Solar System by size and Solar System by apparent size: Difference between pages

Revision as of 2023-09-17T21:56:59

[Image.] Solar eclipses are possible because (by coincidence) the apparent sizes of Sol and Luna are approximately equal. When Luna passes in front of Sol, if Luna appears smaller than Sol, then an annular Solar eclipse occurs, and if Luna appears larger than Sol, then a total Solar eclipse occurs. Photograph shows an Annular Solar Eclipse displaying the relative angular sizes of Luna and Sol.

Solar System objects sorted by apparent angular diameter. ^[1] ^[2]

list

Planet Terra: (3.1415926535897932384626433832795 = π) rad = 180 deg (12.74M / 0)
Star Sol: 9.3099381622456608377567028963016 mrad = 32.005209853467492394412374774496 arcmin (1.393G / 149.6G) ^[3]
Terran Satellite Luna: 9.1924733415766236658905126057414 mrad = 31.601395545531677869275770447370 arcmin (3.475M / 384.4M) ^[4]
Planet Jupiter: 176.38342059183204249972698706792 µrad = 36.381692073574341769062888511907 arcsec (139.8M / 778.5G) ^[5]
Planet Saturn: 80.804366614590771015035932939646 µrad = 16.667097023677906623999609656452 arcsec (116.5M / 1.434T) ^[6]
Planet Venus: 65.557754895471439224993918452156 µrad = 13.522257611509048977196601587376 arcsec (12.1M / 149.6G) ^[7]
Planet Mercury: 30.418531890520777418473660749422 µrad = 6.2742725867193897525492834124436 arcsec (4.879M / 149.6G) ^[8]
Planet Mars: 24.864310071007387989563198840282 µrad = 5.1286320992640655002603020583460 arcsec (6.779M / 227.9G) ^[9]
Planet Uranus: 17.643986266660484646561759683674 µrad = 3.6393334087191538304117174747131 arcsec (50.72M / 2.871T) ^[10]
Planet Neptune: 10.940951094337036545922443091756 µrad = 2.2567331576323856791155130374892 arcsec (49.24M / 4.498T) ^[11]
Jovian Satellite Ganymede: 6.6457516559391904488160888324418 µrad = 1.3707846776786168771797746278470 arcsec (5.268M / 778.5G) ^[12]
Jovian Satellite Callisto: 6.0810996708582598711685808110014 µrad = 1.2543168453788603898364781318473 arcsec (4.821M / 778.5G) ^[13]
Jovian Satellite Io: 4.5958431873590778175870863250252 µrad = 0.94796070458265793885064096711556 arcsec (3.643M / 778.5G) ^[14]
Jovian Satellite Europa: 3.9378516100190881273980359335144 µrad = 0.81224019937040364887742618540130 arcsec (3.122M / 778.5G) ^[15]
Saturnian Satellite Titan: 3.5727667268260305440699972133520 µrad = 0.73693603667484382194570809689712 arcsec (5.149M / 1.434T) ^[16]
Minor Planet Ceres: 2.1340634690465546941919479637938 µrad = 0.44018218796189391383987453951568 arcsec (939.4M / 414G) ^[17]
Minor Planet Vesta: 1.3693765737543177734686736150136 µrad = 0.28245419366474700741821944755938 arcsec (525.4M / 353.3G) ^[18]
Minor Planet Pallas: 1.1631259273490422140561661172389 µrad = 0.23991194404562446380404693996124 arcsec (512M / 414G) ^[19]

Saturnian Satellite Rhea: 1.0594540762423223413932314109441 µrad (1.527M / 1.434T) ^[20]
Neptunian Satellite Triton: 601.39237937640932702910508661970 nrad (2.707M / 4.498T) ^[21]
Uranian Satellite Titania: 548.47877188493312845418689808346 nrad (1.577M / 2.871T) ^[22]

gallery

Terra (180°)
Sol (32.01')
Luna (31.6')
Jupiter (36.38")
Saturn (16.7")
Venus (13.5")
Mercury (6.27")
Mars (5.13")
Uranus (3.64")
Neptune (2.3")
Ganymede (1.4")
Callisto (1.3")
Io (0.95")
Europa (0.81")
Titan (0.74")
Ceres (0.44")
Vesta (0.28")

calculation

The angular diameter (δ) of a sphere is equal to twice the arcsine of the ratio between the object's radius (r) and the distance to the object (D):

δ = 2arcsin(r/D) ^[23]

The simplest approximation of the mean distance (D) from an observer in a heliocentric orbit to an astronomical object in the same solar system as the observer is as the orbital semimajor axis (a) of the observed object if the observed object is superior or as the orbital semimajor axis of the observer if the observed object is inferior. For observers on Terra, the Terran orbital semimajor axis (a_🜨) can be approximated as one astronomical unit (l_A). For these calculations, satellites in orbit around the observer should be considered as superior objects and satellites not in orbit around the observer should use the satellite's heliocentric semimajor axis.

D_superior ≈ a_object
D_inferior ≈ a_observer

For small angles, the mean angular diameter (δ) can be approximated as the ratio between the observed object's mean diameter (d = 2r) and the observed object's mean distance. The dimensionless ratio can be expressed in radians (θ_I) without an arcsine:

δ ≈ (d/a)θ_I

references

↑ Solar System by size
↑ Solar System by orbit
↑ delta_Sol=combine(2*arcsin(Quantity(696.342,0.065)*10^6/((Quantity(149.598023,1E-6)*10^9)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Luna=combine(2*arcsin(Quantity(1.7375,0.0001)*10^6/((Quantity(384.399,0.001)*10^6)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Jupiter=combine(2*arcsin(Quantity(69.911,0.006)*10^6/(sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Saturn=combine(2*arcsin(Quantity(58.232,0.006)*10^6/(sqrt((Quantity(1.43353,0.00001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Venus=combine(2*arcsin(Quantity(6.0518,0.0010)*10^6/(sqrt((Quantity(149.598023,1E-6)*10^9)^2+(Quantity(0.723332,1E-6)*149597870700)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Mercury=combine(2*arcsin(Quantity(2.4397,0.00010)*10^6/(sqrt((Quantity(149.598023,1E-6)*10^9)^2+(Quantity(0.387098,1E-6)*149597870700)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Mars=combine(2*arcsin(Quantity(3.3895,0.0002)*10^6/(sqrt((Quantity(227.939366,1E-6)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Uranus=combine(2*arcsin(Quantity(25.362,0.007)*10^6/(sqrt((Quantity(2.870972,1E-6)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Neptune=combine(2*arcsin(Quantity(24.622,0.019)*10^6/(sqrt((Quantity(30.07,0.01)*149597870700)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Ganymede=combine(2*arcsin(Quantity(2.6341,0.0003)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(1.0704,0.0001)*10^9)^2)),errors);
↑ delta_Callisto=combine(2*arcsin(Quantity(2.4103,0.0015)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(1.8827,0.0001)*10^9)^2)),errors);
↑ delta_Io=combine(2*arcsin(Quantity(1.8216,0.0005)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(421.7,0.1)*10^6)^2)),errors);
↑ delta_Europa=combine(2*arcsin(Quantity(1.5608,0.0005)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(670.9,0.1)*10^6)^2)),errors);
↑ delta_Titan=combine(2*arcsin(Quantity(2.57473,0.00009)*10^6/sqrt((sqrt((Quantity(1.43353,0.00001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(1.22187,0.00001)*10^9)^2)),errors);
↑ delta_Ceres=combine(2*arcsin(Quantity(469.7,0.1)*10^3/(sqrt((Quantity(414.,1.)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Vesta=combine(2*arcsin(Quantity(262.7,0.1)*10^3/(sqrt((Quantity(353.319,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Pallas=combine(2*arcsin(Quantity(256.,2.)*10^3/(sqrt((Quantity(414.,1.)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);
↑ delta_Rhea=combine(2*arcsin(Quantity(763.5,0.5)*10^3/sqrt((sqrt((Quantity(1.43353,0.00001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(527.108,0.001)*10^6)^2)),errors);
↑ delta_Triton=combine(2*arcsin(Quantity(1.3534,0.0009)*10^6/sqrt((sqrt((Quantity(30.07,0.01)*149597870700)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(354.759,0.001)*10^6)^2)),errors);
↑ delta_Titania=combine(2*arcsin(Quantity(788.4,0.6)*10^3/sqrt((sqrt((Quantity(2.870972,0.000001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(435.91,0.01)*10^6)^2)),errors);
↑ wikipedia:Angular diameter#Formula

keywords

angle, angles, astro, astronomics, astronomy, diameter, diameters, radii, radius, size, sizes, Sol, Solar, Sol-Jupiter, SolSys, Sun, Sun-Jupiter

[1] Solar System by size

[2] Solar System by orbit

[3] delta_Sol=combine(2*arcsin(Quantity(696.342,0.065)*10^6/((Quantity(149.598023,1E-6)*10^9)-Quantity(6.3710084,1E-7)*10^6)),errors);

[4] delta_Luna=combine(2*arcsin(Quantity(1.7375,0.0001)*10^6/((Quantity(384.399,0.001)*10^6)-Quantity(6.3710084,1E-7)*10^6)),errors);

[5] delta_Jupiter=combine(2*arcsin(Quantity(69.911,0.006)*10^6/(sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);

[6] delta_Saturn=combine(2*arcsin(Quantity(58.232,0.006)*10^6/(sqrt((Quantity(1.43353,0.00001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);

[7] delta_Venus=combine(2*arcsin(Quantity(6.0518,0.0010)*10^6/(sqrt((Quantity(149.598023,1E-6)*10^9)^2+(Quantity(0.723332,1E-6)*149597870700)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);

[8] delta_Mercury=combine(2*arcsin(Quantity(2.4397,0.00010)*10^6/(sqrt((Quantity(149.598023,1E-6)*10^9)^2+(Quantity(0.387098,1E-6)*149597870700)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);

[9] delta_Mars=combine(2*arcsin(Quantity(3.3895,0.0002)*10^6/(sqrt((Quantity(227.939366,1E-6)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);

[10] delta_Uranus=combine(2*arcsin(Quantity(25.362,0.007)*10^6/(sqrt((Quantity(2.870972,1E-6)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);

[11] delta_Neptune=combine(2*arcsin(Quantity(24.622,0.019)*10^6/(sqrt((Quantity(30.07,0.01)*149597870700)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);

[12] delta_Ganymede=combine(2*arcsin(Quantity(2.6341,0.0003)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(1.0704,0.0001)*10^9)^2)),errors);

[13] delta_Callisto=combine(2*arcsin(Quantity(2.4103,0.0015)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(1.8827,0.0001)*10^9)^2)),errors);

[14] delta_Io=combine(2*arcsin(Quantity(1.8216,0.0005)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(421.7,0.1)*10^6)^2)),errors);

[15] delta_Europa=combine(2*arcsin(Quantity(1.5608,0.0005)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(670.9,0.1)*10^6)^2)),errors);

[16] delta_Titan=combine(2*arcsin(Quantity(2.57473,0.00009)*10^6/sqrt((sqrt((Quantity(1.43353,0.00001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(1.22187,0.00001)*10^9)^2)),errors);

[17] delta_Ceres=combine(2*arcsin(Quantity(469.7,0.1)*10^3/(sqrt((Quantity(414.,1.)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);

[18] delta_Vesta=combine(2*arcsin(Quantity(262.7,0.1)*10^3/(sqrt((Quantity(353.319,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);

[19] delta_Pallas=combine(2*arcsin(Quantity(256.,2.)*10^3/(sqrt((Quantity(414.,1.)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);

[20] delta_Rhea=combine(2*arcsin(Quantity(763.5,0.5)*10^3/sqrt((sqrt((Quantity(1.43353,0.00001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(527.108,0.001)*10^6)^2)),errors);

[21] delta_Triton=combine(2*arcsin(Quantity(1.3534,0.0009)*10^6/sqrt((sqrt((Quantity(30.07,0.01)*149597870700)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(354.759,0.001)*10^6)^2)),errors);

[22] delta_Titania=combine(2*arcsin(Quantity(788.4,0.6)*10^3/sqrt((sqrt((Quantity(2.870972,0.000001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(435.91,0.01)*10^6)^2)),errors);

[23] wikipedia:Angular diameter#Formula

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@@ Line 1: / Line 1: @@
-[[wikipedia:Solar System|Solar System]] objects sorted by mean diameter. <ref><code>[[wikipedia:Solar System by size]]</code></ref>
+[[image:20200621 Annular eclipse in Xiamen, China (cropped).jpg|thumb|[Image.] [[wikipedia:Solar eclipses|Solar eclipses]] are possible because (by coincidence) the apparent sizes of Sol and Luna are approximately equal.&ensp; When Luna passes in front of Sol, if Luna appears smaller than Sol, then an annular Solar eclipse occurs, and if Luna appears larger than Sol, then a total Solar eclipse occurs.&ensp; Photograph shows an Annular Solar Eclipse displaying the relative angular sizes of Luna and Sol.]]
-# [[wikipedia:Star Sol|Star Sol]]: 695508 km
+<u>[[Solar System]]</u> objects sorted by apparent [[wikipedia:angular diameter|angular diameter]]. <ref><u><code>[[Solar System by size]]</code></u></ref> <ref><u><code>[[Solar System by orbit]]</code></u></ref>
-# [[wikipedia:Planet Jupiter|Planet Jupiter]]: (69911 ± 6) km
-# [[wikipedia:Planet Saturn|Planet Saturn]]: (58232 ± 6) km
+== list ==
-# [[wikipedia:Planet Uranus|Planet Uranus]]: (25362 ± 7) km
-# [[wikipedia:Planet Neptune|Planet Neptune]]: (24622 ± 19) km
+<ol start="0">
-# [[wikipedia:Planet Terra|Planet Terra]]: (6371.0084 ± 0.0001) km
+<li>[[wikipedia:Planet Terra|Planet Terra]]: (3.1415926535897932384626433832795 = <var title="Archimedes">π</var>) <abbr title="radians">rad</abbr> = 18<u style="text-decoration: overline;">0</u> <abbr title="degrees">deg</abbr> (12.74M / 0)</li>
-# [[wikipedia:Planet Venus|Planet Venus]]: (6052 ± 1) km
+<li>[[wikipedia:Star Sol|Star Sol]]: 9.309<u>9</u>381622456608377567028963016 <abbr title="milliradians">mrad</abbr> = 32.00<u>5</u>209853467492394412374774496 <abbr title="arcminutes">arcmin</abbr> (1.393G / 149.6G) <ref><code>delta_Sol=combine(2*arcsin(Quantity(696.342,0.065)*10^6/((Quantity(149.598023,1E-6)*10^9)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Planet Mars|Planet Mars]]: (3389.5 ± 0.2) km
+<li>[[wikipedia:Terran Satellite Luna|Terran Satellite Luna]]: 9.192<u>4</u>733415766236658905126057414 mrad = 31.60<u>1</u>395545531677869275770447370 arcmin (3.475M / 384.4M) <ref><code>delta_Luna=combine(2*arcsin(Quantity(1.7375,0.0001)*10^6/((Quantity(384.399,0.001)*10^6)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Jovian Satellite Ganymede|Jovian Satellite Ganymede]]: (2634.1 ± 0.3) km
+<li>[[wikipedia:Planet Jupiter|Planet Jupiter]]: 176.3<u>8</u>342059183204249972698706792 <abbr title="microradians">µrad</abbr> = 36.38<u>1</u>692073574341769062888511907 <abbr title="arcseconds">arcsec</abbr> (139.8M / 778.5G) <ref><code>delta_Jupiter=combine(2*arcsin(Quantity(69.911,0.006)*10^6/(sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Saturnian Satellite Titan|Saturnian Satellite Titan]]: (2574.73 ± 0.09) km
+<li>[[wikipedia:Planet Saturn|Planet Saturn]]: 80.8<u>0</u>4366614590771015035932939646 µrad = 16.6<u>6</u>7097023677906623999609656452 arcsec (116.5M / 1.434T) <ref><code>delta_Saturn=combine(2*arcsin(Quantity(58.232,0.006)*10^6/(sqrt((Quantity(1.43353,0.00001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Planet Mercury|Planet Mercury]]: (2439.4 ± 0.1) km
+<li>[[wikipedia:Planet Venus|Planet Venus]]: 65.5<u>5</u>7754895471439224993918452156 µrad = 13.5<u>2</u>2257611509048977196601587376 arcsec (12.1M / 149.6G) <ref><code>delta_Venus=combine(2*arcsin(Quantity(6.0518,0.0010)*10^6/(sqrt((Quantity(149.598023,1E-6)*10^9)^2+(Quantity(0.723332,1E-6)*149597870700)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Jovian Satellite Callisto|Jovian Satellite Callisto]]: (2410.3 ± 1.5) km
+<li>[[wikipedia:Planet Mercury|Planet Mercury]]: 30.41<u>8</u>531890520777418473660749422 µrad = 6.274<u>2</u>725867193897525492834124436 arcsec (4.879M / 149.6G) <ref><code>delta_Mercury=combine(2*arcsin(Quantity(2.4397,0.00010)*10^6/(sqrt((Quantity(149.598023,1E-6)*10^9)^2+(Quantity(0.387098,1E-6)*149597870700)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Jovian Satellite Io|Jovian Satellite Io]]: (1821.6 ± 0.5) km
+<li>[[wikipedia:Planet Mars|Planet Mars]]: 24.86<u>4</u>310071007387989563198840282 µrad = 5.128<u>6</u>320992640655002603020583460 arcsec (6.779M / 227.9G) <ref><code>delta_Mars=combine(2*arcsin(Quantity(3.3895,0.0002)*10^6/(sqrt((Quantity(227.939366,1E-6)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Terran Satellite Luna|Terran Satellite Luna]]: (1737.5 ± 0.1) km
+<li>[[wikipedia:Planet Uranus|Planet Uranus]]: 17.6<u>4</u>3986266660484646561759683674 µrad = 3.63<u>9</u>3334087191538304117174747131 arcsec (50.72M / 2.871T) <ref><code>delta_Uranus=combine(2*arcsin(Quantity(25.362,0.007)*10^6/(sqrt((Quantity(2.870972,1E-6)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Jovian Satellite Europa|Jovian Satellite Europa]]: (1560.8 ± 0.5) km
+<li>[[wikipedia:Planet Neptune|Planet Neptune]]: 10.9<u>4</u>0951094337036545922443091756 µrad = 2.25<u>6</u>7331576323856791155130374892 arcsec (49.24M / 4.498T) <ref><code>delta_Neptune=combine(2*arcsin(Quantity(24.622,0.019)*10^6/(sqrt((Quantity(30.07,0.01)*149597870700)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Neptunian Satellite Triton|Neptunian Satellite Triton]]: (1353.4 ± 0.9) km
+<li>[[wikipedia:Jovian Satellite Ganymede|Jovian Satellite Ganymede]]: 6.64<u>5</u>7516559391904488160888324418 µrad = 1.37<u>0</u>7846776786168771797746278470 arcsec (5.268M / 778.5G) <ref><code>delta_Ganymede=combine(2*arcsin(Quantity(2.6341,0.0003)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(1.0704,0.0001)*10^9)^2)),errors);</code></ref></li>
-# [[wikipedia:Minor Planet Pluto|Minor Planet Pluto]]: (1188.3 ± 0.8) km
+<li>[[wikipedia:Jovian Satellite Callisto|Jovian Satellite Callisto]]: 6.08<u>1</u>0996708582598711685808110014 µrad = 1.25<u>4</u>3168453788603898364781318473 arcsec (4.821M / 778.5G) <ref><code>delta_Callisto=combine(2*arcsin(Quantity(2.4103,0.0015)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(1.8827,0.0001)*10^9)^2)),errors);</code></ref></li>
-# [[wikipedia:Minor Planet Eris|Minor Planet Eris]]: (1163 ± 6) km
+<li>[[wikipedia:Jovian Satellite Io|Jovian Satellite Io]]: 4.59<u>5</u>8431873590778175870863250252 µrad = 0.947<u>9</u>6070458265793885064096711556 arcsec (3.643M / 778.5G) <ref><code>delta_Io=combine(2*arcsin(Quantity(1.8216,0.0005)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(421.7,0.1)*10^6)^2)),errors);</code></ref></li>
-# [[wikipedia:Minor Planet Haumea|Minor Planet Haumea]]: (798 ± 6) km
+<li>[[wikipedia:Jovian Satellite Europa|Jovian Satellite Europa]]: 3.93<u>7</u>8516100190881273980359335144 µrad = 0.812<u>2</u>4019937040364887742618540130 arcsec (3.122M / 778.5G) <ref><code>delta_Europa=combine(2*arcsin(Quantity(1.5608,0.0005)*10^6/sqrt((sqrt((Quantity(778.479,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(670.9,0.1)*10^6)^2)),errors);</code></ref></li>
-# [[wikipedia:Uranian Satellite Titania|Uranian Satellite Titania]]: (788.9 ± 1.8) km
+<li>[[wikipedia:Saturnian Satellite Titan|Saturnian Satellite Titan]]: 3.572<u>7</u>667268260305440699972133520 µrad = 0.7369<u>3</u>603667484382194570809689712 arcsec (5.149M / 1.434T) <ref><code>delta_Titan=combine(2*arcsin(Quantity(2.57473,0.00009)*10^6/sqrt((sqrt((Quantity(1.43353,0.00001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(1.22187,0.00001)*10^9)^2)),errors);</code></ref></li>
-# [[wikipedia:Saturnian Satellite Rhea|Saturnian Satellite Rhea]]: (763.8 ± 1.0) km
+<li>[[wikipedia:Minor Planet Ceres|Minor Planet Ceres]]: 2.1<u>3</u>40634690465546941919479637938 µrad = 0.44<u>0</u>18218796189391383987453951568 arcsec (939.4M / 414G) <ref><code>delta_Ceres=combine(2*arcsin(Quantity(469.7,0.1)*10^3/(sqrt((Quantity(414.,1.)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Uranian Satellite Oberon|Uranian Satellite Oberon]]: (761.4 ± 2.6) km
+<li>[[wikipedia:Minor Planet Vesta|Minor Planet Vesta]]: 1.36<u>9</u>3765737543177734686736150136 µrad = 0.282<u>4</u>5419366474700741821944755938 arcsec (525.4M / 353.3G) <ref><code>delta_Vesta=combine(2*arcsin(Quantity(262.7,0.1)*10^3/(sqrt((Quantity(353.319,0.001)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Saturnian Satellite Iapetus|Saturnian Satellite Iapetus]]: (735.6 ± 1.5) km
+<li>[[wikipedia:Minor Planet Pallas|Minor Planet Pallas]]: 1.1<u>6</u>31259273490422140561661172389 µrad = 0.23<u>9</u>91194404562446380404693996124 arcsec (512M / 414G) <ref><code>delta_Pallas=combine(2*arcsin(Quantity(256.,2.)*10^3/(sqrt((Quantity(414.,1.)*10^9)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)),errors);</code></ref></li>
-# [[wikipedia:Minor Planet Makemake|Minor Planet Makemake]]: (715 ± 19) km
+</ol>
-# [[wikipedia:Minor Planet Gonggong|Minor Planet Gonggong]]: (615 ± 25) km
-# [[wikipedia:Plutonian Satellite Charon|Plutonian Satellite Charon]]: (606.0 ± 0.5) km
+* [[wikipedia:Saturnian Satellite Rhea|Saturnian Satellite Rhea]]: 1.059<u>4</u>540762423223413932314109441 µrad (1.527M / 1.434T) <ref><code>delta_Rhea=combine(2*arcsin(Quantity(763.5,0.5)*10^3/sqrt((sqrt((Quantity(1.43353,0.00001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(527.108,0.001)*10^6)^2)),errors);</code></ref>
-# [[wikipedia:Uranian Satellite Umbriel|Uranian Satellite Umbriel]]: (584.7 ± 2.8) km
+* [[wikipedia:Neptunian Satellite Triton|Neptunian Satellite Triton]]: 601.<u>3</u>9237937640932702910508661970 <abbr title="nanoradians">nrad</abbr> (2.707M / 4.498T) <ref><code>delta_Triton=combine(2*arcsin(Quantity(1.3534,0.0009)*10^6/sqrt((sqrt((Quantity(30.07,0.01)*149597870700)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(354.759,0.001)*10^6)^2)),errors);</code></ref>
-# [[wikipedia:Uranian Satellite Ariel|Uranian Satellite Ariel]]: (578.9 ± 0.6) km
+* [[wikipedia:Uranian Satellite Titania|Uranian Satellite Titania]]: 548.<u>4</u>7877188493312845418689808346 nrad (1.577M / 2.871T) <ref><code>delta_Titania=combine(2*arcsin(Quantity(788.4,0.6)*10^3/sqrt((sqrt((Quantity(2.870972,0.000001)*10^12)^2+(Quantity(149.598023,1E-6)*10^9)^2)-Quantity(6.3710084,1E-7)*10^6)^2+(Quantity(435.91,0.01)*10^6)^2)),errors);</code></ref>
-# [[wikipedia:Saturnian Satellite Dione|Saturnian Satellite Dione]]: (561.7 ± 0.45) km
-# [[wikipedia:Minor Planet Quaoar|Minor Planet Quaoar]]: (543 ± 2) km
+== gallery ==
-# [[wikipedia:Saturnian Satellite Tethys|Saturnian Satellite Tethys]]: (533.0 ± 0.7) km
-# [[wikipedia:Minor Planet Sedna|Minor Planet Sedna]]: (498 ± 40) km
+<gallery>
-# [[wikipedia:Minor Planet Ceres|Minor Planet Ceres]]: (469.7 ± 0.1) km
+Africa and Europe from a Million Miles Away.png | Terra (180°)
-# [[wikipedia:Minor Planet Orcus|Minor Planet Orcus]]: (455 ± 25) km
+The Sun in white light.jpg | Sol (32.01')
-# [[wikipedia:Minor Planet Salacia|Minor Planet Salacia]]: (423 ± 11) km
+FullMoon2010.jpg | Luna (31.6')
-# [[wikipedia:Minor Planet 307261|Minor Planet 307261]]: (400 ± 12) km
+Jupiter and its shrunken Great Red Spot.jpg | Jupiter (36.38")
-# [[wikipedia:Minor Planet 208996|Minor Planet 208996]]: (386 ± 6) km
+Saturn during Equinox.jpg | Saturn (16.7")
-# [[wikipedia:Minor Planet 55565|Minor Planet 55565]]: (384 ± 19) km
+Venus from Mariner 10.jpg | Venus (13.5")
-# [[wikipedia:Minor Planet Varda|Minor Planet Varda]]: (373 ± 8) km
+Mercury in true color.jpg | Mercury (6.27")
-# [[wikipedia:Minor Planet 532037|Minor Planet 532037]]: (370 ± 40) km
+Mars - August 30 2021 - Flickr - Kevin M. Gill.png | Mars (5.13")
-# [[wikipedia:Minor Planet Ixion|Minor Planet Ixion]]: (354.8 ± 0.1) km
+Uranus.jpg | Uranus (3.64")
-# [[wikipedia:Minor Planet 145452|Minor Planet 145452]]: (340 ± 37) km
+Neptune - Voyager 2 (29347980845) flatten crop.jpg | Neptune (2.3")
-# [[wikipedia:Minor Planet 90568|Minor Planet 90568]]: (340 ± 17) km
+Ganymede - Perijove 34 Composite.png | Ganymede (1.4")
-# [[wikipedia:Minor Planet Varuna|Minor Planet Varuna]]: (334 ± 77) km
+Callisto - July 8 1979 (38926064465).jpg | Callisto (1.3")
-# [[wikipedia:Minor Planet 55637|Minor Planet 55637]]: (332 ± 15) km
+Io highest resolution true color.jpg | Io (0.95")
-# [[wikipedia:Minor Planet 145451|Minor Planet 145451]]: 322 km
+Europa in natural color.png | Europa (0.81")
-# [[wikipedia:Minor Planet Gǃkúnǁʼhòmdímà|Minor Planet Gǃkúnǁʼhòmdímà]]: (321 ± 14) km
+Titan in true color.jpg | Titan (0.74")
-# [[wikipedia:Minor Planet 2014 UZ224|Minor Planet 2014 UZ224]]: (317.5 ± 30.5) km
+Ceres - RC3 - Haulani Crater (22381131691) (cropped).jpg | Ceres (0.44")
-# [[wikipedia:Minor Planet 470599|Minor Planet 470599]]: (309.5 ± 56.5) km
+Vesta in natural color.jpg | Vesta (0.28")
-# [[wikipedia:Minor Planet 278361|Minor Planet 278361]]: (305 ± 85) km
+</gallery>
-# [[wikipedia:Minor Planet Chaos|Minor Planet Chaos]]: (300 ± 70) km
-# [[wikipedia:Eridian Satellite Dysnomia|Eridian Satellite Dysnomia]]: 300 km
+== calculation ==
-# [[wikipedia:Minor Planet 523692|Minor Planet 523692]]: 288 km
-# [[wikipedia:Minor Planet 2012 VP113|Minor Planet 2012 VP113]]: 287 km
+The angular diameter (<var>δ</var>) of a sphere is equal to twice the arcsine of the ratio between the object's radius (<var>r</var>) and the distance to the object (<var>D</var>):
-# [[wikipedia:Minor Planet 78799|Minor Planet 78799]]: (283 ± 37) km
+: <var>δ</var> = 2arcsin(<var>r</var>/<var>D</var>) <ref><code>[[wikipedia:Angular diameter#Formula]]</code></ref>
-# [[wikipedia:Minor Planet 2004 XR190|Minor Planet 2004 XR190]]: 278 km
-# [[wikipedia:Minor Planet 2002 XV93|Minor Planet 2002 XV93]]: (275 ± 12) km
+The simplest approximation of the mean distance (<var style="text-decoration: overline;">D</var>) from an observer in a heliocentric orbit to an astronomical object in the same solar system as the observer is as the orbital semimajor axis (<var>a</var>) of the observed object if the observed object is superior or as the orbital semimajor axis of the observer if the observed object is inferior.&ensp; For observers on Terra, the Terran orbital semimajor axis (<var>a</var><sub>🜨</sub>) can be approximated as one [[wikipedia:astronomical unit|astronomical unit]] (<var>l</var><sub>A</sub>).&ensp; For these calculations, satellites in orbit around the observer should be considered as superior objects and satellites not in orbit around the observer should use the satellite's heliocentric semimajor axis.
-# [[wikipedia:Minor Planet 523794|Minor Planet 523794]]: 270 km
+* <var style="text-decoration: overline;">D</var><sub>superior</sub> ≈ <var>a</var><sub>object</sub>
-# [[wikipedia:Minor Planet 455502|Minor Planet 455502]]: 268 km
+* <var style="text-decoration: overline;">D</var><sub>inferior</sub> ≈ <var>a</var><sub>observer</sub>
-# [[wikipedia:Minor Planet Vesta|Minor Planet Vesta]]: (262.7 ± 0.1) km
-# [[wikipedia:Minor Planet 84922|Minor Planet 84922]]: (262 ± 4) km
+For [[wikipedia:small-angle approximation|small angles]], the mean angular diameter (<var style="text-decoration: overline;">δ</var>) can be approximated as the ratio between the observed object's mean diameter (<var style="text-decoration: overline;">d</var> = 2<var style="text-decoration: overline;">r</var>) and the observed object's mean distance.&ensp; The dimensionless ratio can be expressed in radians (<var>θ</var><sub>I</sub>) without an arcsine:
-# [[wikipedia:Minor Planet 120348|Minor Planet 120348]]: (256 ± 20) km
+: <var style="text-decoration: overline;">δ</var> ≈ (<var style="text-decoration: overline;">d</var>/<var>a</var>)<var>θ</var><sub>I</sub>
-# [[wikipedia:Minor Planet Pallas|Minor Planet Pallas]]: (256 ± 2) km
-# [[wikipedia:Saturnian Satellite Enceladus|Saturnian Satellite Enceladus]]: (252.1 ± 0.2) km
-# [[wikipedia:Minor Planet 84522|Minor Planet 84522]]: (250 ± 7) km
-# [[wikipedia:Minor Planet 202421|Minor Planet 202421]]: (249 ± 38) km
-# [[wikipedia:Uranian Satellite Miranda|Uranian Satellite Miranda]]: (235.8 ± 0.7) km
-# [[wikipedia:Minor Planet Dziewanna|Minor Planet Dziewanna]]: (235 ± 18) km
-# [[wikipedia:Minor Planet 145480|Minor Planet 145480]]: (232 ± 31) km
 == see also ==
-* <code>[[wikipedia:Solar System by size]]</code>
+* <u><code>[[Solar System]]</code></u>
+* <u><code>[[Solar System by orbit]]</code></u>
+* <u><code>[[Solar System by size]]</code></u>
+* <u><code>[[Solar System by mass]]</code></u>
 == references ==
 <references />
+== keywords ==
+<code>angle, angles, astro, astronomics, astronomy, diameter, diameters, radii, radius, size, sizes, Sol, Solar, Sol-Jupiter, SolSys, Sun, Sun-Jupiter</code>
+{{#seo:|keywords=angle, angles, astro, astronomics, astronomy, diameter, diameters, radii, radius, size, sizes, Sol, Solar, Sol-Jupiter, SolSys, Sun, Sun-Jupiter}}
 [[category:astronomy]]
+[[category:pages with images]]

Solar System by size and Solar System by apparent size: Difference between pages

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Solar System by size and Solar System by apparent size: Difference between pages

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