Solar System by apparent size: Difference between revisions

From NikkiWiki
Jump to navigation Jump to search
No edit summary
 
(11 intermediate revisions by the same user not shown)
Line 1: Line 1:
== 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 ==


# (34.142318167779726305388597288522 ± 0.0099504175490098189823746848993722)' ('''Terran Satellite Luna''')
<ol start="0">
# (32.549089711594099381629815789191 ± 0.0030383154609148420537653582447128)' ('''Star Sol''')
<li>180°, '''Planet Terra'''</li>
# (1.0905870349499817398048629211605 ± 0.00018025944492847952922209945619809)' ('''Planet Venus''')
<li>(31.477633133877767054679096275868 ± 0.0029551128269606612047486105298695)', '''Star Sol'''</li>
# (50.115577292011611607058157849591 ± 0.00072639900116543009038607598428538)" ('''Planet Jupiter''')
<li>(29.819303636472614445417667957098 ± 0.0096862578055441211945453588402752)', '''Terran Satellite Luna'''</li>
# (25.700544451492779197449676308284 ± 0.00089158765308439455528175641371082)" ('''Planet Mars''')
<li>(33.159669076755426476443372392270 ± 0.0089971814843987142886486730713841)", '''Planet Jupiter'''</li>
# (20.710741843720512704721266748230 ± 0.0005166370410419963595958474095447)" ('''Planet Saturn''')
<li>(14.678686960924656270109313417449 ± 0.0049094002655546655235419837164275)", '''Planet Saturn'''</li>
# (13.028474261955706245938397191101 ± 0.00084298180037579706377958565685282)" ('''Planet Mercury''')
<li>(13.344787507099331456628082902984 ± 0.0022051026964193540301592173017059)", '''Planet Venus'''</li>
# (4.0813037952907347294343994483903 ± 0.0006389298287894383982434815333879)" ('''Planet Uranus''')
<li>(6.0096928766403224966258023933195 ± 0.00068019592882980055537539875878304)", '''Planet Mercury'''</li>
# (2.3717005756662317185122893669135 ± 0.0023358462167698838697425224493574)" ('''Planet Neptune''')
<li>(4.7698865620477542663584032367593 ± 0.00014196624060303258751810475960605)", '''Planet Mars'''</li>
# (1.8500081168516263639525877660944 ± 0.00021081697115976641880998036484687)" ('''Jovian Satellite Ganymede''')
<li>(3.4223653325507628807299127059015 ± 0.0027408759060746596099586009009516)", '''Planet Uranus'''</li>
# (1.6950999034452036167094676830048 ± 0.0010549338656223241325822742019151)" ('''Jovian Satellite Callisto''')
<li>(2.2118336467437559427103793771768 ± 0.0028217055150323473146748236149033)", '''Planet Neptune'''</li>
# (1.2758186006115165938918458891654 ± 0.000035409569728211189330416823094472)" ('''Jovian Satellite Io''')
<li>(1.3083628992194648224762369447488 ± 0.00014901868607682720204612762319518)", '''Jovian Satellite Ganymede'''</li>
# (1.0956010972639616311861538720115 ± 0.00035099902326891557679784173552623)" ('''Jovian Satellite Europa''')
<li>(1.1973524061827979954954456275039 ± 0.00074514868136640627492683703515084)", '''Jovian Satellite Callisto'''</li>
# (0.92630435820787173323928340729414 ± 0.0059958010235239682526821091198236)" ('''Minor Planet Ceres''')
<li>(0.90220478385668260139264206458912 ± 0.00074600044303443443093994586958067)", '''Jovian Satellite Io'''</li>
# (0.88573281563080150908143581596940 ± 0.00003509052596514345590963105473037)" ('''Saturnian Satellite Titan''')
<li>(0.77505471560751979803462664785578 ± 0.00024828953386270602828053296700135)", '''Jovian Satellite Europa'''</li>
# (0.75246410914813015641116728905938 ± 0.016972874643896973338196523745709)" ('''Minor Planet Pallas''')
<li>(0.69779167912007910714815231706525 ± 0.000024814241932850107938927799477864)", '''Saturnian Satellite Titan'''</li>
# (0.69117155722191649628751546195186 ± 0.00012417891897229293892065704030910)" ('''Minor Planet Vesta''')
</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>d</var><sub>max</sub> = (1.5209124024768575482050243603340E11 ± 1000.0000049665280877186631511073) m = <var>α</var><sub>🜨</sub> − <var>r</var><sub>min,🜨</sub>
'''Number of Solar System objects by minimum angular diameter:'''
* <var>d</var><sub>min</sub> = (1.4709206461346995481837104955408E11 ± 2236.0679886951370999630683009086) m = <var>π</var><sub>🜨</sub> − <var>r</var><sub>max,🜨</sub>
* <var>f</var> = 0.00005
* <var>r</var><sub>e</sub> = (696342 ± 65) km
* <var>r</var><sub>p</sub> = (6.9630718290E8 ± 65368.698385839839208114704073318) m = −(<var>f</var> − 1)<var>r</var><sub>e</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>a</var> = 778.479E6 km
* 9 objects (1 star, 7 planets, and 1 moon) can be at least 4 arcseconds in angular diameter.
* <var>α</var> = 816.363E6 km
* 10 objects (1 star, 8 planets, and 1 moon) can be at least 2 arcseconds in angular diameter.
* <var>d</var><sub>max</sub> = (8.3040452153756847292476118693122E11 ± 983083.23687899791494756689430665) m = <math>\sqrt{\alpha^2+\alpha_\oplus^2}-r_{\mathrm{min},\oplus}</math>
* 14 objects (1 star, 8 planets, and 5 moons) can be at least 1 arcsecond in angular diameter.
* <var>d</var><sub>min</sub> = (5.8849101861346995481837104955408E11 ± 2.2360682011065874613956858897782E6) m = <var>π</var> − <var>α</var><sub>🜨</sub> − <var>r</var><sub>max,🜨</sub>
* 18 objects (1 star, 8 major planets, 3 minor planets, and 6 moons) can be at least 0.5 arcseconds in angular diameter.
* <var>π</var> = (7.40595E11 ± 2.2360679774997896964091736687313E6) m = 2<var>a</var> − <var>α</var>
* <var>r</var> = (69911 ± 6) km
* <var>r</var><sub>e</sub> = 71492 km
* <var>r</var><sub>p</sub> = (6.6749E7 ± 18110.770276274833253147616333968) m = 3<var>r</var> − 2<var>r</var><sub>e</sub>


=== 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>a</var> = 1433.53E6 km
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>α</var> = 1514.50E6 km
* <var>d</var><sub>max</sub> = (1.5221118807749727292166867603896E12 ± 9.9499497656418012341204540508955E6) m = <math>\sqrt{\alpha^2+\alpha_\oplus^2}-r_{\mathrm{min},\oplus}</math>
* <var>d</var><sub>min</sub> = (1.2004560186134699548183710495541E12 ± 2.2360679797358577847444035813535E7) m = <var>π</var> − <var>α</var><sub>🜨</sub> − <var>r</var><sub>max,🜨</sub>
* <var>π</var> = (1.35256E12 ± 2.2360679774997896964091736687313E7) m = 2<var>μ</var> − <var>α</var>
* <var>r</var> = (58232 ± 6) km
* <var>r</var><sub>e</sub> = 60268 km
* <var>r</var><sub>p</sub> = (5.416E7 ± 18110.770276274833253147616333968) m = 3<var>r</var> − 2<var>r</var><sub>e</sub>


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


Planet Uranus (⛢).
* <u>[[Solar System by size]]</u>
 
* <u>[[Solar System data]]</u>
* <var>α</var> = 3.00639E9 km
* <var>d</var><sub>max</sub> = (3.0102286027007139677246575761559E12 ± 9.9872270455085920399321427528095E6) m = <math>\sqrt{\alpha^2+\alpha_\oplus^2}-r_{\mathrm{min},\oplus}</math>
* <var>d</var><sub>min</sub> = (2.5834500186134699548183710495541E12 ± 1.0198039076214605781486501623154E7) m = <var>π</var> − <var>α</var><sub>🜨</sub> − <var>r</var><sub>max,🜨</sub>
* <var>μ</var> = 2.870972E9 km
* <var>π</var> = (2.735554E12 ± 1.0198039027185569660056448218046E7) m = 2<var>a</var> − <var>α</var>
* <var>r</var> = (25362 ± 7) km
* <var>r</var><sub>e</sub> = (25559 ± 4) km
* <var>r</var><sub>p</sub> = (2.4968E7 ± 22472.205054244231864598140445491) m = 3<var>r</var> − 2<var>r</var><sub>e</sub>
 
=== Neptune ===
 
Planet Neptune (♆).
 
* <var>μ</var> = (4.498407971949E12 ± 1.495978707E9) m = 30.07 AU
* <var>α</var> = (4.537303418331E12 ± 1.495978707E9) m = 30.33 AU
* <var>d</var><sub>max</sub> = (4.5398456220033094562651791221215E12 ± 1.4951389016172299508184560415022E9) m = <math>\sqrt{\alpha^2+\alpha_\oplus^2}-r_{\mathrm{min},\oplus}</math>
* <var>d</var><sub>min</sub> = (4.3074085441804699548183710495541E12 ± 3.345110081744389954725670911498E9) m = <var>π</var> − <var>α</var><sub>🜨</sub> − <var>r</var><sub>max,🜨</sub>
* <var>π</var> = (4.459512525567E12 ± 3.3451100817442404828061181678871E9) m = 2<var>μ</var> − <var>α</var>
* <var>r</var> = (24622 ± 19) km
* <var>r</var><sub>e</sub> = (24764 ± 15) km
* <var>r</var><sub>p</sub> = (2.4338E7 ± 64412.731660751665407629096343117) m = 3<var>r</var> − 2<var>r</var><sub>e</sub>
 
=== Terra ===
 
Planet Terra (🜨).
 
* <var>a</var> = 152097597 km
* <var>f</var> = 0.0033528106647474807198455286185206 ± 1.1241339353644443553823696996327E-14 = 298.257223563<sup>−1</sup>
* <var>h</var> = +6263.47 m
* <var>μ</var> = 149598023 km
* <var>φ</var> = −(0.025641801411647532015402479952681 ± 1.7453292519943295769236907684886E-8)<sup>r</sup> = −1.469167°
* <var>π</var> = (1.47098449E11 ± 2236.0679774997896964091736687313) m = 2<var>a</var> − <var>α</var>
* <var>r</var><sub>e</sub> = 6378.1370 km
* <var>r</var><sub>max</sub> = (6.3843865300451816289504459171215E6 ± 0.22375682286241097235424315226049) m = <math>\sqrt{\frac{(\cos[\phi]r_\mathrm{e}^2)^2+(\sin[\phi]r_\mathrm{p}^2)^2}{(\cos[\phi]r_\mathrm{e})^2+(\sin[\phi]r_\mathrm{p})^2}}+h</math>
* <var>r</var><sub>min</sub> = <var>r</var><sub>p</sub> = (6.3567523142451794975639665996337E6 ± 0.099664718933551041988577273088083) m = −(<var>f</var> − 1)<var>r</var><sub>e</sub>
 
=== Venus ===
 
Planet Venus (♀).
 
* <var>α</var> = (1.089391142160591E11 ± 149597.8707) m = 0.728213 AU
* <var>d</var><sub>max</sub> = (1.870802799146427534302927598549E11 ± 87113.48681909334117679296878281) m = <math>\sqrt{\alpha_\oplus^2+\alpha^2}-r_{\mathrm{min},\oplus}</math>
* <var>d</var><sub>min</sub> = (3.8152950397410854818371049554083E10 ± 149614.58123466437589632427285545) m = <var>π</var><sub>🜨</sub> − <var>α</var> − <var>r</var><sub>max,🜨</sub>
* <var>m</var> = (4867.5 ± 0.2)E21 kg
* <var>P</var> = (2.099715264E7 ± 8.64) s = 243.0226 d
* <var>r</var> = (6051.8 ± 1.0) km
* <var>r</var><sub>e</sub> = (6.0518001540473630205875615870764E6 ± 1000.0000254548036656428002788472) m = <math>r\left(1+\frac{5\pi_0^2r^3}{3GmP^2}\right)</math>
* <var>r</var><sub>p</sub> = (6.0517996919052739588248768258477E6 ± 999.99994909041031947990077251405) m = <math>r\left(1-\frac{10\pi_0^2r^3}{3GmP^2}\right)</math>
 
=== Mars ===
 
Planet Mars (♂).
 
* <var>a</var> = 227939366 km
* <var>α</var> = 249261000 km
* <var>d</var><sub>max</sub> = (2.9199488491315266555386091295679E11 ± 853630.09069014407544073581189223) m = <math>\sqrt{\alpha^2+\alpha_\oplus^2}-r_{\mathrm{min},\oplus}</math>
* <var>d</var><sub>min</sub> = (5.4513750613469954818371049554083E10 ± 1.0000024999969000413077806658572E6) m = <var>π</var> − <var>α</var><sub>🜨</sub> − <var>r</var><sub>max,🜨</sub>
* <var>π</var> = (2.06617732E11 ± 1.000001999998000003999990000028E6) m = 2<var>a</var> − <var>α</var>
* <var>r</var><sub>e</sub> = (3396.2 ± 0.1) km
* <var>r</var><sub>p</sub> = (3376.2 ± 0.1) km
 
=== Ganymede ===
 
Jovian Satellite Ganymede.
 
* <var>α</var> = 1071600 km
* <var>d</var><sub>max</sub> = (8.3040521296328458309859346113621E11 ± 983082.42679762933185648526445380) m = <math>\sqrt{d_{\mathrm{max},\text{♃}}^2+\alpha^2}</math>
* <var>d</var><sub>min</sub> = (5.8741941861346995481837104955408E11 ± 2.2383031519434649777754012812165E6) m = <var>d</var><sub>min,♃</sub> − <var>α</var>
* <var>m</var> = 1.4819E23 kg
* <var>P</var> = (618153.375744 ± 0.000864) s = 7.15455296 d
* <var>r</var> = (2634.1 ± 0.3) km
* <var>r</var><sub>e</sub> = (2.6343095368525535298979659694619E6 ± 300.02387325122667051910573765993) m = <math>r\left(1+\frac{5\pi_0^2r^3}{3GmP^2}\right)</math>
* <var>r</var><sub>p</sub> = (2.633680926294892940204068061076E6 ± 299.95230697848851864627090169826) m = <math>r\left(1-\frac{10\pi_0^2r^3}{3GmP^2}\right)</math>
 
=== Titan ===
 
Saturnian Satellite Titan.
 
* <var>α</var> = 1257060 km
* <var>d</var><sub>max</sub> = (1.5221123998562551609898862188965E12 ± 9.9499463724446444116131543055962E6) m = <math>\sqrt{d_{\mathrm{max},\text{♄}}^2+\alpha^2}</math>
* <var>d</var><sub>min</sub> = (1.1991989586134699548183710495541E12 ± 2.2360682033426441307778286882709E7) m = <var>d</var><sub>min,♄</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 = <math>r\left(1+\frac{5\pi_0^2r^3}{3GmP^2}\right)</math>
* <var>r</var><sub>p</sub> = (2.5746451530667626322670034295487E6 ± 89.997036138514569812319048989816) m = <math>r\left(1-\frac{10\pi_0^2r^3}{3GmP^2}\right)</math>
 
=== Mercury ===
 
Planet Mercury (☿).
 
* <var>α</var> = (6.98168774620779E10 ± 149597.8707) m = 0.466697 AU
* <var>d</var><sub>max</sub> = (1.6734977666301418756594260051672E11 ± 62415.182506291192588780899987149) m = <math>\sqrt{\alpha_\oplus^2+\alpha^2}-r_{\mathrm{min},\oplus}</math>
* <var>d</var><sub>min</sub> = (7.7275187151392054818371049554083E10 ± 149614.58123466437589632427285545) m = <var>π</var><sub>🜨</sub> − <var>α</var> − <var>r</var><sub>max,🜨</sub>
* <var>f</var> = 0.0009
* <var>r</var> = (2439.4 ± 0.1) km
* <var>r</var><sub>e</sub> = (2.4401320396118835650695208562569E6 ± 128.94107593360680125894955284279) m = <math>\frac{-3r}{f-3}</math>
* <var>r</var><sub>p</sub> = (2.4379359207762328698609582874862E6 ± 275.93175206073380774470281441497) m = <math>\frac{3(f-1)r}{f-3}</math>
 
=== Callisto ===
 
Jovian Satellite Callisto.
 
* <var>α</var> = 1897000 km
* <var>d</var><sub>min</sub> = (5.8659401861346995481837104955408E11 ± 2.4494899469073250448631436724676E6) m = <var>d</var><sub>min,♃</sub> − <var>α</var>
* <var>m</var> = (1.075938 ± 0.000137)E23 kg
* <var>P</var> = (1.44193118976E6 ± 0.00864) s = 16.6890184 d
* <var>r</var> = (2410.3 ± 1.5) km
* <var>r</var><sub>e</sub> = (2.4103371835504931845570782568187E6 ± 1500.0231420222554972182057151537) m = <math>r\left(1+\frac{5\pi_0^2r^3}{3GmP^2}\right)</math>
 
=== Io ===
 
Jovian Satellite Io.
 
* <var>α</var> = 423400 km
* <var>D</var><sub>min</sub> = (5.8806761861346995481837104955408E11 ± 2.2383031519434649777754012812165E6) m = <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 ===
 
Terran Satellite Luna.
 
* <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> = 356400 km
* <var>r</var><sub>e</sub> = 1738.1 km
 
=== Europa ===
 
Jovian Satellite Europa.
 
* <var>α</var> = 676938 km
* <var>D</var><sub>min</sub> = (5.8781408061346995481837104955408E11 ± 2.2360684247133516703616997354357E6) m = <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 ===
 
Saturnian Satellite Iapetus.
 
* <var>α</var> = (3.659387770584E9 ± 10282.979105009792832064687157625) m = (<var>e</var> + 1)<var>μ</var>
* <var>D</var><sub>min</sub> = (1.1967966308428859548183710495541E12 ± 2.2360682161769111021879173825542E7) m = <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>e</var> = 0.0276812
* <var>μ</var> = 3560820 km
* <var>r</var><sub>e</sub> = (746000 ± 50) m = (1492.0 km)/2
 
=== Ceres ===
 
Minor Planet Ceres.
 
* <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>e</var> = 0.116
* <var>μ</var> = (4.14386101839E11 ± 1.495978707E9) m = 2.77 AU
* <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 ===
 
Minor Planet Vesta.
 
* <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>e</var> = 0.098758
* <var>μ</var> = (3.53276867636757E11 ± 1.495978707E6) m = 2.36151 AU
* <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 ===
 
Minor Planet Pallas.
 
* <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>e</var> = 0.2812580
* <var>μ</var> = (4.1452337284515432E11 ± 14959.78707) m = 2.7709176 AU
* <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 ===
 
Minor Planet Juno.
 
* <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>r</var><sub>e,<var>b</var></sub> = (125000 ± 2500) m = ([250 ± 5] km)/2
 
=== 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 ==
 
* <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>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

Retrieved from "https://www.nicolesharp.net/w/index.php?title=Solar_System_by_apparent_size&oldid=660"