Solar System by apparent size: Difference between revisions

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== maximum angular diameter ==
<u>[[Solar System]]</u> objects sorted by angular diameter (apparent diameter).&ensp; Objects with angular diameters greater than about 1 to ½ of an arcsecond and transiting satellites with angular diameters greater than about ½ to ¼ of an arcsecond can theoretically be resolved by amateur telescopes under ideal seeing conditions.


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


# 34.142318167759912317334133764235' (Terran Satellite Luna)
<ol start="0">
# 32.547126271128421347619794544615' (Star Sol)
<li>180°, '''Planet Terra'''</li>
# 1.0906123267366001865954297950335' (Planet Venus)
<li>(31.477633133877767054679096275868 ± 0.0029551128269606612047486105298695)', '''Star Sol'''</li>
# 50.115577292011594309068223040747" (Planet Jupiter)
<li>(29.819303636472614445417667957098 ± 0.0096862578055441211945453588402752)', '''Terran Satellite Luna'''</li>
# 25.685340680612365924690116419971" (Planet Mars)
<li>(33.159669076755426476443372392270 ± 0.0089971814843987142886486730713841)", '''Planet Jupiter'''</li>
# 20.710914369111405511819166681816" (Planet Saturn)
<li>(14.678686960924656270109313417449 ± 0.0049094002655546655235419837164275)", '''Planet Saturn'''</li>
# 13.030602889883030119235614459212" (Planet Mercury)
<li>(13.344787507099331456628082902984 ± 0.0022051026964193540301592173017059)", '''Planet Venus'''</li>
# 4.0812943165836861322325384913351" (Planet Uranus)
<li>(6.0096928766403224966258023933195 ± 0.00068019592882980055537539875878304)", '''Planet Mercury'''</li>
# 2.3714321979272179525305286226839" (Planet Neptune)
<li>(4.7698865620477542663584032367593 ± 0.00014196624060303258751810475960605)", '''Planet Mars'''</li>
# 1.8500081168516257242353190047029" (Jovian Satellite Ganymede)
<li>(3.4223653325507628807299127059015 ± 0.0027408759060746596099586009009516)", '''Planet Uranus'''</li>
# 1.6950999034452030297333809970279" (Jovian Satellite Callisto)
<li>(2.2118336467437559427103793771768 ± 0.0028217055150323473146748236149033)", '''Planet Neptune'''</li>
# 1.2758186006115161532107678507247" (Jovian Satellite Io)
<li>(1.3083628992194648224762369447488 ± 0.00014901868607682720204612762319518)", '''Jovian Satellite Ganymede'''</li>
# 1.0953739293038257329442022843157" (Jovian Satellite Europa)
<li>(1.1973524061827979954954456275039 ± 0.00074514868136640627492683703515084)", '''Jovian Satellite Callisto'''</li>
# 0.88572560775248785404142250762448" (Saturnian Satellite Titan)
<li>(0.90220478385668260139264206458912 ± 0.00074600044303443443093994586958067)", '''Jovian Satellite Io'''</li>
<li>(0.77505471560751979803462664785578 ± 0.00024828953386270602828053296700135)", '''Jovian Satellite Europa'''</li>
<li>(0.69779167912007910714815231706525 ± 0.000024814241932850107938927799477864)", '''Saturnian Satellite Titan'''</li>
</ol>


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


== data ==
<ol start="0">
<li>180°, '''Planet Terra'''</li>
<li>(34.142318167779726305388597288522 ± 0.0099504175490098189823746848993722)', '''Terran Satellite Luna'''</li>
<li>(32.549089711594099381629815789191 ± 0.0030383154609148420537653582447128)', '''Star Sol'''</li>
<li>(1.0905870349499817398048629211605 ± 0.00018025944492847952922209945619809)', '''Planet Venus'''</li>
<li>(50.115577292011611607058157849591 ± 0.00072639900116543009038607598428538)", '''Planet Jupiter'''</li>
<li>(25.700544451492779197449676308284 ± 0.00089158765308439455528175641371082)", '''Planet Mars'''</li>
<li>(20.710741843720512704721266748230 ± 0.0005166370410419963595958474095447)", '''Planet Saturn'''</li>
<li>(13.026519404358484128366613475607 ± 0.00068880719717083531267935096847384)", '''Planet Mercury'''</li>
<li>(4.0813037952907347294343994483903 ± 0.0006389298287894383982434815333879)", '''Planet Uranus'''</li>
<li>(2.3717005756662317185122893669135 ± 0.0023358462167698838697425224493574)", '''Planet Neptune'''</li>
<li>(1.8500081168516263639525877660944 ± 0.00021081697115976641880998036484687)", '''Jovian Satellite Ganymede'''</li>
<li>(1.6950999034452036167094676830048 ± 0.0010549338656223241325822742019151)", '''Jovian Satellite Callisto'''</li>
<li>(1.2758186006115165938918458891654 ± 0.000035409569728211189330416823094472)", '''Jovian Satellite Io'''</li>
<li>(1.0956010972639616311861538720115 ± 0.00035099902326891557679784173552623)", '''Jovian Satellite Europa'''</li>
<li>(0.92630435820787173323928340729414 ± 0.0059958010235239682526821091198236)", '''Minor Planet Ceres'''</li>
<li>(0.88573281563080150908143581596940 ± 0.00003509052596514345590963105473037)", '''Saturnian Satellite Titan'''</li>
<li>(0.75246410914813015641116728905938 ± 0.016972874643896973338196523745709)", '''Minor Planet Pallas'''</li>
<li>(0.69117155722191649628751546195186 ± 0.00012417891897229293892065704030910)", '''Minor Planet Vesta'''</li>
</ol>


=== Sol ===
* (0.26224700443933629069282618928564 ± 0.000017870938636195757578407958897337)", '''Saturnian Satellite Rhea'''
* (0.25714234397864741689302828177689 ± 0.000017891855224446917628298178731762)", '''Saturnian Satellite Iapetus'''


Star Sol.
== catalog ==


* <var>r</var><sub>e</sub> = 696.3 Mm
'''Number of Solar System objects by minimum angular diameter:'''
* <var>d</var><sub>min</sub> = 147.09206561347015794307232373387 Gm = <var>π</var><sub>0</sub> − <var>r</var><sub>max,0</sub>


=== Jupiter ===
* 8 objects (1 star, 6 planets, and 1 moon) are always at least 4 arcseconds in angular diameter.
* 10 objects (1 star, 8 planets, and 1 moon) are always at least 2 arcseconds in angular diameter.
* 12 objects (1 star, 8 planets, and 3 moons) are always at least 1 arcsecond in angular diameter.
* 15 objects (1 star, 8 planets, and 6 moons) are always at least 0.5 arcseconds in angular diameter.


Planet Jupiter.
'''Number of Solar System objects by maximum angular diameter:'''


* <var>r</var><sub>e</sub> = 71.492 Mm
* 9 objects (1 star, 7 planets, and 1 moon) can be at least 4 arcseconds in angular diameter.
* <var>π</var> = 740.595 Gm
* 10 objects (1 star, 8 planets, and 1 moon) can be at least 2 arcseconds in angular diameter.
* <var>d</var><sub>min</sub> = 588.49101861347015794307232373387 Gm = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* 14 objects (1 star, 8 planets, and 5 moons) can be at least 1 arcsecond in angular diameter.
* 18 objects (1 star, 8 major planets, 3 minor planets, and 6 moons) can be at least 0.5 arcseconds in angular diameter.


=== Saturn ===
== notes ==


Planet Saturn.
Minimum angular diameter is calculated using the polar radius and a theoretical maximum observable distance.&ensp; Maximum observable distance is simplified here as when there is a right angle between Sol (or the host planet for satellites of superior planets), the object, and the observer.&ensp; Otherwise the maximum distance between the object and observer is when the object is behind Sol (or the host planet for satellites of superior planets) and thus invisible (occulted).


* <var>r</var><sub>e</sub> = 60.268 Mm
Maximum angular diameter for inferior planets and satellites of superior planets is when those objects are in transit.&ensp; Maximum resolvable angular diameter for triaxial ellipsoids is calculated using the second equatorial radius.
* <var>π</var> = 1.35255 Tm
* <var>d</var><sub>min</sub> = 1.2004460186134701579430723237339 Tm = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>


=== Uranus ===
== see also ==


Planet Uranus.
* <u>[[Solar System by size]]</u>
 
* <u>[[Solar System data]]</u>
* <var>r</var><sub>e</sub> = 25.559 Mm
* <var>π</var> = 2.73556 Tm
* <var>d</var><sub>min</sub> = 2.5834560186134701579430723237339 Tm = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
 
=== Neptune ===
 
Planet Neptune.
 
* <var>r</var><sub>e</sub> = 24.764 Mm
* <var>π</var> = 4.46 Tm
* <var>d</var><sub>min</sub> = 4.3078960186134701579430723237339 Tm = <var>π</var> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
 
=== Venus ===
 
Planet Venus.
 
* <var>m</var> = 4.8675 Rg
* <var>P</var> = 20.99715264 Ms = 243.0226 d
* <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>α</var> = 108.94 Gm
* <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>
 
=== Mars ===
 
Planet Mars.
 
* <var>r</var><sub>e</sub> = 3.3962 Mm
* <var>π</var> = 206.650 Gm
* <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>
 
=== Ganymede ===
 
Jovian Satellite Ganymede.
 
* <var>m</var> = 148.19 Yg
* <var>P</var> = 618.153375744 ks = 7.15455296 d
* <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>α</var> = 1.0716 Gm
* <var>d</var><sub>min</sub> = 587.41941861347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
 
=== Titan ===
 
Saturnian Satellite Titan.
 
* <var>r</var> = 2.57473 Mm
* <var>α</var> = 1.25706 Gm
* <var>d</var><sub>min</sub> = 1.1991889586134701579430723237339 Tm = <var>d</var><sub>min,Saturn</sub> − <var>α</var>
 
=== Mercury ===
 
Planet Mercury.
 
* <var>r</var><sub>e</sub> = 2.4407983592616677504877194737632 Mm = −2(2.4397 Mm)/(0.0009 − 2)
* <var>α</var> = 69.82 Gm
* <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>
 
=== Callisto ===
 
Jovian Satellite Callisto.
 
* <var>m</var> = 107.5938 Yg
* <var>P</var> = 1.44193118976 Ms = 16.6890184 d
* <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>α</var> = 1.897 Gm
* <var>d</var><sub>min</sub> = 586.59401861347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
 
=== Io ===
 
Jovian Satellite Io.
 
* <var>r</var><sub>e,<var>b</var></sub> = 1.8187 Mm = (3.6374/2) Mm
* <var>α</var> = 423.4 Mm
* <var>d</var><sub>min</sub> = 588.06761861347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
 
=== Luna ===
 
Terran Satellite Luna.
 
* <var>r</var><sub>e</sub> = 1.7381 Mm
* <var>π</var><sub>min</sub> = 356.4 Mm
* <var>d</var><sub>min</sub> = 350.01561347015794307232373387065 Mm = <var>π</var><sub>min</sub> − <var>r</var><sub>max,0</sub>
 
=== Europa ===
 
Jovian Satellite Europa.
 
* <var>r</var> = 1.5608 Mm
* <var>α</var> = 676.938 Mm
* <var>d</var><sub>min</sub> = 587.81408061347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
 
=== Iapetus ===
 
Saturnian Satellite Iapetus.
 
* <var>r</var><sub>e</sub> = 746.00 km = (1.4920/2) Mm
* <var>α</var> = 3.659387770584 Gm = (0.0276812 + 1)(3.56082 Gm)
* <var>d</var><sub>min</sub> = 1.1967866308428861579430723237339 Tm = <var>d</var><sub>min,Saturn</sub> − <var>α</var>
* <var>δ</var><sub>p,max</sub> = 0.25714449258506853269763466887060" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
 
=== Ceres ===
 
Minor Planet Ceres.
 
* <var>r</var><sub>e,<var>b</var></sub> = 481.0 km = (962.0/2) km
* <var>π</var> = 381 Gm
* <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>δ</var><sub>p,max</sub> = 0.86688595464357998161003398040218" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
 
=== Vesta ===
 
Minor Planet Vesta.
 
* <var>r</var><sub>e,<var>b</var></sub> = 278.6 km = (557.2/2) km
* <var>π</var> = 322 Gm
* <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>δ</var><sub>p,max</sub> = 0.67647700622350749837333046252586" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
 
=== Pallas ===
 
Minor Planet Pallas.
 
* <var>r</var><sub>e,<var>b</var></sub></sub> = 266 km = (532/2) km
* <var>π</var> = 319 Gm
* <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>δ</var><sub>p,max</sub> = 0.65749247846134773534338734227922" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
 
=== Juno ===
 
Minor Planet Juno.
 
* <var>r</var><sub>e,<var>b</var></sub> = 125 km = (250/2) km
* <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>δ</var><sub>p,max</sub> = 0.35588418546778944267259225024255" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
 
== formulae ==
 
* <var>δ</var><sub>p,max</sub> = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>) = maximum polar angular diameter
* <var>d</var><sub>min,S,0</sub> = <var>π</var><sub>S,0</sub> − <var>r</var><sub>max,0</sub> = minimum distance of Terran satellite
* <var>d</var><sub>min,P,inf</sub> = <var>π</var><sub>0</sub> − <var>α</var><sub>P,inf</sub> − <var>r</var><sub>max,0</sub> = minimum distance of inferior planet
* <var>d</var><sub>min,P,sup</sub> = <var>π</var><sub>P,sup</sub> − <var>α</var><sub>0</sub> − <var>r</var><sub>max,0</sub> = minimum distance of superior planet
* <var>d</var><sub>min,S,sup</sub> = <var>d</var><sub>min,P,sup</sub> − <var>α</var><sub>S,sup</sub> = minimum distance of superior satellite
 
== constants ==
 
* <var>α</var><sub>0</sub> = 152.097597 Gm = Terran aphelion distance
* <var>π</var><sub>0</sub> = 147.098450 Gm = Terran perihelion distance
* <var>r</var><sub>max,0</sub> = 6.3843865298420569276762661293493 Mm = √([{cos(<var>φ</var>)<var>a</var><sup>2</sup>}<sup>2</sup> + {sin(<var>φ</var>)<var>b</var><sup>2</sup>}<sup>2</sup>]/[{cos(<var>φ</var>)<var>a</var>}<sup>2</sup> + {sin(<var>φ</var>)<var>b</var>}<sup>2</sup>]) + <var>h</var> = Terran maximum radius
* <var>a</var> = 6.378137 Mm = Terran equatorial radius
* <var>b</var> = 6.356752 Mm = Terran polar radius
* <var>h</var> = +6.26347 km = Terran elevation of Chimborazo
* <var>φ</var> = −25.641801411647532015402479952681<sup>mr</sup> = −1.469167° = Terran latitude angle of Chimborazo
* <var>G</var> = 6.67430 × 10<sup>−11</sup> N·m<sup>2</sup>/kg<sup>2</sup> = gravitational constant


[[category:astronomy]]
[[category:astronomy]]

Latest revision as of 12:55, 10 June 2024

Solar System objects sorted by angular diameter (apparent diameter).  Objects with angular diameters greater than about 1 to ½ of an arcsecond and transiting satellites with angular diameters greater than about ½ to ¼ of an arcsecond can theoretically be resolved by amateur telescopes under ideal seeing conditions.

minimum angular diameters

  1. 180°, Planet Terra
  2. (31.477633133877767054679096275868 ± 0.0029551128269606612047486105298695)', Star Sol
  3. (29.819303636472614445417667957098 ± 0.0096862578055441211945453588402752)', Terran Satellite Luna
  4. (33.159669076755426476443372392270 ± 0.0089971814843987142886486730713841)", Planet Jupiter
  5. (14.678686960924656270109313417449 ± 0.0049094002655546655235419837164275)", Planet Saturn
  6. (13.344787507099331456628082902984 ± 0.0022051026964193540301592173017059)", Planet Venus
  7. (6.0096928766403224966258023933195 ± 0.00068019592882980055537539875878304)", Planet Mercury
  8. (4.7698865620477542663584032367593 ± 0.00014196624060303258751810475960605)", Planet Mars
  9. (3.4223653325507628807299127059015 ± 0.0027408759060746596099586009009516)", Planet Uranus
  10. (2.2118336467437559427103793771768 ± 0.0028217055150323473146748236149033)", Planet Neptune
  11. (1.3083628992194648224762369447488 ± 0.00014901868607682720204612762319518)", Jovian Satellite Ganymede
  12. (1.1973524061827979954954456275039 ± 0.00074514868136640627492683703515084)", Jovian Satellite Callisto
  13. (0.90220478385668260139264206458912 ± 0.00074600044303443443093994586958067)", Jovian Satellite Io
  14. (0.77505471560751979803462664785578 ± 0.00024828953386270602828053296700135)", Jovian Satellite Europa
  15. (0.69779167912007910714815231706525 ± 0.000024814241932850107938927799477864)", Saturnian Satellite Titan

maximum angular diameters

  1. 180°, Planet Terra
  2. (34.142318167779726305388597288522 ± 0.0099504175490098189823746848993722)', Terran Satellite Luna
  3. (32.549089711594099381629815789191 ± 0.0030383154609148420537653582447128)', Star Sol
  4. (1.0905870349499817398048629211605 ± 0.00018025944492847952922209945619809)', Planet Venus
  5. (50.115577292011611607058157849591 ± 0.00072639900116543009038607598428538)", Planet Jupiter
  6. (25.700544451492779197449676308284 ± 0.00089158765308439455528175641371082)", Planet Mars
  7. (20.710741843720512704721266748230 ± 0.0005166370410419963595958474095447)", Planet Saturn
  8. (13.026519404358484128366613475607 ± 0.00068880719717083531267935096847384)", Planet Mercury
  9. (4.0813037952907347294343994483903 ± 0.0006389298287894383982434815333879)", Planet Uranus
  10. (2.3717005756662317185122893669135 ± 0.0023358462167698838697425224493574)", Planet Neptune
  11. (1.8500081168516263639525877660944 ± 0.00021081697115976641880998036484687)", Jovian Satellite Ganymede
  12. (1.6950999034452036167094676830048 ± 0.0010549338656223241325822742019151)", Jovian Satellite Callisto
  13. (1.2758186006115165938918458891654 ± 0.000035409569728211189330416823094472)", Jovian Satellite Io
  14. (1.0956010972639616311861538720115 ± 0.00035099902326891557679784173552623)", Jovian Satellite Europa
  15. (0.92630435820787173323928340729414 ± 0.0059958010235239682526821091198236)", Minor Planet Ceres
  16. (0.88573281563080150908143581596940 ± 0.00003509052596514345590963105473037)", Saturnian Satellite Titan
  17. (0.75246410914813015641116728905938 ± 0.016972874643896973338196523745709)", Minor Planet Pallas
  18. (0.69117155722191649628751546195186 ± 0.00012417891897229293892065704030910)", Minor Planet Vesta
  • (0.26224700443933629069282618928564 ± 0.000017870938636195757578407958897337)", Saturnian Satellite Rhea
  • (0.25714234397864741689302828177689 ± 0.000017891855224446917628298178731762)", Saturnian Satellite Iapetus

catalog

Number of Solar System objects by minimum angular diameter:

  • 8 objects (1 star, 6 planets, and 1 moon) are always at least 4 arcseconds in angular diameter.
  • 10 objects (1 star, 8 planets, and 1 moon) are always at least 2 arcseconds in angular diameter.
  • 12 objects (1 star, 8 planets, and 3 moons) are always at least 1 arcsecond in angular diameter.
  • 15 objects (1 star, 8 planets, and 6 moons) are always at least 0.5 arcseconds in angular diameter.

Number of Solar System objects by maximum angular diameter:

  • 9 objects (1 star, 7 planets, and 1 moon) can be at least 4 arcseconds in angular diameter.
  • 10 objects (1 star, 8 planets, and 1 moon) can be at least 2 arcseconds in angular diameter.
  • 14 objects (1 star, 8 planets, and 5 moons) can be at least 1 arcsecond in angular diameter.
  • 18 objects (1 star, 8 major planets, 3 minor planets, and 6 moons) can be at least 0.5 arcseconds in angular diameter.

notes

Minimum angular diameter is calculated using the polar radius and a theoretical maximum observable distance.  Maximum observable distance is simplified here as when there is a right angle between Sol (or the host planet for satellites of superior planets), the object, and the observer.  Otherwise the maximum distance between the object and observer is when the object is behind Sol (or the host planet for satellites of superior planets) and thus invisible (occulted).

Maximum angular diameter for inferior planets and satellites of superior planets is when those objects are in transit.  Maximum resolvable angular diameter for triaxial ellipsoids is calculated using the second equatorial radius.

see also

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