Solar System by apparent size: Difference between revisions

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(Created page with "Theoretical maximum polar angular diameters of Solar System objects. # 34.101066538719571684354526654789' (Terran Satellite Luna) # 32.547126271128421347619794544615' (Star Sol) # 1.0906122989752812163642065160574' (Planet Venus) # 46.864359694029502762359234633631" (Planet Jupiter) # 25.534081386616069677232424794313" (Planet Mars) # 18.682022776170470577149147085716" (Planet Saturn) # 13.024739118580633892606960873327" (Planet Mercury) # 3.9877210754712245044006428590...")
 
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Theoretical maximum polar angular diameters of Solar System objects.
== maximum angular diameter ==


# 34.101066538719571684354526654789' (Terran Satellite Luna)
Theoretical maximum angular diameters of Solar System objects.
 
# 34.142318167759912317334133764235' (Terran Satellite Luna)
# 32.547126271128421347619794544615' (Star Sol)
# 32.547126271128421347619794544615' (Star Sol)
# 1.0906122989752812163642065160574' (Planet Venus)
# 1.0906123267366001865954297950335' (Planet Venus)
# 46.864359694029502762359234633631" (Planet Jupiter)
# 50.115577292011594309068223040747" (Planet Jupiter)
# 25.534081386616069677232424794313" (Planet Mars)
# 25.685340680612365924690116419971" (Planet Mars)
# 18.682022776170470577149147085716" (Planet Saturn)
# 20.710914369111405511819166681816" (Planet Saturn)
# 13.024739118580633892606960873327" (Planet Mercury)
# 13.030602889883030119235614459212" (Planet Mercury)
# 3.9877210754712245044006428590578" (Planet Uranus)
# 4.0812943165836861322325384913351" (Planet Uranus)
# 2.3309251788780344136643886924446" (Planet Neptune)
# 2.3714321979272179525305286226839" (Planet Neptune)
# 1.8498609644868093537366885461724" (Jovian Satellite Ganymede)
# 1.8500081168516257242353190047029" (Jovian Satellite Ganymede)
# 1.6950737536462117296784747781491" (Jovian Satellite Callisto)
# 1.6950737536462117296784747781491" (Jovian Satellite Callisto)
# 1.2734334995821583999203032911068" (Jovian Satellite Io)
# 1.2758186006115161532107678507247" (Jovian Satellite Io)
# 1.0953739293038257329442022843157" (Jovian Satellite Europa)
# 1.0953739293038257329442022843157" (Jovian Satellite Europa)
# 0.88572560775248785404142250762448" (Saturnian Satellite Titan)
# 0.88572560775248785404142250762448" (Saturnian Satellite Titan)
''Angular diameters of triaxial ellipsoids are calculated with the middle radius (second equatorial radius).''


== data ==
== data ==
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Star Sol.
Star Sol.


* <var>r</var> = 696.3 Mm
* <var>r</var><sub>e</sub> = 696.3 Mm
* <var>d</var><sub>min</sub> = 147.09206561347015794307232373387 Gm = <var>π</var><sub>0</sub> − <var>r</var><sub>max,0</sub>
* <var>d</var><sub>min</sub> = 147.09206561347015794307232373387 Gm = <var>π</var><sub>0</sub> − <var>r</var><sub>max,0</sub>


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Planet Jupiter.
Planet Jupiter.


* <var>r</var><sub>p</sub> = 66.854 Mm
* <var>r</var><sub>e</sub> = 71.492 Mm
* <var>π</var> = 740.595 Gm
* <var>π</var> = 740.595 Gm
* <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>
* <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>
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Planet Saturn.
Planet Saturn.


* <var>r</var><sub>p</sub> = 54.364 Mm
* <var>r</var><sub>e</sub> = 60.268 Mm
* <var>π</var> = 1.35255 Tm
* <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>
* <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>
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Planet Uranus.
Planet Uranus.


* <var>r</var><sub>p</sub> = 24.973 Mm
* <var>r</var><sub>e</sub> = 25.559 Mm
* <var>π</var> = 2.73556 Tm
* <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>
* <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>
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Planet Neptune.
Planet Neptune.


* <var>r</var><sub>p</sub> = 24.341 Mm
* <var>r</var><sub>e</sub> = 24.764 Mm
* <var>π</var> = 4.46 Tm
* <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>
* <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>
Line 61: Line 65:
Planet Venus.
Planet Venus.


* <var>r</var> = 6.0518 Mm
* <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>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>
* <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>
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Planet Mars.
Planet Mars.


* <var>r</var><sub>p</sub> = 3.3762 Mm
* <var>r</var><sub>e</sub> = 3.3962 Mm
* <var>π</var> = 206.650 Gm
* <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>
* <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>
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Jovian Satellite Ganymede.
Jovian Satellite Ganymede.


* <var>r</var> = 2.6341 Mm
* <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>α</var> = 1.0716 Gm
* <var>d</var><sub>min</sub> = 587.41941861347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
* <var>d</var><sub>min</sub> = 587.41941861347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
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Planet Mercury.
Planet Mercury.


* <var>r</var> = 2.4397 Mm
* <var>r</var><sub>e</sub> = 2.4407983592616677504877194737632 Mm = −2(2.4397 Mm)/(0.0009 − 2)
* <var>α</var> = 69.82 Gm
* <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>
* <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>
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Jovian Satellite Io.
Jovian Satellite Io.


* <var>r</var><sub>p</sub> = 1.8153 Mm = (3.6306/2) Mm
* <var>r</var><sub>e,<var>b</var></sub> = 1.8187 Mm = (3.6374/2) Mm
* <var>α</var> = 423.4 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>
* <var>d</var><sub>min</sub> = 588.06761861347015794307232373387 Gm = <var>d</var><sub>min,Jupiter</sub> − <var>α</var>
Line 117: Line 125:
Terran Satellite Luna.
Terran Satellite Luna.


* <var>r</var><sub>p</sub> = 1.7360 Mm
* <var>r</var><sub>e</sub> = 1.7381 Mm
* <var>π</var><sub>min</sub> = 356.4 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>
* <var>d</var><sub>min</sub> = 350.01561347015794307232373387065 Mm = <var>π</var><sub>min</sub> − <var>r</var><sub>max,0</sub>
Line 133: Line 141:
Saturnian Satellite Iapetus.
Saturnian Satellite Iapetus.


* <var>r</var><sub>p</sub> = 712.0 km = (1.424/2) Mm
* <var>r</var><sub>e</sub> = 746.00 km = (1.4920/2) Mm
* <var>a</var> = 3.56082 Gm
* <var>α</var> = 3.659387770584 Gm = (0.0276812 + 1)(3.56082 Gm)
* <var>d</var><sub>min</sub> = 1.1968851986134701579430723237339 Tm = <var>d</var><sub>min,Saturn</sub> − <var>a</var>
* <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> = 0.24540455879656902560059531597654" = 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>)


=== Ceres ===
=== Ceres ===
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Minor Planet Ceres.
Minor Planet Ceres.


* <var>r</var><sub>p</sub> = 445.9 km = (891.8/2) km
* <var>r</var><sub>e,<var>b</var></sub> = 481.0 km = (962.0/2) km
* <var>π</var> = 381 Gm
* <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>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> = 0.80362670930464097512720672506318" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</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 ===
=== Pallas ===
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Minor Planet Pallas.
Minor Planet Pallas.


* <var>r</var><sub>p</sub> = 224 km = (448/2) km
* <var>r</var><sub>e,<var>b</var></sub></sub> = 266 km = (532/2) km
* <var>π</var> = 319 Gm
* <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>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> = 0.55367787659896149150062534328033" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>δ</var><sub>p,max</sub> = 0.65749247846134773534338734227922" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)


=== Juno ===
=== Juno ===
Line 160: Line 177:
Minor Planet Juno.
Minor Planet Juno.


* <var>r</var><sub>p</sub> = 112.5 km = (225/2) km
* <var>r</var><sub>e,<var>b</var></sub> = 125 km = (250/2) km
* <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>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> = 0.32029576692100294990513108282479" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)
* <var>δ</var><sub>p,max</sub> = 0.35588418546778944267259225024255" = 2asin(<var>r</var><sub>p</sub>/<var>d</var><sub>min</sub>)


== formulae ==
== formulae ==
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* <var>h</var> = +6.26347 km = Terran elevation of Chimborazo
* <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>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]]

Revision as of 06:05, 8 June 2024

maximum angular diameter

Theoretical maximum angular diameters of Solar System objects.

  1. 34.142318167759912317334133764235' (Terran Satellite Luna)
  2. 32.547126271128421347619794544615' (Star Sol)
  3. 1.0906123267366001865954297950335' (Planet Venus)
  4. 50.115577292011594309068223040747" (Planet Jupiter)
  5. 25.685340680612365924690116419971" (Planet Mars)
  6. 20.710914369111405511819166681816" (Planet Saturn)
  7. 13.030602889883030119235614459212" (Planet Mercury)
  8. 4.0812943165836861322325384913351" (Planet Uranus)
  9. 2.3714321979272179525305286226839" (Planet Neptune)
  10. 1.8500081168516257242353190047029" (Jovian Satellite Ganymede)
  11. 1.6950737536462117296784747781491" (Jovian Satellite Callisto)
  12. 1.2758186006115161532107678507247" (Jovian Satellite Io)
  13. 1.0953739293038257329442022843157" (Jovian Satellite Europa)
  14. 0.88572560775248785404142250762448" (Saturnian Satellite Titan)

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

data

Sol

Star Sol.

  • re = 696.3 Mm
  • dmin = 147.09206561347015794307232373387 Gm = π0 − rmax,0

Jupiter

Planet Jupiter.

  • re = 71.492 Mm
  • π = 740.595 Gm
  • dmin = 588.49101861347015794307232373387 Gm = π − α0 − rmax,0

Saturn

Planet Saturn.

  • re = 60.268 Mm
  • π = 1.35255 Tm
  • dmin = 1.2004460186134701579430723237339 Tm = π − α0 − rmax,0

Uranus

Planet Uranus.

  • re = 25.559 Mm
  • π = 2.73556 Tm
  • dmin = 2.5834560186134701579430723237339 Tm = π − α0 − rmax,0

Neptune

Planet Neptune.

  • re = 24.764 Mm
  • π = 4.46 Tm
  • dmin = 4.3078960186134701579430723237339 Tm = π − α0 − rmax,0

Venus

Planet Venus.

  • m = 4.8675 Rg
  • P = 20.99715264 Ms = 243.0226 d
  • re = 6.0518001540473630205875615870764 Mm = (6.0518 Mm)([5nπ2{6.0518 Mm}3/{3GmP2}] + 1)
  • α = 108.94 Gm
  • dmin = 38.152065613470157943072323733871 Gm = π0 − α − rmax,0

Mars

Planet Mars.

  • re = 3.3962 Mm
  • π = 206.650 Gm
  • dmin = 54.546018613470157943072323733871 Gm = π − α0 − rmax,0

Ganymede

Jovian Satellite Ganymede.

  • m = 148.19 Yg
  • P = 618.153375744 ks = 7.15455296 d
  • r = 2.6343095368525535298979659694619 Mm = (2.6341 Mm)([5nπ2{2.6341 Mm}3/{3GmP2}] + 1)
  • α = 1.0716 Gm
  • dmin = 587.41941861347015794307232373387 Gm = dmin,Jupiter − α

Titan

Saturnian Satellite Titan.

  • r = 2.57473 Mm
  • α = 1.25706 Gm
  • dmin = 1.1991889586134701579430723237339 Tm = dmin,Saturn − α

Mercury

Planet Mercury.

  • re = 2.4407983592616677504877194737632 Mm = −2(2.4397 Mm)/(0.0009 − 2)
  • α = 69.82 Gm
  • dmin = 77.272065613470157943072323733871 Gm = π0 − α − rmax,0

Callisto

Jovian Satellite Callisto.

  • r = 2.4103 Mm
  • α = 1.897 Gm
  • dmin = 586.59401861347015794307232373387 Gm = dmin,Jupiter − α

Io

Jovian Satellite Io.

  • re,b = 1.8187 Mm = (3.6374/2) Mm
  • α = 423.4 Mm
  • dmin = 588.06761861347015794307232373387 Gm = dmin,Jupiter − α

Luna

Terran Satellite Luna.

  • re = 1.7381 Mm
  • πmin = 356.4 Mm
  • dmin = 350.01561347015794307232373387065 Mm = πmin − rmax,0

Europa

Jovian Satellite Europa.

  • r = 1.5608 Mm
  • α = 676.938 Mm
  • dmin = 587.81408061347015794307232373387 Gm = dmin,Jupiter − α

Iapetus

Saturnian Satellite Iapetus.

  • re = 746.00 km = (1.4920/2) Mm
  • α = 3.659387770584 Gm = (0.0276812 + 1)(3.56082 Gm)
  • dmin = 1.1967866308428861579430723237339 Tm = dmin,Saturn − α
  • δp,max = 0.25714449258506853269763466887060" = 2asin(rp/dmin)

Ceres

Minor Planet Ceres.

  • re,b = 481.0 km = (962.0/2) km
  • π = 381 Gm
  • dmin = 228.89601861347015794307232373387 Gm = π − α0 − rmax,0
  • δp,max = 0.86688595464357998161003398040218" = 2asin(rp/dmin)

Vesta

Minor Planet Vesta.

  • re,b = 278.6 km = (557.2/2) km
  • π = 322 Gm
  • dmin = 169.89601861347015794307232373387 Gm = π − α0 − rmax,0
  • δp,max = 0.67647700622350749837333046252586" = 2asin(rp/dmin)

Pallas

Minor Planet Pallas.

  • re,b = 266 km = (532/2) km
  • π = 319 Gm
  • dmin = 166.89601861347015794307232373387 Gm = π − α0 − rmax,0
  • δp,max = 0.65749247846134773534338734227922" = 2asin(rp/dmin)

Juno

Minor Planet Juno.

  • re,b = 125 km = (250/2) km
  • π = 297.0 Gm
  • dmin = 144.89601861347015794307232373387 Gm = π − α0 − rmax,0
  • δp,max = 0.35588418546778944267259225024255" = 2asin(rp/dmin)

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

  • α0 = 152.097597 Gm = Terran aphelion distance
  • π0 = 147.098450 Gm = Terran perihelion distance
  • rmax,0 = 6.3843865298420569276762661293493 Mm = √([{cos(φ)a2}2 + {sin(φ)b2}2]/[{cos(φ)a}2 + {sin(φ)b}2]) + h = Terran maximum radius
  • a = 6.378137 Mm = Terran equatorial radius
  • b = 6.356752 Mm = Terran polar radius
  • h = +6.26347 km = Terran elevation of Chimborazo
  • φ = −25.641801411647532015402479952681mr = −1.469167° = Terran latitude angle of Chimborazo
  • G = 6.67430 × 10−11 N·m2/kg2 = gravitational constant
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