tary heatisradiatedmostabundantlyarethoseobtainedbyF.E. water vaporandtheatmosphereinlongwave-lengthswhereplane- could bemadethanadeterminationofthetransmissioncoefficients cm, whichnecessitatesanextrapolationoftheobservationaldata Fowle. Theadmirableexperimentaldatafromwhichthesetrans- the atmosphere.Theonlycompletedataontransmissionof shown inFigure1.Allofthesearewelldeterminedexceptthat TRANSMISSION IO4 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Fig. i.—Transmissioncurvesof(a)theatmosphereaboveMountWilson(the 2 3 1 AstrophysicalJournal,35,149,1912;AnnalsoftheAstrophysical Observatory, SmithsonianMiscellaneousCollections,68,No.8,1917. Ibid.,p.23,1917. The shadedcurveinFigure1isthatfortheatmosphere having EDISON PETTITANDSETHB.NICHOLSON 1930ApJ 11. . 102P o 2 1 3 * curve(thebrokenline)for0.082cmofprécipitablewater,thedata in thenearinfra-redfromradiation-curveswhichweobservedfor made asnearlysymmetricalpossiblewithFowle’slaboratory not toincludeobservationswhenpdifferedlargelyfromthemean for whicharegiveninhistableonlystepsof1¡x. the purpose.Thatportionofcurvebetween2and14/xwas from acelestialobjectbetween300and500K,is to beappliedagalvanometerdeflection,5,forplanetaryheat tainty. FromFowle’sextrapolations,whichapplytotheshaded value 0.7cmthantoapplycorrectionswhichcouldbeoflittlecer- uncertainty inthetransmissionsthemselvesitwasthoughtbetter efficient 1.7variesoveralargerange.Onaccountofthisandthe vapor pressuree.Fowlehasshownthatinactualpracticetheco- gives theprécipitablewaterpinopticalpathforagiven transmission oftheatmosphere11percent.TheformulaHann, ed curve,avariationof50percentinthewatervaporchanges course, affecttheatmospherictransmission.Accordingtoshad- curve only,itfollowsthatthecorrectionduetoavariationofp, wires exceptthereceiver0.62mmsquareover onejunction.The thermocouple employedformostofthelunarobservationshada from celestialobjectshasalreadybeendiscussed.Thevacuum Smithsonian Institution,3,171,1913. silver shieldcoveringallthethermocoupleandplatinumlead- cell ofthethermocouplewasprovidedwith arock-saltwindow 285, 1922. w 2 mmthick. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 3 1 Variation intheamountofatmosphericwatervaporwill, AstrophysicalJournal,35,149,1912;Annalsofthe Observatory, The generalmethodwhichwehaveusedformeasuringradiation Mt.WilsonContr.,No.369;AstrophysicalJournal,68,279, 1928. SeealsoAnnalsoftheAstrophysicalObservatory>Smithsonian Institution,4,284- LUNAR RADIATIONANDTEMPERATURES105 OBSERVATIONAL DATA />= i.7^sec£,(1) > (o-3—10/4B r LUNAR RADIATIONANDTEMPERATURES107 2 — {asecZ—0.162)—P+10/4logAs, log r=2.6l2—O.I(w—ÄWr),(4) r C-c=D {S-S),(6) vs 1930ApJ 11. . 102P 6 2 1 6 w=+D(205Xio~—)+io/4 log6—10/4 ^ equation (5)andobtain(8): and s=256sq.sec.ofarcattheNewtonianfocus100-inch telescope. the sameasmeanvalueforstellarradiation. urements onthemoonandMarswhichgaveavalueof0.16mag., light fromtheplanetthroughcover-glass.Then, heat throughthecover-glass,andtrtransmissionofreflected r8 light reflectedfromtheplanet,Trtransmissionofplanetary observed withthecover-glassscreen.LetRbethatpartof value forSinequation(6). planetary heatisofstilllongerwave-length,wemaysubstitutethis increases withspectralclassbutbecomesnearlyconstantat205X the freedeflection,F,iscombinedasfollowswithCg,deflection planetary heat,andSthecoefficientforcomparisonstar. where Disthenumberofdayssincesilvering,Scoefficientfor io~ mag.perdayfortheradiationfromM-typestars,and,since 108 EDISONPETTITANDSETHB.NICHOLSON p s p © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 2 For planetsingeneralwesubstituteBfromequation(7c)into P isequivalenttohBinequation(2)expressedmagnitudes, The coefficient,a,ofsecZwasdeterminedfromaseriesmeas- Ibid,TableL In obtainingJ5,thatpartofthedeflectionduetoplanetaryheat, + 10/4logAs. + 10/4log(i——)—0.16(secZ—sec2)—10/4 ^ / Tr\'b~\~2,^ Cg =BTr-\-Rtr, B F=B+R, F— i — Çi Tr tr tr (?a) (7¿0 (7¿) (8) 1930ApJ 11. . 102P f 2 3 lect theconstantsandthosevariableswhicharefunctionsof planetary temperature,T,weobtain If wesubstitutethevalueofmfrom(8)intoequation(4)andcol- which appliestoanyplanetforthespectraldistributionof which willbecalledmcanobtainedfromobservations. for asolidangleof1sq.sec.arc;thesecondmembercanbecal- ric magnitudeoftheplanetaryheateliminatedbycover-glass of aKodwarfstar.Theabsorptionthecover-glassscreenfor Wilson scaleof0.92mag.,whichcorrespondsapproximatelytothat the reflectedlightisknown.Thisequationrepresentsradiomet- moon is0.90.Substitutingthisvalueoftrintoequation(9),wehave radiation reflectedbyitis0.08mag.Hence,thevalueoftrfor star ofthistypeis0.03mag.withsufficientapproximations,andthe equation (10),whichappliestoobservationsofthemoon: culated foranyplanetarytemperature,T,andthefirstmember, the energy-curveofmoonlightgivesacolor-indexonMount ing powerofsilver,wehavecomputedTable I fordifferentvalues of T.TheapplicationAmiwillbediscussed later. r black-body energy-curvesforvarioustemperatures, andthereflect- rj © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 1 3 2 -6 It hasalreadybeenshownthat,inthevisiblespectrumatleast, PublicationsoftheAstronomicalSocietyPacific,38, 242, 1926. From theatmospherictransmission-curvesinFigure1, Mt.WilsonContr.,No.369;AstrophysicalJournal,68,279, 1928. Mt.WilsonContr.,No.226;AstrophysicalJournal,55,165, 1922. In equation(10)thefirstandthirdtermsof left-handmem- m+F> (205x1o—5)10/4logb10/4(F—i.nCg) rS 6 mr+D (205Xio~—S)+io/4log¿—10/4F s L2 — 0.16(secZ—secz)—10/4log^+10/4As = 26.12—10logT+Aw—10/4(1—i.iiTr)m'r. r — 0.16(secZ—sec2)—10/4log^+10/4As* = 20.12—IOlogT+AWr—I0/4íI—Jffîry LUNAR RADIATIONANDTEMPERATURES109 pA~ 23 3 f- 2.'i / Tr\ Çé tr ' (10) c (9) 1930ApJ 11. . 102P 1 of about10percent,andwitheffortthismight beincreasedto+15 etary heateliminatedbythecover-glassofradiometric magnitude or +16ifalargesurfacewereavailable.Table Ishowsthatplan- radiometric magnitude+12couldbemeasured withanaccuracy planet. Ashasbeenpointedout,starsofradiometricmagnitude tion (8)forthethermocoupledescribedabove, planetaryheatof tional magnitudescanbemade.Byaddingthelasttermofequa- and withespeciallyconstructedthermocouplesagainoftwoaddi- is fixedbythesensitivenessofthermocouplecircuitand area ofthereceiver,ifreceiverissmallerthanimage 650.. . 450.. . 400.. . 800.. . 600.. . SSO.• . 500.. . 350.. . 300.. . 750.■ • 700.. . of thetelescope,was5.07mag.forthermocouplepreviouslyde- which dependsontheareaofthermocouplereceiverandscale 250.. . scribed whenusedattheNewtonianfocusof100-inchreflector. by thesixthtermwouldnothaveexceeded0.1mag.Thelastterm, + 7canbeobservedwiththeroutineequipmentwhichwehaveused; 200.. . 150.•• exceed 0.16mag.Thecorrectionforatmosphericwatervaporgiven mag. Thereductionforairmassgivenbythefifthtermdidnot ioo° K ber arefixedby‘theconditionsofobserving.Thecorrectiondue to tarnishedsilvergivenbythesecondtermdidnotexceed0.05 no EDISONPETTITANDSETHB.NICHOLSON © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 'Ibid. The lowerlimitofplanetarytemperaturewhichcanbemeasured I 25 I-3I 1.30 1.28 6-35 1.28 2.12 1-39 Aw, TABLE I 0.000 Tr 468* 364 013 063 000 249 147 + .27 — 0.85 — .01 +12.47 0.99 3-76 2 .OI 2.76 523 1-45 7.80 .67 .46 • 25 .60 — o.16 -0.49 Am' . 16 • 17 .17 • 17 ■ 17 .18 .18 .19 . 20 .24 .18 .28 .38 1930ApJ 11. . 102P 1 o free deflectionminuscover-glass,oroftheenergy between8and10fx puted {a)byassumingunitemissivityand(6)the to thatbetween8and14¿t. fluorite screentothatwithoutaandthesimilarratiocom- 1927. seen thatthisratioisessentiallyoffluorite minuscover-glassto emissivity tobethatofsilica.FromthecurvesinFigure1itwill is abnormallylowbetween8and10¡jl,someindicationofitspres- lunar crusthasahighsilicatecontent. lunar surfacewereperfectoverthewholeatmospherictransmission the ratio,H,ofobservedplanetaryheattransmittedby through afluoritescreen,which,asanexaminationofFigures1and ence shouldberevealedbythetransmissionofplanetaryheat band 8-14jjl.Thiswoulddecreasethecomputedtemperatureabout moon. AsimplecalculationfromPlanck’sblack-bodyformula lengths isplanetaryheatradiatedbythewarmedsurfaceof lunar surfacewouldbegreatenoughtoaffectthetemperaturescal- It isnoteasy,therefore,todeterminebythismeanswhetherthe shows, however,thatthereflectedsolarradiationwouldbelessthan reflecting powerintheregion8-14ju.Ifthesesubstancesarepres- which thelunarcrustmaycontainalargepercentage,havehigh culated ontheassumptionthatallradiationinthesewave- ent, itmightbesupposedthatthesolarradiationreflectedfrom 2 willshow,isolatesjustthisspectralregion.Wenowcompare tial objectsmuchbelowioo°Kcanbedeterminedonlywithdiffi- culty. i°, whichislessthantheuncertaintyarisingfromothersources. + i6to70K.Fromthisitisseenthatthetemperaturesofceles- + 12correspondstoatemperatureofioo°K,andmagnitude © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 per centoftheplanetaryheat,evenifreflectingpower Wood,PhysicalOptics,p.602,1911;Sosman,TheProperties ofSilica,p.738, From drift-curvesinFigure3wefindthefollowing data,which Since theemissivityofsilica(andtoalessextentsilicates) It iswellknownthatsilicaandtoalessextentthesilicates,of REFLECTION OFSOLARRADIATIONWAVE-LENGTH8-14¡1 LUNAR RADIATIONANDTEMPERATURESin CU OCM

112 EDISON PETTIT AND SETH B. NICHOLSON

apply to the subsolar point where the temperature is approximately o CT)00 400o K: F= 145 mm , Fl= 79 mm, Cg— 41 mm,

where FI is the deflection with the fluorite screen in place.

Fig. 2.—Energy-curve (a) of a black body at 400o K; (b) the same after the radia- tion has passed through the earth’s atmosphere, the dotted line between 8 and 10 p being the deformation due to presence of silica; (c) after passage through fluorite screen, the dotted line between 8 and 10 p being the deformation due to presence of silica; (d) after passage through microscope cover-glass (red limit at 6 /x). The dash-and-cross line is the deformation of (a) necessary to explain the discrepancy between the observed and theoretical lunar temperatures.

From these data it can also be seen that the reflected light, R, which is essentially represented by Cg, is 0.39 as great as the planet- ary heat represented by F — Cg. From the ordinates of the curves in Figure 1 multiplied into those of a black body at 400o K, we obtain Figure 2, where (a) is the spec- tral energy-curve for a black body at 400o K, (b) the same after transmission by the atmosphere, (c) after further transmission by the fluorite screen, and (d) after transmission by the cover-glass.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1930ApJ 11. . 102P ess 1 place itis773.TheratioofthesenumbersrepresentsHapproxi- the freedeflectionis2054,andthatwhenfluoritescreenin mately, buttogetamoreexactvaluewemustapplyequations(ja) From thiswefindthattheareawhichrepresentsplanetaryheatin by thecover-glass.Fromthesewefind whence and (76),whichallowforthesmallamountofplanetarylightlost where Ristakenat0.39Cgasabove,andthereflectingpowerused interpreted asimplyingthepresenceofsilicates,sincewithsucha equal emissivitiesintheregions8-10juand8-14/x,itcanscarcelybe the 0.38computedfromtransmissionsonassumptionof for fluoriteis0.05.Whiletheobservedvalue¿7=0.37^lthan been interchanged.Fromthis,togetherwiththenatureoflunar planetary heatintheregion8-10/zisaccountedforbyassump- of eclipseobservationstofollow,itappearsthatpracticallyallthe surface indicatedbythelowconductivityasshownindiscussion close agreementnosurprisewouldhavebeencausedhadthefigures fluorite usedabovemustbe,multipliedbytheemissivitycoefficients relatively smoothsilicasurface.Thecomputedspectralenergy- tion ofunitemissivity. of silicabeforetheratioHisdetermined.Theadoptedcoefficients, e, areasfollowsi curves ofplanetaryheattransmittedbytheatmosphereand © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 We willnowcomputeHontheassumptionthatmoonhasa Ibid. 8.0. 8.62 8.5. 8.25 8.75 7-75 LUNAR RADIATIONANDTEMPERATURES113 P x Fl-Cg=o.o$R+ 773, F— Cg=o.ioR-\-2054, Fl-Cg 4i+773 = F-Cg 82+2054 0.76 0.32 I .00 .40 •SO ■38 e 10.o. 10.25 9-25. 9-75- 9-5- • 9.0 ß X 0.38 ? 0.20 0.98 i .00 .24 .68 .42 e * 1930ApJ 11. . 102P 111111 2 1 per centofthereflectedfight,whileNo.4represents about60per planetary heatandabout90percentofthereflected fight.Number 3 representsabout11percentoftheplanetary heatandabout95 telescope mirrors.Number2representsabout 35percentofthe reflected lighttransmittedbyouratmosphere andreflectedbythe of water.Number1representsalltheplanetaryheatand mitted by0.165°fglass,and(4)radiationtransmitted1cm mocouple. Theyrepresent(1)freeradiation,thatis,withoutfilters, when thephaseanglewaso°.Thecurvesweremadebyunclamping showed noeffectofthiskind. through thecenterofdiskfullmoononJune16,1924, by theforegoingmethods.Itwillberecalled,however,that the telescopeandallowingimageofmoontotransitther- energy-curve oflunarradiationobtainedbyLangleyandVery small amountsofnon-poroussilicateswhichwouldescapedetection band at8-14¡xmightrevealadeformationduetotheemissivityof body. Wecanonlysaythenthatifsilicaorsilicatesarepresent, like sandorporouspumice,whichprobablywouldbeitsstate if present,itsradiatingpropertieswouldbenearlythoseofablack silica contentofthelunarcrustissmall,forifitwerefinelydivided that spectroscopicexaminationofthevioletslopeV(Fig.2) they areprobablyinthefinelydividedorporousstate.Itispossible silica contentitmayhave.Thisdoesnotnecessarilymeanthatthe region 8-10/xisunityforpracticalpurposesandunaffectedbyany that weconcludetheemissivityoflunarsurfacein From thesedatawefind (2) radiationtransmittedby4mmoffluorite,(3)trans- 114 EDISONPETTITANDSETHB.NICHOLSON © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 1 MemoirsoftheNationalAcademySciences,4,PartII, 193 ff.,1889. Ibid.,p.740. Figure 3showsdrift-curvesalongaparallelofdeclinationpassing This valueofHissoradicallydifferentfromtheobserved DISTRIBUTION OFRADIATIONOVERTHEDISK ff4i+ 505 = 82+1691 0.30 . 1930ApJ 11. . 102P © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem from thesubsolarpointbetweenfirstandlastquarters.These measureswereusedtoobtain The blacksquaresrepresentthesizeandpositionof receiver inmeasuringtheenergy the distribution-curvesinFigure7. recording drift-curvessuchasinFigure3;theblacklinesareaxesoflunarco-ordinates. The whitelinesrepresentthewidthofpathtraversedbythermocouple-receiverin PLATE VIII 1930ApJ 11. . 102P responding topointsonthecurveareindicatedbelow. cent ofthereflectedlight.Theprincipalfeaturesmooncor- Observatory, uponwhichareplottedtheaxesofco-ordinates(in cover-glass; (4)water-cell. black) andthepaths(inwhite)traversedby thermocouplejunc- of thewhitelinesisthatthermocouple-receiver asusedatthe tion onthethreedateswhendrift-curveswere taken.Thewidth refer tothedimensionsofthermocouple-receiver asusedatthe Snow telescopeinthefocusofa27-inchmirror of67inchesfocal 100-inch telescopeinmakingthedrift-curves. Theblacksquares © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Plate VIIIisaphotographofthefullmoonmadeatLick 2.—Drift-curves acrossfullmoon:(1)freeradiation;(2)fluoritescreen;(3) LUNAR RADIATIONANDTEMPERATURES115 1930ApJ 11. . 102P 1 at thecenterofdiskhigherandlimb lowerthanthecosine toward thehorizonlessthanitshouldbe,thus makingdeflections make theradiationtowardselenographic zenithgreater,and of thisdepression,orre-emissionabsorbedradiation, willtendto ous difl&cultyistheroughnessoflunarsurface,whichmakes observed towardthelimborterminatortobetoolow.Amoreseri- explain theeffectofroughness.Consideracavity orbowl-shaped but thesecondmayneedaddedexplanation. crater. Reflectionofplanetaryheatfromthe interiorbythesides The firstconsiderationisobviousfromanexaminationofTableI, quarter-phase lower,thanthosecalculatedfromthecosinelaw. deflections anywhereonthedisknearfullmoonhigher,but etary heatfromthemoonasreceivermovesawaysub- solar point,duetothefallingtemperature,causesdeflection The increasingabsorption,Aw,oftheearth’satmosphereforplan- over animageofthissphereasseenfromanydirection,thegalva- nometer deflectionsduetoplanetaryheatemittedbyitwillfollow follow thesamelaw.Hence,ifwepassathermocouplejunction unit solidangle,ifitisaconstantfractionofthatabsorbed,will sorbed byanysmall-unitareaandconvertedintoheatwillvarywith the amountofsolarradiationwhichisincidentonandcanbeab- smooth sphere,notinrapidrotation,exposedtoparallelsunlight, planetary heatoverthedisk. amount ofplanetaryheatradiatedbythesmallareainanydirected the cosineofitsangulardistancefromsubsolarpoint.The surface isindependentoftheangleprojection.Ifweconsidera receiver fromagivensolidanglepresentedbyuniformlyheated point tobedescribedlater.Wewillfirstdiscussthedistributionof length inthestudyofdistributionenergyaboutsubsolar than ahundredyears,theradiationincidentonthermocouple- the cosinelaw(eq.[13]) r lió EDISONPETTITANDSETHB.NICHOLSON © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 MémoiresdeVAcadémiedesSciences,Paris,5,179-213,1826. Two factorswhichunfortunatelycannotbeseparatedappearto Two circumstancesmodifythisprincipleasappliedtothemoon. As hasbeenknownfromexperimentalobservationsformore DISTRIBUTION OFPLANETARYHEATOVERTHEDISK « 1930ApJ 11. . 102P 0an mountain faceattheterminatorisinvisible,andareacovered image intheheldoftelescope,willgivesamedeflectionas near theterminatorandfacingsun,itisclearthatitstempera- of asmallareathemoonasseenfromparticulardirection tional temperature.Thethermocouplemeasuresthemeanradiation that fromthesubsolarpoint.Atquarter-phase,however,sucha measured atfullmoonwithathermocouple-receiversmallerthanits ture oughttobeequalthatofthesubsolarpoint,anditsradiation, i =180—(aOaC).^dYarepositivewest ofthecentralme- passing throughthecenter.Thismaybedonebyusualformulae of themeasuredpointstopositionstheywouldhaveforequato- of theapparentdisk,andwereplottedafterreducingpositions by itsshadowwillgivenodeflection.Thusarisestheideaofdirec- where 7isthedistanceinlunarradiifrom subsolarmeridian, mula ofprojectioninoneplaneapplies: in everycasepassveryclosetothesubsolarpoint,simplerfor- rial phaseangleo°whenthesubsolarpointisonhourcircle urements weremadeforpointslocatedatintervalsof0.025diameter of temperaturecanbeobtainedfromequation(10).Therealdis- not bethesamebecauseofitsroughcharacter. Viewed fromadifferentdirection,themeansurfaceinvolvedwpuld the earthattime,andthisisinterpretedintermsoftemperature. for themeasurementofpositionsonasphere;but,sincepaths taken onApril19andJune16,1924,14,1927.Themeas- face canbeobtainedfromtheordinatesofcurvesNos.1and3in law predicts.Again,ifweconsideranalmostverticalmountainside from thedistributionoftemperature.Thishasbeendoneforplates Figure 3byapplyingequation(7c)where^=0.90.Thedistribution ridian. and ithecomponentofphaseangleinright ascensiongivenby tribution ofplanetaryheatoverthelunarsurfacecanbeobtained 0 7 theobserveddistancefromcentralmeridian inthesameunits, 0 0 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The apparentdistributionofplanetaryheatoverthelunarsur- The resultsofsuchmeasurementsareplotted inFigure4.The LUNAR RADIATIONANDTEMPERATURES117 -1 7= sin(sinF—i),(11) 0 1930ApJ 11. . 102P o o -21 f middle ofthefigure.Thescalesordinatesshowgalvanometer of radiationovermostthelunarsurfaceat fullmoonisnearly nearly constantoverthisrange(TableI),the apparent distribution 4 showsthatfromthecenterto0.95radius fromthecenter tion ofplanetaryheatoverthelimardisk.An inspectionofFigure observations isalsothelocusofequation scale ofabscissaegivesfractionalpartsaradiusthelunardisk, the realoneandispracticallyrepresentedby equation (12). temperature variesonlybetween400and320 K,andsinceAmis and, asthe.observedpointsshow,representstheapparentdistribu- and theenergyEemittedbylunarsurfaceincalcmmin". heat eliminatedbythecover-glass,absolutetemperatureT, deflection Binmillimetersduetoapparentplanetaryheat,the radiometric magnitudemofasquaresecondarcplanetary the centerofwhichisonsubsolarmeridianindicatedin The temperaturesarecomputedfromthedatainTableI. Ii8 EDISONPETTITANDSETHB.NICHOLSON r r © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The semicircle(dottedline)isthatwhichrepresents theideal The heavyfulllineinFigure4whichrepresentstheplotted Fig. 4.—Distributionofplanetaryheatoverthediskatfullmoon 3/2 E=acos0, (12) 1930ApJ 11. . 102P / plot. where 9istheangulardistanceofapointfromsubsolar sphere withoutatmosphereexposedtosunlightaccordingthe in partatleast,thedeviationofdrift-curveplanetaryheat distribution ofplanetaryheatemittedbyasmooth,slowlyrotating from thecosine-curveisillustratedbyfollowingsimplecon- and aisconstant,madeequaltotheradiusofsphereinthis simple formula law, anditsradiationinthedirectionofearthatthatphasewill sideration. Iftheroughnessonmoonisduetonon-conducting spheres uniformlydistributedoveritssurface,eachspherewillpre- point, 9theangulardistancefromsubsolarnnumber beam ofunitcross-section,smallcomparedtotheradius It iseasilyseenthenthattheenergyEemittedinanearthward be two-thirdsthatwhichthesurfaceitoccultswouldhaveradiated. sent atfullmoonadistributionofenergyapproximatingthecosine moon, willbegivenby begin toocculteachother.Theconstantna/kwasdeterminedfrom of spheressectionalareaainthek(atsubsolarpoint). where Eistheenergyfromareakinbeamatsubsolar locus ofthisequationappearsinFigure4as abrokenline.An tion (14)andwasfoundtobe0.316.Fromthisitappearsthatthe Figure 4byinsertingtheobservedvalueofEforcos0=0.6inequa- This equationwillholdtoavalue0=0',wherethesphereswould spheres wouldbeseparated3.39radii,whichgives 0=S3°50'.The orientation theirmaximumoccultationis0.78 radius. additional pointwasfoundforthecasewhere for oneorientationof of June24,1927,apoint0.05radiusfromthe southlimbofthe the heldspheresappearmutuallytangent, whileforanother 0 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem That roughnessofthelunarsurfacewillexplainqualitatively, In anextendedseriesofmeasurementsduring thelunareclipse LUNAR RADIATIONANDTEMPERATURES119 E —acos9,(13) <»> 1930ApJ 11. . 102P o 2 3 21 o 1 e lower thanthatmeasuredatfullmoonmay beexplainedbythe perature ofthesubsolarpointmeasuredat first quarteris49C. rough surface.TheworkofRosseandLangley showedthatthe of themoonattimeobservation,andaveragetempera- tures to1.93calcm“min“bythefourth-power law.Thatthetem- other symbolshavethemeaningspreviouslydefined. magnitude ofthemoonlighttransmittedbywater-celland phase byobservingdeflectionsonthemiddleoflimb.When due toplanetaryheatwerereducedquarter-phasebyequation the phaseangleinlattercasewasnotexactly90,deflections A discussionofthelawsdiffusereflectionwhichapplytomoon full moonfromthedrift-curvesdescribedabove,andatquarter- will begiveninanothersection. give adistributionmorelikethatobtainedaboveforplanetaryheat. of diffusereflectivity,butnotfromLambert’slaw,whichwould which wouldbeexpectedfromtheLommel-SeeligerorEulerlaws gions; (e)thegeneraltrendofcurveistowarduniformbrightness, (13). TheresultsaregiveninTableII,wherem°istheradiometric the mariaareonlythree-fourthsasbrightmountainousre- the limb;(c)brightestpointonE.-W.diameteris maria; (b)thecenterofmoonis10to15percentbrighterthan brighter thantheneighboringsurface,whichinthiscaseconsistsof eastern boundaryofMareTranquilitatisnearlongitude17W.;(d) through thewater-cell:{a)limbofmoonis60percent follow directlyfromanexaminationofcurveNo.4Figure3taken similar pointsobtainedfromthedrift-curvesabove. indicated inFigure4byatriangle,whichagreesfairlywellwith moon wasselectedforcontinuousobservation.Thisgavethepoint r 120 EDISONPETTITANDSETHB.NICHOLSON © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 1 DISTRIBUTION OFREFLECTEDSOLARRADIATIONOVERTHEDISK 3 MemoirsoftheNationalAcademySciences,4,PartII, 107, 1889. PhilosophicalTransactionsoftheRoyalSociety,163,587, 1873. Müller,PhotometriederGestirne,p.68,1897. The solarconstanthasbeenreducedtotheheliocentricdistance The temperatureofthesubsolarpointhasbeendeterminedat Several conclusionsconcerningthereflectedlightfrommoon TEMPERATURE OFTHESUBSOLARPOINT 1930ApJ 11. . 102P 1 o 2 hm lunar temperaturewasprobablyashighboilingwater,andthe is insubstantialagreementwiththatfoundbyMenzelfromthe value of407Kobtainedbyusforthesubsolarpointatfullmoon the moonbeingusedtointerpreteliminatedplanetaryheatin water-cell observationsofCoblentz,theknownvisualalbedo terms oftemperature. 1924 Apr.19. 1929 Oct.17* 1927 June14 being n'north.Thedurationoftotalphasefor thispointwas240, to thecenterofearth’sshadow,distance atmid-totality made duringtheeclipseofJune14,1927.Apoint 48"(0.05radius) 1923 Mar.24t. 1924 June9t. from thesouthlimbwaschosen,sincethis limb passednearest © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 1 Corrected average.. ScientificPapers,BureauofStandards,18,535(No.438), 1922. A continuousseriesofmeasurementslunar radiationwas * CorrespondstoGreenwichCivildate,Oct.18,onPlateVIH. AstrophysicalJournal,58,65,1923. Corrected average.... t Firstquarter. Î Lastquarter. June 16. Apr. 20. July 24t Oct. 14t. July 19t. Nov. 14t. P.S.T. Date LUNAR RADIATIONANDTEMPERATURES121 TEMPERATURES DURINGALUNARECLIPSE Temperature oftheMoon’sSubsolarPoint Const. 1-93 1.87 1-93 I .92 I .92 1-93 1.88 i .90 i .98 1-95 1-85 1-93 Solar TABLE II 2.50 2 .00 2 .01 2.42 2.23 2.38 2.36 2.30 i .90 2 .89 2-35 2.49 Wc. +3-44 +3-35 +3-05 +4.08 +4.0.5 +4 Quarter-Phase 3-55 4.20 4.28 3.80 3-99 Full Moon + 1-37 + 1.40 + 1.39 + 1.69 + 1.92 + 2.21 1.44 1-35 2 .02 I .80 1.8l 1 .96 401 410 4o8°K 407 405 354 358 335 366 367 349 377 2.24 i .36 1930ApJ 11. . 102P h hm and thepartialphaseswereieach.Forpointselectedtime of mid-totalitywasi2ióa.m.,P.S.T.,whichmadeitafavorable eclipse forcontinuousmeasurement.Figure5showsthecircum- stances oftheeclipse,Pbeingpositionthermocouple junction. 122 EDISONPETTITANDSETHB.NICHOLSON measurements weremadeatthepointP. radiation, andwiththecover-glasswater-cell inthebeam, all taken,intheusualmanner.Arcturusand Vegawereusedas and aftereclipse,deflectionsonoffthe southlimbforfree described. Sincetheradiationvariedgreatlyduring theeclipse, comparison stars. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The programofobservationincludedseveraldrift-curves before Fig. 5.—CircumstancesofthetotallunareclipseJune14,1927.Theradiation The deflectionshavebeenreducedtothezenith aspreviously 1930ApJ 11. . 102P 1 -2-1 formula givenbyJeans: tions oftheeclipseanddistributionenergy onthesolardisk. received bythemoonfromsun,wascalculated fromthecondi- black-body formulabyusingthetemperatureT.Theenergy,E absolute temperatures,T,werereadfromTableI.E,theradiation emitted bythemoonincalcmmin,wasobtainedfrom free radiationorforthatthroughwater-cellcover-glasswas3min- h read forthesameinstantfromaplotofobserveddeflections utes. TosimplifytherecordinTableIIIdeflectionshavebeen sensitivity usedintheelectricalcircuitwaschangedfoursteps,so ii 34-■ IO 30.. IO 04.. against thetime. eclipse. Thetimerequiredtoobtainasinglesetofdeflectionsfor 12 28.. 12 02f. 11 47-• 10 52.. 12 58.. 11 13.. that duringtotalityitwas4.2timesasgreatbeforeandafterthe Ry Q2 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 41. ■ 1 46. . 04.. 59- ■ 54- - 28.. 22. . MonthlyNoticesoftheRoyalAstronomicalSociety,78,35, 1917. The totalradiationalongaradiusofthesunis expressedbythe The valuesofm'werecomputedfromequation(10),andthe r m* P.S.T. Time t A.M. LUNAR RADIATIONANDTEMPERATURES123 603 617 513 347 617 617 100 55-0 79-5 Free mm 4- 47 4.08 8.92 5- 13 6.46 2 .89 1 .48 2-57 Observed Deelections Radiation duringLunarEclipse j 0 ^=0.465+0.5351/1-^, (15) 309 302 263 289 166 289 31 -6 63.1 33-9 mm o .42 o .07 Cg 1.00 . 20 .09 .12 .01 TABLE III 200 204 174 113 182 191 39-8 20 21 .9 mm Wc O .20 O.80 6.3I .16 .14 .07 .07 .64 + 2.23 + 2.09 4.6 4.2 6- 5 8.0 6.8 6.7 5-0 6.4 2.15 2.41 7.6 7-3 2.74 7- 3 2 .09 333 339 320 300 342 342° 219 205 170 231 156 160 149 173 169 160 174 0.87 0.67 I .02 1.09 113 113 cal cm' •05 •19 •IS •05 .07 •05 .07 .08 .04 .07 .24 mm 0 .48 0.19 1-85 1.85 1 63 I .00 1.85 1.85 . OO ZR .09 .28 .OO .OO .OO • OO .OQ .OO 1930ApJ 11. . 102P 1 -2-1 o o P inFigure5obtainedfromthedataTableI.Thedottedline perature ofthemoonasdeterminedfromdirect observationswith represents thesolarradiationEreceived,andbrokenline is eclipsedbytheearthsummationoveralluneclipsed where Jisthetotalradiationatcenterofdiskandr the moonasafunctionoffractionsolardiameterocculted tion isJ;theconstantshavebeenderivedfromAbbot’sdata.The energy receivedbythemoon,asmightbeexpected. energy Eradiatedbythemoonincalcmmin. by theearth. totality thetemperaturedoesnotchangematerially,thenitrises to fallslowly,reaching156Kattheend.Forafewminutesafter area, eachelementofwhichistobeweightedaccordingequation total radiationwhichreachesthemoonatanyinstantassun distance inradiifromthecentertopointwheretotalradia- III. Thefulllineindicatestheabsolutetemperature,T,ofpoint surface materialsofthemoonhavelowheatconductivity. abruptly duringthenext20minutes.Fromthisitfollowsthat 124 EDISONPETTITANDSETHB.NICHOLSON (15). TableIVgivestheresultingintensityofsolarradiationon 175 Kduringthefirstpartialphase,andtotalitycontinues R 0 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 0o 1 The temperaturefallsfrom342toavaluebetween200and Abbot,TheSun,2ded.,p.107,1929. In general,thefallandriseintemperaturelagsbehindE, Figure 6isaplotofthedatainlastthreecolumnsTable It willnowbeourpurposetocomparetheradiation andtem- R DISTRIBUTION OFPLANETARYHEATANDREFLECTED Fraction ofSolarDiam-Total eter OccultedRadiationReceived by EarthMoon LIGHT ABOUTTHESUBSOLARPOINT TABLE IV 05 41 67 96 54 89 79 27 15 1930ApJ 11. . 102P 1 light andconductedheat.Beforethiscanbedonethedistributionof from thesolarconstantbymakingsuitableallowancesforreflected the thermocouple(TableII)withvaluesderivedtheoretically last quartersinOctober,1929. both reflectedlightandplanetaryheatoverthehemisphereabout the subsolarpointmustbeinvestigatedinmuchsamemanner the subsolarpointmadethroughoutlunationbetweenfirstand This wasaccomplishedbyacontinuousseriesofmeasurementson as westudythedistributionofradiationaboutanelectriclight. moon, E,andofenergyradiated,E,duringthetotallunareclipseJune14,1927. telescope. Theimageofthemoonwasapproximately15.5mmin the cover-glassandlighttransmittedbyit werereducedtothe zenith byBouguer’sformulaintheusualmanner. at intervalsduringthenight.Theplanetary heateliminatedby free radiationand50mmwiththecover-glass, werereadvisually diameter. Thedeflections,whichwereofthe orderof200mmfor aperture and67inchesfocallengthfedbythecoelostatofSnow r © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 Fig. 6.—Marchofabsolutetemperature,T,energyreceivedfromthesunby The apparatusemployedwasareflectingtelescopeof27inches Mt.WilsonContr.,No.4;AstrophysicalJournal,23,6,1906. Simultaneous observationsmadewiththe100-inch telescopeat LUNAR RADIATIONANDTEMPERATURES125 CU OCM

126 EDISON PETTIT AND SETH B. NICHOLSON

the time of full moon, with suitable comparison stars, furnished the scale of absolute units. The settings of the thermocouple upon the subsolar point were made from the photograph in Plate VIII, upon which were plotted the night-to-night positions of the subsolar 0 *

Fig. 7.—Distribution of planetary heat and reflected solar radiation about the sub- solar point on the moon.

point. These are shown by the black squares which give the size and position of the thermocouple-receiver for each Greenwich Civil date. The angle between the sun and earth as seen from the subsolar point (which is equivalent to the zenith distance of the earth) was com- puted by the usual formula. The resulting distribution-curves of planetary heat and reflected light about the subsolar point are

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1930ApJ 11. . 102P plotted inpolarco-ordinatesFigure7.TheintensityscalesEon Here rjistheemissivity,whichwifibetaken asunityinthecal- it, E,areknown.Theradiatedenergycanthenbefoundfromthe light fromthesubsolarpointafterfullmoon(indicatedbycircles) The errorinthemeasurementofthisquantity arisingfromuncer- the heliocentricdistanceofmoonby inverse-squarelaw. times ofobservation,reducedfromthemean distance ofthesunto reflected fromthelunarsurface,E,andthatpartconductedinto is theradiusofhemispherehavingvolumegeneratedby of bothplanetaryheatandreflectedfightaboutthesubsolarpoint, reflected lightshowsasharpdropfromfullmoon(0=o)to075°, the outsideoffigureareforplanetaryheatandoninside culation following.ThevalueofEisthesolar constantforthe equation revolution ofthecurvesinFigure7aboutaxis0=o.Thearc heat for6=0and71-/2giveninFigure7.Thedistributionof of heatbythemoon,whichmighttendtomakemaximumtem- moon (indicatedbycrosses).Astheseobservationsareallonthe reflected lightoutsidetheatmosphereandwerecalibratedby mean sphericalintensities,arealsoshowninFigure7. and adefiniteincreaseagainnearquarter-phase(0=7r/2). perature ofafixedpointonthesurfaceoccurinlunarafternoon* are somewhatgreaterthanthecorrespondingintensitiesbeforefull computed fromthesolarradiationreceived,Er,ifthatpartofit quadrants ofthesehemispheresandtheirradii,whichrepresentthe solute unitsatfullmoonandfirstquarterinTableIIagreewiththe subsolar point,thisdifferencecanhavenorelationtoaccumulation corresponding valuesreadfromthedistribution-curveofplanetary 100-inch measurementsinTableII. c r R © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The temperatureofthesubsolarpointonmoonmaybe Simple considerationsshowthatthemeanvalueofintensity It willbenotedthatthevaluesofplanetaryheatEinab- Curiously, theintensitiesofbothplanetaryheatandreflected LUNAR RADIATIONANDTEMPERATURES127 THEORETICAL LUNARTEMPERATURE 4 Er—E—E=7]