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Jeff Bryant

Solar eclipses on other planets

Jeff Bryant, Wolfram|Alpha, LLC
Posted 6 years ago
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Here is some analysis of eclipses on other planets. We want to compare the angular diameter of the Sun to the angular diameter of the moon in question, when observed from the "surface" of the planet in question.

angularDiameterSun[entity_] := angularDiameterSun[entity] = 
  Quantity[SetPrecision[ArcTan[StarData["Sun", "Diameter"]/
   PlanetData[PlanetaryMoonData[entity, "OrbitCenter"], 
  "DistanceFromSun"]]/Degree, 2], "AngularDegree"]

We use the semimajor axis of the moon's orbit as an estimate of the moon's distance from its host planet:

angularDiameterMoon[entity_] := angularDiameterMoon[entity] = 
  With[{data = PlanetaryMoonData[ entity, {"Diameter", "SemimajorAxis", "OrbitCenter"}]}, 
   If[QuantityQ[#[[1]]], Quantity[SetPrecision[ArcTan[#[[1]]/(#[[2]] - PlanetData[#[[3]], "Radius"])]/Degree, 2], 
  "AngularDegree"], #[[1]]] & /@ data]

coverageratio[entity_] := 
 If[QuantityQ[#[[1]]], #[[1]]/#[[2]], #[[1]]] & /@ 
  Transpose[{angularDiameterMoon[entity], angularDiameterSun[entity]}]

Here, we generate a grid showing that the ratio of the angular diameter of the Moon to the Sun is essentially 1. So, the Moon just basically covers the Sun during an eclipse.

With[{ents = EntityList[EntityClass["PlanetaryMoon", "EarthMoon"]]}, 
 With[{list = Reverse@SortBy[ Transpose[{ents, angularDiameterSun[ents], 
        angularDiameterMoon[ents], coverageratio[ents]}], #[[4]] &]}, 
  Grid[Prepend[TakeLargestBy[list, #[[4]] &, Min[Length[list], 10]], 
    Text /@ {"moon", "Sun angular diameter", "moon angular diameter", "ratio"}], Dividers -> All]]]

enter image description here

Mars only has 2 moons. Phobos, the larger of the 2, covers about 60% of the Sun during an eclipse:

With[{ents = EntityList[EntityClass["PlanetaryMoon", "MarsMoon"]]}, 
 With[{list = Reverse@SortBy[ Transpose[{ents, angularDiameterSun[ents], 
        angularDiameterMoon[ents], coverageratio[ents]}], #[[4]] &]}, 
  Grid[Prepend[TakeLargestBy[list, #[[4]] &, Min[Length[list], 10]], 
    Text /@ {"moon", "Sun angular diameter", "moon angular diameter", "ratio"}], Dividers -> All]]]

enter image description here

And for Jupiter we have:

With[{ents = EntityList[EntityClass["PlanetaryMoon", "JupiterMoon"]]},
  With[{list = Reverse@SortBy[ Transpose[{ents, angularDiameterSun[ents], 
        angularDiameterMoon[ents], coverageratio[ents]}], #[[4]] &]}, 
  Grid[Prepend[TakeLargestBy[list, #[[4]] &, Min[Length[list], 10]], 
    Text /@ {"moon", "Sun angular diameter", "moon angular diameter", "ratio"}], Dividers -> All]]]

enter image description here
POSTED BY: Jeff Bryant
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5 Replies
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This is very interesting, because ratio 1 is unique to Earth. Looks like Jupiter's Amalthea is the closest with 0.9 ratio. I wonder if its orbit allows for blocking of the sun. Generally it is possible - Here is a quote from NASA:

Images taken with a telephoto-lens camera on NASA's Mars rover Curiosity catch the larger of Mars' two moons, Phobos, passing directly in front of the sun -- the sharpest images of a solar eclipse ever taken at Mars. Phobos does not fully cover the sun, as seen from the surface of Mars, so the solar eclipse is whatÂ’s called a ring, or annular, type.

enter image description here

Image Credit: NASA/JPL-Caltech/Malin Space Science Systems/Texas A&M Univ.

And for the Saturn and Titan:

The shadow of Saturn's largest moon darkens a huge portion of the gas giant planet. Titan (5,150 kilometers, or 3,200 miles across) is not pictured here, but its shad ow is elongated in the bottom right of the image. This view looks toward the northern, sunlit side of the rings from just above the ringplane. The image was taken with the Cassini spacecraft wide-angle camera on Nov. 7, 2009 using a spectral filter sensitive to wavelengths of near-infrared light centered at 752 nanometers. The view was obtained at a distance of approximately 2.1 million kilometers (1.3 million miles) from Saturn and at a Sun-Saturn-spacecraft, or phase, angle of 95 degrees. Image scale is 123 kilometers (76 miles) per pixel.

enter image description here
POSTED BY: Vitaliy Kaurov
Answer

Related to Vitaliy's question about if these other Moon's orbits can block the Sun, this link seems relevant. In all cases, it appears that yes it's possible, but depending on the orbital plane of the moon with respect to the orbit of the planet around the Sun (the ecliptic), this may happen more or less frequently. Most of Jupiter's moons have orbital planes that are almost the same as the ecliptic, so eclipses are frequent (at least one per orbit of the moon). As the planet's axis tilts more, the orbital plane of its moon's also changes so you end up with 2 points along the moon's orbit where it intersects the ecliptic. If the moon happens to be at one of those points when the Sun is also there, you get an eclipse. This obviously happens far less frequently.
POSTED BY: Jeff Bryant
Answer

Hello, I found that planetaryMoonData & StaData not function as before. Two days ago, they still work correctly. Now they can not accept "moon", "star". The code example from wolfram Language Documentation PlanetaryMoonData Scope now can not accept date object. moon now must use entityClass as the code you post here. Could you find out what is going on?
POSTED BY: Peterson Philips
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Your comments are not entirely clear. The issue with supporting dates is a known recent problem dealing with how dates are exposed via EntityValue (used by StarData and PlanetaryMoonData under-the-hood). Its more general and doesn't affect the Alpha website, its only in the exposed data that the problem presents. It was fixed this morning internally but will take some time to be tested before being pushed out since the fix touches a number of components. It would be better to report such issues to support@wolfram.com since that is a more appropriate forum for reporting and tracking issues.
POSTED BY: Jeff Bryant
Answer

I should add that if you are not using Mathematica 10.1, you might have additional problems with the presented code. It makes use of:

http://reference.wolfram.com/language/ref/TakeLargestBy.html

If you have an older 10.0 or even earlier, this code won't work without modification.
POSTED BY: Jeff Bryant
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