Solar System by apparent size: Difference between revisions

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Theoretical maximum angular diameters of Solar System objects.
Theoretical maximum angular diameters of Solar System objects.


# 34.142318167759912317334133764235' (Terran Satellite Luna)
# (34.142318167779726305388597288522 ± 0.0099504175490098189823746848993722)' ('''Terran Satellite Luna''')
# 32.547126271128421347619794544615' (Star Sol)
# (32.549089711594099381629815789191 ± 0.0030383154609148420537653582447128)' ('''Star Sol''')
# 1.0906123267366001865954297950335' (Planet Venus)
# (1.0905870349499817398048629211605 ± 0.00018025944492847952922209945619809)' ('''Planet Venus''')
# 50.115577292011594309068223040747" (Planet Jupiter)
# (50.115577292011611607058157849591 ± 0.00072639900116543009038607598428538)" ('''Planet Jupiter''')
# 25.685340680612365924690116419971" (Planet Mars)
# (25.700544451492779197449676308284 ± 0.00089158765308439455528175641371082)" ('''Planet Mars''')
# 20.710914369111405511819166681816" (Planet Saturn)
# (20.710741843720512704721266748230 ± 0.0005166370410419963595958474095447)" ('''Planet Saturn''')
# 13.030602889883030119235614459212" (Planet Mercury)
# (13.028474261955706245938397191101 ± 0.00084298180037579706377958565685282)" ('''Planet Mercury''')
# 4.0812943165836861322325384913351" (Planet Uranus)
# (4.0813037952907347294343994483903 ± 0.0006389298287894383982434815333879)" ('''Planet Uranus''')
# 2.3714321979272179525305286226839" (Planet Neptune)
# (2.3717005756662317185122893669135 ± 0.0023358462167698838697425224493574)" ('''Planet Neptune''')
# 1.8500081168516257242353190047029" (Jovian Satellite Ganymede)
# (1.8500081168516263639525877660944 ± 0.00021081697115976641880998036484687)" ('''Jovian Satellite Ganymede''')
# 1.6950999034452030297333809970279" (Jovian Satellite Callisto)
# (1.6950999034452036167094676830048 ± 0.0010549338656223241325822742019151)" ('''Jovian Satellite Callisto''')
# 1.2758186006115161532107678507247" (Jovian Satellite Io)
# (1.2758186006115165938918458891654 ± 0.000035409569728211189330416823094472)" ('''Jovian Satellite Io''')
# 1.0953739293038257329442022843157" (Jovian Satellite Europa)
# (1.0956010972639616311861538720115 ± 0.00035099902326891557679784173552623)" ('''Jovian Satellite Europa''')
# 0.88572560775248785404142250762448" (Saturnian Satellite Titan)
# (0.92630435820787173323928340729414 ± 0.0059958010235239682526821091198236)" ('''Minor Planet Ceres''')
# (0.88573281563080150908143581596940 ± 0.00003509052596514345590963105473037)" ('''Saturnian Satellite Titan''')
# (0.75246410914813015641116728905938 ± 0.016972874643896973338196523745709)" ('''Minor Planet Pallas''')
# (0.69117155722191649628751546195186 ± 0.00012417891897229293892065704030910)" ('''Minor Planet Vesta''')


''Angular diameters of triaxial ellipsoids are calculated with the middle radius (second equatorial radius).''
''Angular diameters of triaxial ellipsoids are calculated with the middle radius (second equatorial radius).''
Line 65: Line 68:


* <var>α</var> = (4.537303418331E12 ± 1.495978707E9) m = 30.33 AU
* <var>α</var> = (4.537303418331E12 ± 1.495978707E9) m = 30.33 AU
* <var>D</var><sub>min</sub> = (4.3074085441804699548183710495541E12 ± 3.3451100817443899547256709114980E9) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>D</var><sub>min</sub> = (4.3074085441804699548183710495541E12 ± 3.345110081744389954725670911498E9) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>μ</var> = (4.498407971949E12 ± 1.495978707E9) m = 30.07 AU
* <var>μ</var> = (4.498407971949E12 ± 1.495978707E9) m = 30.07 AU
* <var>π</var> = (4.459512525567E12 ± 3.3451100817442404828061181678871E9) m = 2<var>μ</var> − <var>α</var>
* <var>π</var> = (4.459512525567E12 ± 3.3451100817442404828061181678871E9) m = 2<var>μ</var> − <var>α</var>
Line 88: Line 91:
Planet Venus.
Planet Venus.


* <var>m</var> = 4.8675 Rg
* <var>α</var> = (1.089391142160591E11 ± 149597.8707) m = 0.728213 AU
* <var>P</var> = 20.99715264 Ms = 243.0226 d
* <var>D</var><sub>min</sub> = (3.8152950397410854818371049554083E10 ± 149614.58123466437589632427285545) m = <var>π</var><sub>0</sub> − <var>α</var> − <var>r</var><sub>max,0</sub>
* <var>r</var><sub>e</sub> = 6.0518001540473630205875615870764 Mm = (6.0518 Mm)([5<var>n</var><sub><var>π</var></sub><sup>2</sup>{6.0518 Mm}<sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)
* <var>m</var> = (4867.5 ± 0.2)E21 kg
* <var>α</var> = 108.94 Gm
* <var>P</var> = (2.099715264E7 ± 8.64) s = 243.0226 d
* <var>d</var><sub>min</sub> = 38.152065613470157943072323733871 Gm = <var>π</var><sub>0</sub> − <var>α</var> − <var>r</var><sub>max,0</sub>
* <var>r</var> = (6051.8 ± 1.0) km
* <var>r</var><sub>e</sub> = (6.0518001540473630205875615870764E6 ± 1000.0000254548036656428002788472) m = <var>r</var>([5<var>n</var><sub><var>π</var></sub><sup>2</sup><var>r</var><sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)


=== Mars ===
=== Mars ===
Line 98: Line 102:
Planet Mars.
Planet Mars.


* <var>r</var><sub>e</sub> = 3.3962 Mm
* <var>α</var> = 249261000 km
* <var>π</var> = 206.650 Gm
* <var>D</var><sub>min</sub> = (5.4513750613469954818371049554083E10 ± 1.0000024999969000413077806658572E6) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>d</var><sub>min</sub> = 54.546018613470157943072323733871 Gm = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>μ</var> = 227939366 km
* <var>π</var> = (2.06617732E11 ± 1.000001999998000003999990000028E6) m = 2<var>μ</var> − <var>α</var>
* <var>r</var><sub>e</sub> = (3396.2 ± 0.1) km


=== Ganymede ===
=== Ganymede ===
Line 106: Line 112:
Jovian Satellite Ganymede.
Jovian Satellite Ganymede.


* <var>m</var> = 148.19 Yg
* <var>α</var> = 1071600 km
* <var>P</var> = 618.153375744 ks = 7.15455296 d
* <var>D</var><sub>min</sub> = (5.8741941861346995481837104955408E11 ± 2.2383031519434649777754012812165E6) m = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
* <var>r</var> = 2.6343095368525535298979659694619 Mm = (2.6341 Mm)([5<var>n</var><sub><var>π</var></sub><sup>2</sup>{2.6341 Mm}<sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)
* <var>m</var> = 1.4819E23 kg
* <var>α</var> = 1.0716 Gm
* <var>P</var> = (618153.375744 ± 0.000864) s = 7.15455296 d
* <var>d</var><sub>min</sub> = 587.41941861347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
* <var>r</var> = (2634.1 ± 0.3) km
* <var>r</var><sub>e</sub> = (2.6343095368525535298979659694619E6 ± 300.02387325122667051910573765993) m = <var>r</var>([5<var>n</var><sub><var>π</var></sub><sup>2</sup><var>r</var><sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)


=== Titan ===
=== Titan ===
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Saturnian Satellite Titan.
Saturnian Satellite Titan.


* <var>r</var> = 2.57473 Mm
* <var>α</var> = 1257060 km
* <var>α</var> = 1.25706 Gm
* <var>D</var><sub>min</sub> = (1.1991989586134699548183710495541E12 ± 2.2360682033426441307778286882709E7) m = <var>d</var><sub>min,Saturn</sub> − <var>α</var>
* <var>d</var><sub>min</sub> = 1.1991889586134701579430723237339 Tm = <var>d</var><sub>min,Saturn</sub> − <var>α</var>
* <var>m</var> = (1.3452 ± 0.0002)E23 kg
* <var>P</var> = (1.377648E6 ± 86.4) s = 15.945 d
* <var>r</var> = (2574.73 ± 0.09) km
* <var>r</var><sub>e</sub> = (2.5747724234666186838664982852257E6 ± 90.001483410749923414670832269485) m = <var>r</var>([5<var>n</var><sub><var>π</var></sub><sup>2</sup><var>r</var><sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)


=== Mercury ===
=== Mercury ===
Line 124: Line 134:
Planet Mercury.
Planet Mercury.


* <var>r</var><sub>e</sub> = 2.4407983592616677504877194737632 Mm = −2(2.4397 Mm)/(0.0009 − 2)
* <var>α</var> = (6.98168774620779E10 ± 149597.8707) m = 0.466697 AU
* <var>α</var> = 69.82 Gm
* <var>D</var><sub>min</sub> = (7.7275187151392054818371049554083E10 ± 149614.58123466437589632427285545) m = <var>π</var><sub>0</sub> − <var>α</var> − <var>r</var><sub>max,0</sub>
* <var>d</var><sub>min</sub> = 77.272065613470157943072323733871 Gm = <var>π</var><sub>0</sub> − <var>α</var> − <var>r</var><sub>max,0</sub>
* <var>f</var> = 0.0009
* <var>r</var> = (2439.4 ± 0.1) km
* <var>r</var><sub>e</sub> = (2.440498224200890400680306137762E6 ± 157.83692583384913207056767644741) m = −2<var>r</var>/(<var>f</var> − 2)


=== Callisto ===
=== Callisto ===
Line 132: Line 144:
Jovian Satellite Callisto.
Jovian Satellite Callisto.


* <var>m</var> = 107.5938 Yg
* <var>α</var> = 1897000 km
* <var>P</var> = 1.44193118976 Ms = 16.6890184 d
* <var>D</var><sub>min</sub> = (5.8659401861346995481837104955408E11 ± 2.4494899469073250448631436724676E6) m = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
* <var>r</var> = 2.4103371835504931845570782568187 Mm = (2.4103 Mm)([5<var>n</var><sub><var>π</var></sub><sup>2</sup>{2.4103 Mm}<sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)
* <var>m</var> = (1.075938 ± 0.000137)E23 kg
* <var>α</var> = 1.897 Gm
* <var>P</var> = (1.44193118976E6 ± 0.00864) s = 16.6890184 d
* <var>d</var><sub>min</sub> = 586.59401861347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
* <var>r</var> = (2410.3 ± 1.5) km
* <var>r</var><sub>e</sub> = (2.4103371835504931845570782568187E6 ± 1500.0231420222554972182057151537) m = <var>r</var>([5<var>n</var><sub><var>π</var></sub><sup>2</sup><var>r</var><sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)


=== Io ===
=== Io ===
Line 142: Line 155:
Jovian Satellite Io.
Jovian Satellite Io.


* <var>r</var><sub>e,<var>b</var></sub> = 1.8187 Mm = (3.6374/2) Mm
* <var>α</var> = 423400 km
* <var>α</var> = 423.4 Mm
* <var>D</var><sub>min</sub> = (5.8806761861346995481837104955408E11 ± 2.2383031519434649777754012812165E6) m = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
* <var>d</var><sub>min</sub> = 588.06761861347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
* <var>r</var><sub>e,<var>b</var></sub> = (1.8187E6 ± 50) m = (3637.4 km)/2


=== Luna ===
=== Luna ===
Line 150: Line 163:
Terran Satellite Luna.
Terran Satellite Luna.


* <var>r</var><sub>e</sub> = 1.7381 Mm
* <var>D</var><sub>min</sub> = (3.5001561346995481837104955408288E8 ± 100000.00000025033557888708846853) m = <var>π</var><sub>min</sub> − <var>r</var><sub>max,0</sub>
* <var>π</var><sub>min</sub> = 356.4 Mm
* <var>π</var><sub>min</sub> = 356400 km
* <var>d</var><sub>min</sub> = 350.01561347015794307232373387065 Mm = <var>π</var><sub>min</sub> − <var>r</var><sub>max,0</sub>
* <var>r</var><sub>e</sub> = 1738.1 km


=== Europa ===
=== Europa ===
Line 158: Line 171:
Jovian Satellite Europa.
Jovian Satellite Europa.


* <var>r</var> = 1.5608 Mm
* <var>α</var> = 676938 km
* <var>α</var> = 676.938 Mm
* <var>D</var><sub>min</sub> = (5.8781408061346995481837104955408E11 ± 2.2360684247133516703616997354357E6) m = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
* <var>d</var><sub>min</sub> = 587.81408061347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
* <var>m</var> = 4.79984E22 kg
* <var>P</var> = (306822.0384 ± 0.0864) s = 3.551181 d
* <var>r</var> = (1560.8 ± 0.5) km
* <var>r</var><sub>e</sub> = (1.5611236919764961281816837445995E6 ± 500.10379105762958101929535520387) m = <var>r</var>([5<var>n</var><sub><var>π</var></sub><sup>2</sup><var>r</var><sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)
 
=== Triton ===
 
Neptunian Satellite Triton.
 
* <var>α</var> = (3.54764676144E8 ± 1061.077729639539649875635565355) m = (<var>e</var> + 1)<var>μ</var>
* <var>D</var><sub>min</sub> = (4.3070537795043259548183710495541E12 ± 3.3451100817445582430511405849429E9) m = <var>d</var><sub>min,Neptune</sub> − <var>α</var>
* <var>δ</var><sub>e,max</sub> = (0.12964301445610937405886506320230 ± 0.00013255405415211872345259729107566)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>e</var> = 0.000016
* <var>m</var> = (2.1389 ± 0.0028)E22 kg
* <var>μ</var> = 354759 km
* <var>P</var> = (507760.1856 ± 0.0864) s = 5.876854 d
* <var>r</var> = (1353.4 ± 0.9) km
* <var>r</var><sub>e</sub> = (1.3535499476595055629104446323691E6 ± 900.09978509397542743014661489434) m = <var>r</var>([5<var>n</var><sub><var>π</var></sub><sup>2</sup><var>r</var><sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)
 
=== Pluto ===
 
Minor Planet Pluto.
 
* <var>α</var> = 7.37593E9 km
* <var>D</var><sub>min</sub> = (4.2847260186134699548183710495541E12 ± 2.2360679797358577847444035813535E7) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>δ</var><sub>e,max</sub> = (0.11442039523774482823901011264408 ± 0.000077033637152452133799197524223804)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>m</var> = (1.3025 ± 0.0006)E22 kg
* <var>μ</var> = 5.90638E9 km
* <var>P</var> = (551856.672 ± 0.0864) s = 6.387230 d
* <var>π</var> = (4.43683E12 ± 2.2360679774997896964091736687313E7) m = 2<var>μ</var> − <var>α</var>
* <var>r</var> = (1188.3 ± 0.8) km
* <var>r</var><sub>e</sub> = (1.1884238844601665333822436493119E6 ± 800.08344398125573239541609846271) m = <var>r</var>([5<var>n</var><sub><var>π</var></sub><sup>2</sup><var>r</var><sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)
 
=== Titania ===
 
Uranian Satellite Titania.
 
* <var>α</var> = (4.363895010E8 ± 44725.780060273962761153068913132) m = (<var>e</var> + 1)<var>μ</var>
* <var>D</var><sub>min</sub> = (2.5830136291124699548183710495541E12 ± 1.0198137153196266465042571925247E7) m = <var>d</var><sub>min,Uranus</sub> − <var>α</var>
* <var>δ</var><sub>e,max</sub> = (0.12592207643833554251135657615094 ± 0.000095832468162855897894667048059053)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>e</var> = 0.0011
* <var>m</var> = (3.4550 ± 0.0509)E21 kg
* <var>μ</var> = 435910 km
* <var>P</var> = (752218.6176 ± 0.0864) s = 8.706234 d
* <var>r</var> = (788.4 ± 0.6) km
* <var>r</var><sub>e</sub> = (788448.70718447305101466061189134 ± 600.03750723732683370355217787133) m = <var>r</var>([5<var>n</var><sub><var>π</var></sub><sup>2</sup><var>r</var><sup>3</sup>/{3<var>Gm</var><var>P</var><sup>2</sup>}] + 1)
 
=== Rhea ===
 
Saturnian Satellite Rhea.
 
* <var>α</var> = (5.277712599964E8 ± 1002.6448083721024284511827755561) m = (<var>e</var> + 1)<var>μ</var>
* <var>D</var><sub>min</sub> = (1.1999282473534735548183710495541E12 ± 2.2360679819837693428021622512036E7) m = <var>d</var><sub>min,Uranus</sub> − <var>α</var>
* <var>δ</var><sub>e,<var>b</var>,max</sub> = (0.26224700443933629069282618928564 ± 0.000017870938636195757578407958897337)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>e</var> = 0.0012583
* <var>μ</var> = 527108 km
* <var>r</var><sub>e,<var>b</var></sub> = (762800 ± 50) m = (1525.6 km)/2


=== Iapetus ===
=== Iapetus ===
Line 166: Line 235:
Saturnian Satellite Iapetus.
Saturnian Satellite Iapetus.


* <var>r</var><sub>e</sub> = 746.00 km = (1.4920/2) Mm
* <var>α</var> = (3.659387770584E9 ± 10282.979105009792832064687157625) m = (<var>e</var> + 1)<var>μ</var>
* <var>α</var> = 3.659387770584 Gm = (0.0276812 + 1)(3.56082 Gm)
* <var>D</var><sub>min</sub> = (1.1967966308428859548183710495541E12 ± 2.2360682161769111021879173825542E7) m = <var>d</var><sub>min,Saturn</sub> − <var>α</var>
* <var>d</var><sub>min</sub> = 1.1967866308428861579430723237339 Tm = <var>d</var><sub>min,Saturn</sub> − <var>α</var>
* <var>δ</var><sub>e,max</sub> = (0.25714234397864741689302828177689 ± 0.000017891855224446917628298178731762)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>δ</var><sub>p,max</sub> = 0.25714449258506853269763466887060" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>e</var> = 0.0276812
* <var>μ</var> = 3560820 km
* <var>r</var><sub>e</sub> = (746000 ± 50) m = (1492.0 km)/2


=== Ceres ===
=== Ceres ===
Line 175: Line 246:
Minor Planet Ceres.
Minor Planet Ceres.


* <var>r</var><sub>e,<var>b</var></sub> = 481.0 km = (962.0/2) km
* <var>D</var><sub>min</sub> = (2.1421333263914595481837104955408E11 ± 1.3858488689381482206124694225818E9) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>π</var> = 381 Gm
* <var>e</var> = 0.116
* <var>d</var><sub>min</sub> = 228.89601861347015794307232373387 Gm = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>μ</var> = (4.14386101839E11 ± 1.495978707E9) m = 2.77 AU
* <var>δ</var><sub>p,max</sub> = 0.86688595464357998161003398040218" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>π</var> = (3.66317314025676E11 ± 1.3858488689377874308927240594534E9) m = (1 − <var>e</var>)<var>μ</var>
* <var>r</var><sub>e,<var>b</var></sub> = (481000 ± 100) m = ([962.0 ± 0.2] km)/2


=== Vesta ===
=== Vesta ===
Line 184: Line 256:
Minor Planet Vesta.
Minor Planet Vesta.


* <var>r</var><sub>e,<var>b</var></sub> = 278.6 km = (557.2/2) km
* <var>D</var><sub>min</sub> = (1.6628396935615610701237104955408E11 ± 1.3937551864984601676427401574957E6) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>π</var> = 322 Gm
* <var>e</var> = 0.098758
* <var>d</var><sub>min</sub> = 169.89601861347015794307232373387 Gm = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>μ</var> = (3.53276867636757E11 ± 1.495978707E6) m = 2.36151 AU
* <var>δ</var><sub>p,max</sub> = 0.67647700622350749837333046252586" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>π</var> = (3.18387950742686152194E11 ± 1.3937548277553363927812064795903E6) m = (1 − <var>e</var>)<var>μ</var>
* <var>r</var><sub>e,<var>b</var></sub> = (278600 ± 50) m = (557.2 km)/2


=== Pallas ===
=== Pallas ===
Line 193: Line 266:
Minor Planet Pallas.
Minor Planet Pallas.


* <var>r</var><sub>e,<var>b</var></sub></sub> = 266 km = (532/2) km
* <var>D</var><sub>min</sub> = (1.4583137665894186108381104955408E11 ± 42835.810460907372898385327366829) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>π</var> = 319 Gm
* <var>e</var> = 0.2812580
* <var>d</var><sub>min</sub> = 166.89601861347015794307232373387 Gm = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>μ</var> = (4.1452337284515432E11 ± 14959.78707) m = 2.7709176 AU
* <var>δ</var><sub>p,max</sub> = 0.65749247846134773534338734227922" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>π</var> = (2.9793535804547190626544E11 ± 42824.136392841763911853830943063) m = (1 − <var>e</var>)<var>μ</var>
* <var>r</var><sub>e,<var>b</var></sub></sub> = (266000 ± 6000) m = ([532 ± 12] km)/2
 
=== Hygiea ===
 
Minor Planet Hygiea.
 
* <var>D</var><sub>min</sub> = (2.5416712890433203721837104955408E11 ± 4.7018145369079983416485072354168E7) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>δ</var><sub>e,<var>b</var>,max</sub> = (0.34895884085642794334252320577349 ± 0.0081155786230332483023028347131361)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>e</var> = 0.1356
* <var>μ</var> = (4.7000359820784600E11 ± 1.495978707E6) m = 3.14178 AU
* <var>π</var> = (4.06271110290862082400E11 ± 4.7018145358445790571037145847674E7) m = (1 − <var>e</var>)<var>μ</var>
* <var>r</var><sub>e,<var>b</var></sub></sub> = (215000 ± 5000) m = ([430 ± 10] km)/2
 
=== Interamnia ===
 
Minor Planet Interamnia.
 
* <var>α</var> = 528 Gm
* <var>D</var><sub>min</sub> = (2.3429601861346995481837104955408E11 ± 1.0198039027190472563680375871356E9) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>δ</var><sub>e,<var>b</var>,max</sub> = (0.30636522549030376051566194015575 ± 0.0071680086934872835122149192626709)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>μ</var> = 457.2 Gm
* <var>π</var> = (3.864E11 ± 1.0198039027185569660056448218046E9) m = 2<var>μ</var> − <var>α</var>
* <var>r</var><sub>e,<var>b</var></sub></sub> = (174000 ± 4000) m = ([348 ± 8] km)/2
 
=== Davida ===
 
Minor Planet Davida.
 
* <var>α</var> = (5.623383959613E11 ± 1.495978707E8) m = 3.759 AU
* <var>D</var><sub>min</sub> = (2.3191375270036995481837104955408E11 ± 3.3451100817591876747613594681338E8) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>δ</var><sub>e,<var>b</var>,max</sub> = (0.26148450590163578376496130902861 ± 0.0018183519488171012974178530212999)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>μ</var> = (4.731780650241E11 ± 1.495978707E8) m = 3.163 AU
* <var>π</var> = (3.840177340869E11 ± 3.3451100817442404828061181678871E8) m = 2<var>μ</var> − <var>α</var>
* <var>r</var><sub>e,<var>b</var></sub></sub> = (147000 ± 1000) m = ([294 ± 2] km)/2
 
=== Eunomia ===
 
Minor Planet Eunomia.
 
* <var>α</var> = 469 Gm
* <var>D</var><sub>min</sub> = (1.6996955887506995481837104955408E11 ± 1.0437998331446962221295594512127E9) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>δ</var><sub>e,<var>b</var>,max</sub> = (0.30945262164076352844160432509796 ± 0.018302025092013898866195236722060)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>μ</var> = (3.955367701308E11 ± 1.495978707E8) m = 2.644 AU
* <var>π</var> = (3.220735402616E11 ± 1.0437998331442172030598520886818E9) m = 2<var>μ</var> − <var>α</var>
* <var>r</var><sub>e,<var>b</var></sub></sub> = (127500 ± 7500) m = ([255 ± 15] km)/2


=== Juno ===
=== Juno ===
Line 202: Line 320:
Minor Planet Juno.
Minor Planet Juno.


* <var>r</var><sub>e,<var>b</var></sub> = 125 km = (250/2) km
* <var>D</var><sub>min</sub> = (1.4489601861346995481837104955408E11 ± 1.0000000000500000025021057887489E8) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>δ</var><sub>p,max</sub> = (0.35588418546778994157428432646140 ± 0.0071219202030624044772353466753741)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>π</var> = 297.0 Gm
* <var>π</var> = 297.0 Gm
* <var>d</var><sub>min</sub> = 144.89601861347015794307232373387 Gm = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>r</var><sub>e,<var>b</var></sub> = (125000 ± 2500) m = ([250 ± 5] km)/2
* <var>δ</var><sub>p,max</sub> = 0.35588418546778944267259225024255" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
 
=== Bamberga ===
 
Minor Planet Bamberga.
 
* <var>α</var> = 537.718 Gm
* <var>D</var><sub>min</sub> = (1.1271601861346995481837104955408E11 ± 2.2360682011065874613956858897782E6) m = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>δ</var><sub>p,max</sub> = (0.41539890775119500822400183187286 ± 0.0054898595913885011434361461216848)" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>μ</var> = 401.269 Gm
* <var>π</var> = (2.6482E11 ± 2.2360679774997896964091736687313E6) m = 2<var>μ</var> − <var>α</var>
* <var>r</var> = (113500 ± 1500) m = ([227 ± 3] km)/2


== formulae ==
== formulae ==

Revision as of 13:33, 8 June 2024

maximum angular diameter

Theoretical maximum angular diameters of Solar System objects.

  1. (34.142318167779726305388597288522 ± 0.0099504175490098189823746848993722)' (Terran Satellite Luna)
  2. (32.549089711594099381629815789191 ± 0.0030383154609148420537653582447128)' (Star Sol)
  3. (1.0905870349499817398048629211605 ± 0.00018025944492847952922209945619809)' (Planet Venus)
  4. (50.115577292011611607058157849591 ± 0.00072639900116543009038607598428538)" (Planet Jupiter)
  5. (25.700544451492779197449676308284 ± 0.00089158765308439455528175641371082)" (Planet Mars)
  6. (20.710741843720512704721266748230 ± 0.0005166370410419963595958474095447)" (Planet Saturn)
  7. (13.028474261955706245938397191101 ± 0.00084298180037579706377958565685282)" (Planet Mercury)
  8. (4.0813037952907347294343994483903 ± 0.0006389298287894383982434815333879)" (Planet Uranus)
  9. (2.3717005756662317185122893669135 ± 0.0023358462167698838697425224493574)" (Planet Neptune)
  10. (1.8500081168516263639525877660944 ± 0.00021081697115976641880998036484687)" (Jovian Satellite Ganymede)
  11. (1.6950999034452036167094676830048 ± 0.0010549338656223241325822742019151)" (Jovian Satellite Callisto)
  12. (1.2758186006115165938918458891654 ± 0.000035409569728211189330416823094472)" (Jovian Satellite Io)
  13. (1.0956010972639616311861538720115 ± 0.00035099902326891557679784173552623)" (Jovian Satellite Europa)
  14. (0.92630435820787173323928340729414 ± 0.0059958010235239682526821091198236)" (Minor Planet Ceres)
  15. (0.88573281563080150908143581596940 ± 0.00003509052596514345590963105473037)" (Saturnian Satellite Titan)
  16. (0.75246410914813015641116728905938 ± 0.016972874643896973338196523745709)" (Minor Planet Pallas)
  17. (0.69117155722191649628751546195186 ± 0.00012417891897229293892065704030910)" (Minor Planet Vesta)

Angular diameters of triaxial ellipsoids are calculated with the middle radius (second equatorial radius).

data

Sol

Star Sol.

  • de = (1.392684E9 ± 130000) m = 2re
  • Dmin = (1.4709206461346995481837104955408E11 ± 2236.0679886951370999630683009086) m = π0 − rmax,0
  • re = (696342 ± 65) km

Jupiter

Planet Jupiter.

  • α = 816.363E6 km
  • Dmin = (5.8849101861346995481837104955408E11 ± 2.2360682011065874613956858897782E6) m = π − α0 − rmax,0
  • μ = 778.479E6 km
  • π = (7.40595E11 ± 2.2360679774997896964091736687313E6) m = 2μ − α
  • re = 71492 km

Saturn

Planet Saturn.

  • α = 1514.50E6 km
  • Dmin = (1.2004560186134699548183710495541E12 ± 2.2360679797358577847444035813535E7) m = π − α0 − rmax,0
  • μ = 1433.53E6 km
  • π = (1.35256E12 ± 2.2360679774997896964091736687313E7) m = 2μ − α
  • re = 60268 km

Uranus

Planet Uranus.

  • α = 3.00639E9 km
  • Dmin = (2.5834500186134699548183710495541E12 ± 1.0198039076214605781486501623154E7) m = π − α0 − rmax,0
  • μ = 2.870972E9 km
  • π = (2.735554E12 ± 1.0198039027185569660056448218046E7) m = 2μ − α
  • re = (25559 ± 4) km

Neptune

Planet Neptune.

  • α = (4.537303418331E12 ± 1.495978707E9) m = 30.33 AU
  • Dmin = (4.3074085441804699548183710495541E12 ± 3.345110081744389954725670911498E9) m = π − α0 − rmax,0
  • μ = (4.498407971949E12 ± 1.495978707E9) m = 30.07 AU
  • π = (4.459512525567E12 ± 3.3451100817442404828061181678871E9) m = 2μ − α
  • re = (24764 ± 15) km

Terra

Planet Terra.

  • α = 152097597 km
  • f = 0.0033528106647474807198455286185206 ± 1.1241339353644443553823696996327E-14 = 298.257223563−1
  • h = +6263.47 m
  • μ = 149598023 km
  • φ = −(0.025641801411647532015402479952681 ± 1.7453292519943295769236907684886E-8)r = −1.469167°
  • π = (1.47098449E11 ± 2236.0679774997896964091736687313) m = 2μ − α
  • re = 6378.1370 km
  • rmax = (6.3843865300451816289504459171215E6 ± 0.22375682286241097235424315226049) m = √([{cos(φ)re2}2 + {sin(φ)rp2}2]/[{cos(φ)re}2 + {sin(φ)rp}2]) + h
  • rp = (6.3567523142451794975639665996337E6 ± 0.099664718933551041988577273088083) m = −(f − 1)a

Venus

Planet Venus.

  • α = (1.089391142160591E11 ± 149597.8707) m = 0.728213 AU
  • Dmin = (3.8152950397410854818371049554083E10 ± 149614.58123466437589632427285545) m = π0 − α − rmax,0
  • m = (4867.5 ± 0.2)E21 kg
  • P = (2.099715264E7 ± 8.64) s = 243.0226 d
  • r = (6051.8 ± 1.0) km
  • re = (6.0518001540473630205875615870764E6 ± 1000.0000254548036656428002788472) m = r([5nπ2r3/{3GmP2}] + 1)

Mars

Planet Mars.

  • α = 249261000 km
  • Dmin = (5.4513750613469954818371049554083E10 ± 1.0000024999969000413077806658572E6) m = π − α0 − rmax,0
  • μ = 227939366 km
  • π = (2.06617732E11 ± 1.000001999998000003999990000028E6) m = 2μ − α
  • re = (3396.2 ± 0.1) km

Ganymede

Jovian Satellite Ganymede.

  • α = 1071600 km
  • Dmin = (5.8741941861346995481837104955408E11 ± 2.2383031519434649777754012812165E6) m = dmin,Jupiter − α
  • m = 1.4819E23 kg
  • P = (618153.375744 ± 0.000864) s = 7.15455296 d
  • r = (2634.1 ± 0.3) km
  • re = (2.6343095368525535298979659694619E6 ± 300.02387325122667051910573765993) m = r([5nπ2r3/{3GmP2}] + 1)

Titan

Saturnian Satellite Titan.

  • α = 1257060 km
  • Dmin = (1.1991989586134699548183710495541E12 ± 2.2360682033426441307778286882709E7) m = dmin,Saturn − α
  • m = (1.3452 ± 0.0002)E23 kg
  • P = (1.377648E6 ± 86.4) s = 15.945 d
  • r = (2574.73 ± 0.09) km
  • re = (2.5747724234666186838664982852257E6 ± 90.001483410749923414670832269485) m = r([5nπ2r3/{3GmP2}] + 1)

Mercury

Planet Mercury.

  • α = (6.98168774620779E10 ± 149597.8707) m = 0.466697 AU
  • Dmin = (7.7275187151392054818371049554083E10 ± 149614.58123466437589632427285545) m = π0 − α − rmax,0
  • f = 0.0009
  • r = (2439.4 ± 0.1) km
  • re = (2.440498224200890400680306137762E6 ± 157.83692583384913207056767644741) m = −2r/(f − 2)

Callisto

Jovian Satellite Callisto.

  • α = 1897000 km
  • Dmin = (5.8659401861346995481837104955408E11 ± 2.4494899469073250448631436724676E6) m = dmin,Jupiter − α
  • m = (1.075938 ± 0.000137)E23 kg
  • P = (1.44193118976E6 ± 0.00864) s = 16.6890184 d
  • r = (2410.3 ± 1.5) km
  • re = (2.4103371835504931845570782568187E6 ± 1500.0231420222554972182057151537) m = r([5nπ2r3/{3GmP2}] + 1)

Io

Jovian Satellite Io.

  • α = 423400 km
  • Dmin = (5.8806761861346995481837104955408E11 ± 2.2383031519434649777754012812165E6) m = dmin,Jupiter − α
  • re,b = (1.8187E6 ± 50) m = (3637.4 km)/2

Luna

Terran Satellite Luna.

  • Dmin = (3.5001561346995481837104955408288E8 ± 100000.00000025033557888708846853) m = πmin − rmax,0
  • πmin = 356400 km
  • re = 1738.1 km

Europa

Jovian Satellite Europa.

  • α = 676938 km
  • Dmin = (5.8781408061346995481837104955408E11 ± 2.2360684247133516703616997354357E6) m = dmin,Jupiter − α
  • m = 4.79984E22 kg
  • P = (306822.0384 ± 0.0864) s = 3.551181 d
  • r = (1560.8 ± 0.5) km
  • re = (1.5611236919764961281816837445995E6 ± 500.10379105762958101929535520387) m = r([5nπ2r3/{3GmP2}] + 1)

Triton

Neptunian Satellite Triton.

  • α = (3.54764676144E8 ± 1061.077729639539649875635565355) m = (e + 1)μ
  • Dmin = (4.3070537795043259548183710495541E12 ± 3.3451100817445582430511405849429E9) m = dmin,Neptune − α
  • δe,max = (0.12964301445610937405886506320230 ± 0.00013255405415211872345259729107566)" = 2asin(rp/dmin)
  • e = 0.000016
  • m = (2.1389 ± 0.0028)E22 kg
  • μ = 354759 km
  • P = (507760.1856 ± 0.0864) s = 5.876854 d
  • r = (1353.4 ± 0.9) km
  • re = (1.3535499476595055629104446323691E6 ± 900.09978509397542743014661489434) m = r([5nπ2r3/{3GmP2}] + 1)

Pluto

Minor Planet Pluto.

  • α = 7.37593E9 km
  • Dmin = (4.2847260186134699548183710495541E12 ± 2.2360679797358577847444035813535E7) m = π − α0 − rmax,0
  • δe,max = (0.11442039523774482823901011264408 ± 0.000077033637152452133799197524223804)" = 2asin(rp/dmin)
  • m = (1.3025 ± 0.0006)E22 kg
  • μ = 5.90638E9 km
  • P = (551856.672 ± 0.0864) s = 6.387230 d
  • π = (4.43683E12 ± 2.2360679774997896964091736687313E7) m = 2μ − α
  • r = (1188.3 ± 0.8) km
  • re = (1.1884238844601665333822436493119E6 ± 800.08344398125573239541609846271) m = r([5nπ2r3/{3GmP2}] + 1)

Titania

Uranian Satellite Titania.

  • α = (4.363895010E8 ± 44725.780060273962761153068913132) m = (e + 1)μ
  • Dmin = (2.5830136291124699548183710495541E12 ± 1.0198137153196266465042571925247E7) m = dmin,Uranus − α
  • δe,max = (0.12592207643833554251135657615094 ± 0.000095832468162855897894667048059053)" = 2asin(rp/dmin)
  • e = 0.0011
  • m = (3.4550 ± 0.0509)E21 kg
  • μ = 435910 km
  • P = (752218.6176 ± 0.0864) s = 8.706234 d
  • r = (788.4 ± 0.6) km
  • re = (788448.70718447305101466061189134 ± 600.03750723732683370355217787133) m = r([5nπ2r3/{3GmP2}] + 1)

Rhea

Saturnian Satellite Rhea.

  • α = (5.277712599964E8 ± 1002.6448083721024284511827755561) m = (e + 1)μ
  • Dmin = (1.1999282473534735548183710495541E12 ± 2.2360679819837693428021622512036E7) m = dmin,Uranus − α
  • δe,b,max = (0.26224700443933629069282618928564 ± 0.000017870938636195757578407958897337)" = 2asin(rp/dmin)
  • e = 0.0012583
  • μ = 527108 km
  • re,b = (762800 ± 50) m = (1525.6 km)/2

Iapetus

Saturnian Satellite Iapetus.

  • α = (3.659387770584E9 ± 10282.979105009792832064687157625) m = (e + 1)μ
  • Dmin = (1.1967966308428859548183710495541E12 ± 2.2360682161769111021879173825542E7) m = dmin,Saturn − α
  • δe,max = (0.25714234397864741689302828177689 ± 0.000017891855224446917628298178731762)" = 2asin(rp/dmin)
  • e = 0.0276812
  • μ = 3560820 km
  • re = (746000 ± 50) m = (1492.0 km)/2

Ceres

Minor Planet Ceres.

  • Dmin = (2.1421333263914595481837104955408E11 ± 1.3858488689381482206124694225818E9) m = π − α0 − rmax,0
  • e = 0.116
  • μ = (4.14386101839E11 ± 1.495978707E9) m = 2.77 AU
  • π = (3.66317314025676E11 ± 1.3858488689377874308927240594534E9) m = (1 − e)μ
  • re,b = (481000 ± 100) m = ([962.0 ± 0.2] km)/2

Vesta

Minor Planet Vesta.

  • Dmin = (1.6628396935615610701237104955408E11 ± 1.3937551864984601676427401574957E6) m = π − α0 − rmax,0
  • e = 0.098758
  • μ = (3.53276867636757E11 ± 1.495978707E6) m = 2.36151 AU
  • π = (3.18387950742686152194E11 ± 1.3937548277553363927812064795903E6) m = (1 − e)μ
  • re,b = (278600 ± 50) m = (557.2 km)/2

Pallas

Minor Planet Pallas.

  • Dmin = (1.4583137665894186108381104955408E11 ± 42835.810460907372898385327366829) m = π − α0 − rmax,0
  • e = 0.2812580
  • μ = (4.1452337284515432E11 ± 14959.78707) m = 2.7709176 AU
  • π = (2.9793535804547190626544E11 ± 42824.136392841763911853830943063) m = (1 − e)μ
  • re,b = (266000 ± 6000) m = ([532 ± 12] km)/2

Hygiea

Minor Planet Hygiea.

  • Dmin = (2.5416712890433203721837104955408E11 ± 4.7018145369079983416485072354168E7) m = π − α0 − rmax,0
  • δe,b,max = (0.34895884085642794334252320577349 ± 0.0081155786230332483023028347131361)" = 2asin(rp/dmin)
  • e = 0.1356
  • μ = (4.7000359820784600E11 ± 1.495978707E6) m = 3.14178 AU
  • π = (4.06271110290862082400E11 ± 4.7018145358445790571037145847674E7) m = (1 − e)μ
  • re,b = (215000 ± 5000) m = ([430 ± 10] km)/2

Interamnia

Minor Planet Interamnia.

  • α = 528 Gm
  • Dmin = (2.3429601861346995481837104955408E11 ± 1.0198039027190472563680375871356E9) m = π − α0 − rmax,0
  • δe,b,max = (0.30636522549030376051566194015575 ± 0.0071680086934872835122149192626709)" = 2asin(rp/dmin)
  • μ = 457.2 Gm
  • π = (3.864E11 ± 1.0198039027185569660056448218046E9) m = 2μ − α
  • re,b = (174000 ± 4000) m = ([348 ± 8] km)/2

Davida

Minor Planet Davida.

  • α = (5.623383959613E11 ± 1.495978707E8) m = 3.759 AU
  • Dmin = (2.3191375270036995481837104955408E11 ± 3.3451100817591876747613594681338E8) m = π − α0 − rmax,0
  • δe,b,max = (0.26148450590163578376496130902861 ± 0.0018183519488171012974178530212999)" = 2asin(rp/dmin)
  • μ = (4.731780650241E11 ± 1.495978707E8) m = 3.163 AU
  • π = (3.840177340869E11 ± 3.3451100817442404828061181678871E8) m = 2μ − α
  • re,b = (147000 ± 1000) m = ([294 ± 2] km)/2

Eunomia

Minor Planet Eunomia.

  • α = 469 Gm
  • Dmin = (1.6996955887506995481837104955408E11 ± 1.0437998331446962221295594512127E9) m = π − α0 − rmax,0
  • δe,b,max = (0.30945262164076352844160432509796 ± 0.018302025092013898866195236722060)" = 2asin(rp/dmin)
  • μ = (3.955367701308E11 ± 1.495978707E8) m = 2.644 AU
  • π = (3.220735402616E11 ± 1.0437998331442172030598520886818E9) m = 2μ − α
  • re,b = (127500 ± 7500) m = ([255 ± 15] km)/2

Juno

Minor Planet Juno.

  • Dmin = (1.4489601861346995481837104955408E11 ± 1.0000000000500000025021057887489E8) m = π − α0 − rmax,0
  • δp,max = (0.35588418546778994157428432646140 ± 0.0071219202030624044772353466753741)" = 2asin(rp/dmin)
  • π = 297.0 Gm
  • re,b = (125000 ± 2500) m = ([250 ± 5] km)/2

Bamberga

Minor Planet Bamberga.

  • α = 537.718 Gm
  • Dmin = (1.1271601861346995481837104955408E11 ± 2.2360682011065874613956858897782E6) m = π − α0 − rmax,0
  • δp,max = (0.41539890775119500822400183187286 ± 0.0054898595913885011434361461216848)" = 2asin(rp/dmin)
  • μ = 401.269 Gm
  • π = (2.6482E11 ± 2.2360679774997896964091736687313E6) m = 2μ − α
  • r = (113500 ± 1500) m = ([227 ± 3] km)/2

formulae

  • δp,max = 2asin(rp/dmin) = maximum polar angular diameter
  • dmin,S,0 = πS,0 − rmax,0 = minimum distance of Terran satellite
  • dmin,P,inf = π0 − αP,inf − rmax,0 = minimum distance of inferior planet
  • dmin,P,sup = πP,sup − α0 − rmax,0 = minimum distance of superior planet
  • dmin,S,sup = dmin,P,sup − αS,sup = minimum distance of superior satellite

constants

  • G = 6.67430 × 10−11 N·m2/kg2 = gravitational constant
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