[Physics] Occultations and eclipses

[carmam at tiscali.co.uk]

I replied to Carl personally with this email thinking I was replying to tuks. My apologies if you did actually receive it. Apologies to Carl for him receiving it twice.Carl et al. I feel that I must enter into this exchange as I am confused by the perhaps incorrect terminology. Are you are talking about eclipses where the shadow of one body falls on another, or are you talking about occultations where one body passes in front of another? There is a difference in the visibility of these two events from Earth. If anybody on Earth is watching Io (or any of the Galilean moons), and a shadow from another moon falls on it, that event would be visible from anywhere on Earth where Io was visible just before that event. That event is an eclipse. The moon would just disappear from view and then reappear.If one moon passes in front of another as seen from Earth, that is an occultation, when the light dims compared to when the moons were adjacent, and if both moons are for sake of argument 3,000 Km in diameter, then a disc 3,000 Km in diameter would be figuratively created on Earth where that occultation could be seen. It could be seen from nowhere else on Earth. The 3,000 Km figure is approximate, as the disc of visibility (to give it a name) would be greater if the occulting moon was larger than the occulted moon. Would it be as large as the Earth? If Io or Europa was on the opposite side of Jupiter, and Callisto on this side occulted one, they would be around 2,500,000 Km apart, and with a distance to Earth of between 588 million Km and 968 million Km, the disc of visibility of the occultation would be quite large.The size of the disc of visibility surprised me. These are ball park figures, so please feel free to work them out more accurately, and for the other moons.The moons I used were Callisto and Io, with Callisto being the occulting moon and being on the near side of Jupiter. Io is therefore occulted, and is on the far side of Jupiter, with a maximum separation of about 2.5 million kilometers from each other and a distance to Earth of 588 million Km (closest). The disc of visibility is 388,000 Km, so easily covers the entire Earth, and would be seen anywhere. With a distance to Earth of 968 million Km (farthest), the disc of visibility is 639,000 Km, and again covers the entire Earth. When both moons are on the near side of Jupiter, using a moon to moon separation of about 1.5 million Km, the disc of visibility is much larger, but I did not work out the actual figures, as it still encompasses the whole of the Earth.The final finding then on whether the occultation can be seen from the whole of the Earth depends on which moon is occulting which. The occulting of Europa by Io at their farthest apart gives a disc of visibility of 281,000 Km, so that event could also be seen from everywhere on Earth. Whether Jupiter and Earth are at their closest or farthest makes little practical difference to the size of the disc of visibility. The (annular?) occultation of Io by Europa (because Europa is smaller) should also be visible from anywhere on Earth as should the occultation of any larger moon by a smaller one. It would appear to me that for an occultation to be visible on one part of the Earth and not another is a 50/50 chance. I am not a natural mathematician, and doing these figures made my head spin, so please do correct me if I am wrong.Tom Hollings 

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