[Physics] Fw: Occultations and eclipses

[carmam at tiscali.co.uk]

Further to my previous posting, I was dealing with a static situation when calculating the visibility of the occultations of any two of the four Galilean moons of Jupiter from Earth. I stated that the only occasion when the occultation could not be seen from any where on Earth was when Europa occulted Io, and that is because the disc of visibility would be only some 3,000 Km across. I did not go into how long that occultation could be seen from any given point on Earth, so here it is. Because of the very high visual approach and recession velocity between the two moons, and the ratio of that distance and the distance from Jupiter to Earth, the zone of visibility would race across the Earth's surface at a tremendous speed. Carl mentioned an occultation time of just a few seconds, and I can readily believe that to be so, given that ratio.The visual approach and recession velocity between the two moons can be as high as 30Km/s, and the ratio of the distance is 600:1, which gives a speed of the disc of visibility across the Earth of 18,000Km/s, so a zone 3,000Km across would take 0.16 seconds to cross any point. That is at the maximum speed when the moons are on the opposite sides of Jupiter looking from the north, but on the same side when looking from Earth. When they are on the same side looking from the north and from Earth, the approach speed is far slower, and can be as low as 3.6Km/s . This gives a speed of the zone of one second to cross any point. This is lower than Carl's figure which was (from memory 8 or 9 seconds). I will leave to anybody who wants to go with it to work out how long a much larger zone would take to cross a given point.My head hurts!


Tom Hollings.
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