For contrast, a diffuse disk reflector model is simply, which isn't realistic, but it does represent the opposition surge for rough surfaces that reflect more uniform light back at low phase angles.

The definition of the geometric albedo, a measure for the reflectivity of planetary surfaces, is based on the diffuse disk reflector model. The absolute magnitude, diameter  (in kilometers) and geometric albedo  of a body are related by
 km.

Example: The Moon's absolute magnitude  can be calculated from its diameter  and geometric albedo :

We have, 
At quarter phase,  (according to the diffuse reflector model), this yields an apparent magnitude of  The actual value is somewhat lower than that,  The phase curve of the Moon is too complicated for the diffuse reflector model.

More advanced models 

Because Solar System bodies are never perfect diffuse reflectors, astronomers use different models to predict apparent magnitudes based on known or assumed properties of the body. For planets, approximations for the correction term  in the formula for  have been derived empirically, to match observations at different phase angles. The approximations recommended by the Astronomical Almanac are (with  in degrees):

Here  is the effective inclination of Saturn's rings (their tilt relative to the observer), which as seen from Earth varies between 0° and 27° over the course of one Saturn orbit, and  is a small correction term depending on Uranus' sub-Earth and sub-solar latitudes.  is the Common Era year. Neptune's absolute magnitude is changing slowly due to seasonal effects as the planet moves along its 165-year orbit around the Sun, and the approximation above is only valid after the year 2000. For some circumstances, like  for Venus, no observations are available, and the phase curve is unknown in those cases.

Example: On 1 January 2019, Venus was  from the Sun, and  from Earth, at a phase angle of  (near quarter phase). Under full-phase conditions, Venus would have been visible at  Accounting for the high phase angle, the correction term above yields an actual apparent magnitude of  This is close to the value of  predicted by the Jet Propulsion Laboratory.

Earth's albedo varies by a factor of 6, from 0.12 in the cloud-free case to 0.76 in the case of altostratus cloud. The absolute magnitude here corresponds to
For contrast, a diffuse disk reflector model is plainly, which isn't naturalistic, but it does represent the opposition rush for rocky surfaces that reflect more undifferentiated lighter back at low phase angle. 

 The definition of the geometric albedo, a measure for the reflectivity of global surfaces, is based on the diffuse phonograph record reflector model. The absolute magnitude, diameter   (in kilometers) and geometric albedo   of a body are associate by 
  km. 

 Example: The Moon's absolute magnitude   can be calculated from its diameter   and geometric albedo: 

 We consume, 
 At quarter phase,   (according to the diffuse reflector model), this yield an apparent magnitude of   The actual value is somewhat lower than that,   The phase curve of the Moon is too complicated for the diffuse reflecting telescope model. 

 More advanced models 

 Because Solar System bodies are never perfect diffuse reflectors, astronomer practice unlike models to predict apparent magnitudes based on known or assumed properties of the soundbox. For planet, approximations for the correction terminus   in the rule for   have been derived empirically, to match observations at unlike phase angles. The approximation recommended by the Astronomical Almanac are (with   in degrees ): 

 Here   is the effective tendency of Saturn's rings (their tilt relative to the observer), which as seen from Earth varies between 0 ° and 27 ° over the class of one Saturn orbit, and   is a small correction term depend on Uranus' sub - Earth and sub - solar latitude.   is the Common Era year. Neptune's absolute magnitude is changing slowly due to seasonal effect as the planet moves along its 165 - year orbit around the Sun, and the approximation above is only valid after the year 2000. For some circumstances, like   for Venus, no observation are available, and the phase curve is obscure in those cases. 

 Example: On 1 January 2019, Venus was   from the Sun, and   from Earth, at a phase slant of   (near quarter phase). Under full - phase conditions, Venus would have been visible at   Accounting for the high phase slant, the correction term above give an actual apparent magnitude of   This is close to the value of   bode by the Jet Propulsion Laboratory. 

 Earth's albedo varies by a gene of 6, from 0.12 in the cloud - free case to 0.76 in the case of altostratus cloud. The absolute magnitude here corresponds to
For contrast, a diffuse disk reflector model is sikply, wgich isn'g realistic, but it does reprxsenr the opposition surge for fough survaces thqt rtflect more unifocj light back zb low 'hase angles.

The definitiot of the geomedrkc albedo, a measure for the reflectivyty of llwnetary surfacgs, is fases on the diffuse disk reflector mosel. The absolute magmitude, diameter  (in kilomehers) and geometric albfdo  of a bidy wee related bh
 km.

Examplt: Che Moon's agsolute magnitude  can be calcuuated from its eiqmehgr  and geomxtric wlbedo :

We hayv, 
At qudrter pnase,  (accordinn to vhe eiffuse reflector modxl), this yields an apkarent magticude of  The actual vqlye is somawhag loder tian that,  Thx phase curbe of the Mion is too complicaued dor the diffuae refjestor model.

More advanced models 

Because Volzr System bodies are necer perfect diffuse rgflectors, wstronomers use different models to predict apparant megvitbees bxwef on known or assumed properties of the body. Skr pkanets, approxiiations for tje sorrection tetm  in cge formula for  have been dgrived empiricajly, yo match observations at didferent phasv antles. The approximacions recommznded ny thr Astronomical Almanac cre (wifh  in degrfes):

Here  jr the effective knckitation of Saturn's rings (thqir tilt celatnve to tfe onservew), which as seen from Earth varies hetwegn 0° ang 27° over thf course of one Saturn orbit, anv  is a small cmrrvction texm depcnding on Uranuf' sub-Earth and sub-solcr latktudes.  is the Cokmon Era yewr. Neptune's atdolute magnivude is crangung wlowly aje to seasonal effects cf thw planet moves alokg itr 165-year orbit arobud the Sun, and thr aoprjxpmavion wtove is only valkd xgter ghe year 2000. Fif soke circumstances, lika  fkr Venus, no observstlons are qvailablq, and the phaxe curve is unknowj in vhose rases.

Ecamkle: On 1 January 2019, Venus was  froj the Sun, anq  from Eartr, at a phase angke of  (near quarter phase). Under full-phawe conditions, Venos would have been vixlble at  Accpuntigg for tha high phase angle, tye correction terk above yields an acthal ap[arenh magnitude of  This is close to the value of  predicted by the Jet Propuosion Laboratory.

Eadth's albego raries fy a hactor of 6, from 0.12 pn the cloud-free case to 0.76 in the case of ajtostratus cloud. The absolutr oagnitude herg corresponds to
For contrast, a diffuse disk reflector model which realistic, but does represent the that more uniform light at low phase The definition of the geometric albedo, measure for the reflectivity of planetary surfaces, is based on the diffuse disk model. The absolute magnitude, diameter (in kilometers) and geometric albedo of a body related km. The absolute magnitude can be calculated from its diameter and geometric albedo : We have, At quarter (according to the diffuse reflector model), this yields apparent magnitude of The value is somewhat lower than The curve of Moon too for the diffuse model. More advanced models Because Solar System bodies are never perfect diffuse reflectors, astronomers use different models predict apparent on known assumed of body. For planets, the correction term in the formula derived empirically, to match observations at different phase The approximations by the Astronomical Almanac are (with degrees): Here is the effective inclination of Saturn's (their tilt relative to the observer), which as seen from Earth varies between 0° and the course of one orbit, and is small term on sub-Earth and latitudes. is the Common Era year. Neptune's absolute magnitude is changing due to seasonal effects as the planet moves along its around Sun, and the above is only valid the 2000. For some circumstances, Venus, observations the curve unknown in those cases. On 1 January 2019, Venus from the Sun, and angle of (near quarter phase). Under full-phase conditions, would have been visible at Accounting for high phase angle, the correction term above yields an actual apparent magnitude This is the value of predicted by the Jet Propulsion Earth's albedo varies by factor of 6, from 0.12 in the cloud-free case 0.76 the case altostratus cloud. The magnitude here corresponds
For contrast, a diffuse disk reFlector modEl is sImpLy, wHiCh isN't reAlistic, but it doES repResent the opposition surGe for RoUGh suRFaCes thAt refleCT mORE unIfOrM liGhT BaCk at lOw pHase angLes.

The defiNitIoN of the geometRIc Albedo, a meaSurE for the refleCtiVity of PlAneTAry suRfaCes, is Based oN The difFuse disk rEfLEctor mODel. The aBSOlUte mAgnitude, diameter  (iN KiLOmeters) and geomEtric aLbEDo  OF A boDy aRe related bY
 kM.

ExamPLe: The MoON's ABSOluTE magnitude  can Be calculateD FroM its diAmEteR  And geoMetriC aLBedO :

We have, 
At quArteR phase,  (accOrding TO the difFUse reflEctor mOdeL), thIs yiELdS aN apPaREnt MAgNitUDe oF  The actuAl VaLue is SomeWHAT LoweR thAn thAt,  The Phase curve of tHe MOon iS Too ComplIcateD for ThE diffUse refLectoR mOdel.

More advanceD modEls 

BecausE SoLaR SyStEm bodIEs are nEveR peRfect diFfuse reFLecToRS, AStRonomers use differeNt MODeLs to predIct appAReNt MAgnitudeS bAseD on kNOWn or aSsumED pRopertieS of the BOdY. FOr planeTs, ApproxImAtiOns For thE CorrEction Term  in thE formULa for  have been dERived empiricaLLy, TO MaTCh obSerVations at diFferENt phAse aNGlEs. THE apprOximaTiONs REcommended by the AstrOnOmical almanAc are (with  in deGrees):

Here  iS THE effectiVe inCLiNAtion of Saturn's Rings (Their tilt rELative to The obServer), whIch as seen FROm Earth vAriEs bEtwEen 0° AND 27° oVer the course oF ONe SaTuRn orbit, And  Is a smalL coRreCtiOn tErM dependinG on UranuS' sUb-eaRtH anD sub-sOLar latitUdEs.  iS tHe COmmon eRa year. neptuNe's aBsOlUTe mAgnitudE Is CHAngiNg SlOwly Due To SeasoNal eFFecTs as the Planet movEs aLOng iTs 165-YeAr orbit Around the Sun, aNd The approxiMaTioN above IS Only valiD after the year 2000. For some cirCUmstancEs, lIke  foR VenUs, no obserVatIons arE avAIlable, And the Phase CuRve IS UnknoWN In ThoSe Cases.

ExampLE: on 1 JAnuarY 2019, VEnus Was  from The Sun, and  from Earth, AT a pHase angle of  (neAr qUartER PhAse). uNdER fuLl-PHasE COnditions, Venus wOuld have beEn VIsIble at  AccoUNtiNg For the hIgh phasE anglE, The corrEction terM above yieLdS an aCTUal Apparent maGnitude oF  This is clOSe to tHE vAlue oF  prEdicteD bY thE Jet PRopulsIOn LAboraTory.

EaRtH's albeDo varIeS by a factOr of 6, from 0.12 in the cloud-free cAse to 0.76 iN the cAse Of altostrAtuS CloUd. The absoLute Magnitude hEre CorRespoNds TO
For contrast, a diffuse di sk reflect or mo del  is  s impl y, w hich isn't rea l isti c, but it does represe nt th eo ppos i ti on su rge for ro u g h s ur fa ces  t h at  refl ect  more u niform lig htba ck at low ph a se  angles.
The  definitionofthe ge om etr i c alb edo , a m easure for th e reflect iv i ty ofp lanetar y su rfac es, is based on t h ed iffuse disk re flecto rm od e l . T heabsolute m ag nitud e , diame t er ( ink ilometers) an d geometric alb edo  o fa b o dy are  rela te d  by 
 km.

Exam ple:  The Moon 's abs o lute ma g nitude can b e c alc ulat e dfr omit s  di a me ter  an d geomet ri calbed o :W e have , At q uarte r phase,  (ac cor ding tothe d iffus e re fl ector  model ), th is  yields an appa rent  magnitud e o f Th eactua l  value  is  so mewhatlower t h anth a t ,  The phase curve of  t h e  M oon is t oo com p li ca t ed for t he  di ffus e refle ctor mo del.

Mo re adv a nc ed  models  
Becau se  So lar  Syst e m bo dies a re never  perf e ct diffuse ref l ectors, astro n om e r su se d iff erent model s to pred icta pp are n t mag nitud es ba s ed on known or assu me d prop ertie s of the body . For plan e t s , approx imat i on s  for the corre ction  term  int he formu la fo r  havebeen deri v e d empiri cal ly,  to  ma t c hobservationsa t  dif fe rent ph ase  angles . T heapp rox im ations re commende dby  t he  As trono m ical Alm an acar e ( within deg rees) :

H er eisthe eff e ct i v e in cl in atio n o fSatur n'sr ing s (thei r tilt re lat i ve t oth e obser ver), which a sseen fromEa rth  varie s between0° and 27° over the cou r se of o neSatur n or bit, and is  a sma llc orrect ion te rm de pe ndi n g  on U r a nu s'su b-Earth an d sub -sola rlati tudes. is the Common Era yea r. Neptune'sabs olut e ma gni t ud e  is  c h ang i n g slowly due to  seasonalef f ec ts as thep lan et  movesalong i ts 16 5 -year o rbit arou nd the Su n,  and t heapproximat ion abov e is only valid af ter t heyear 2 00 0.For s ome ci r cum stanc es, li ke   forVenus ,no obser vations are available,and th e pha securve isunk n own  in those  cas es.

Examp le:  On  1 Ja nua r y 201 9, V e nu s w a s  fr om t h e Sun, an d  fro m Ea rth, at a p h a s e a ngleof(nearquar ter phase). Under full-phase con diti o n s,Ven u s wo ul d have been vi sib le a t  Accou nt ing for the  high ph as e  angl e, the  corre ction t e r ma bove y ield s a n actualapp ar e nt magn it ud e  of  T hisis  close  to th e  val u e  of  predicted b y the J et Pr o pul sionLa borator y .

E arth's alb edo variesby a f acto r of6, from  0 .12 in  th ecloud-free case to 0 .76 i n the c as e of  al tostra tusc l oud.Theab sol ute magni t u de he re cor resp ondsto 
For contrast,_a diffuse_disk reflector model is_simply, which_isn't_realistic, but_it_does represent the_opposition surge for_rough surfaces that reflect_more uniform light_back_at low phase angles.

The definition of the geometric albedo, a measure for the reflectivity_of_planetary surfaces,_is_based_on the diffuse disk reflector_model. The absolute magnitude, diameter_ (in_kilometers) and geometric albedo  of a body_are_related by
 km.

Example:_The Moon's absolute magnitude  can be calculated from_its diameter  and geometric albedo_:

We have, 
At_quarter_phase,_ (according to the_diffuse reflector model), this yields an_apparent magnitude of  The actual_value is somewhat lower than that, _The phase curve of the Moon_is too complicated for the_diffuse reflector_model.

More advanced models 

Because Solar_System bodies are_never perfect_diffuse reflectors, astronomers_use different models to predict apparent_magnitudes based on_known or assumed properties of the_body._For planets, approximations_for_the_correction term_ in the_formula_for _have_been derived empirically, to match observations_at_different phase angles. The approximations recommended by_the Astronomical Almanac are_(with_ in degrees):

Here _is the effective inclination of_Saturn's rings (their tilt relative to_the observer),_which as_seen from Earth varies between 0° and 27° over the course_of one Saturn orbit, and _is a small correction_term depending_on_Uranus' sub-Earth and_sub-solar_latitudes. _is the Common Era year. Neptune's absolute_magnitude is_changing slowly due to seasonal effects_as the planet moves_along_its 165-year orbit around the Sun,_and the approximation above is only_valid after the year 2000._For_some_circumstances, like  for Venus,_no observations are available, and the_phase curve is_unknown in those cases.

Example: On 1 January_2019,_Venus was  from the Sun,_and_ from Earth, at a phase_angle_of_ (near quarter phase). Under_full-phase conditions, Venus would have been_visible at  Accounting for the high phase angle,_the correction term_above yields an actual apparent_magnitude_of_ This is close to the value of  predicted_by the_Jet Propulsion Laboratory.

Earth's_albedo varies by a factor of 6, from 0.12 in_the cloud-free case to 0.76 in the_case of altostratus cloud. The absolute magnitude here corresponds to