[Physics] Fw: Occultations and eclipses

Sat Aug 5 15:04:54 CEST 2017

Ruud, I had just finished amending and updating my previous post when I read yours.I did the calculations for the
speed of the disc of visibility using Callisto and Io again,
with Callisto being the occulting moon and being on the near side of
Jupiter. 

Some things I got wrong.

The ratio of the distance Io to
Callisto to Earth is not 600:1 but 300:1 - sorry for that error. The maximum
distance apart of Callisto and Io is 2.224 million Km (but reduce that to 2 M Km to
cater for them being in line of sight of each other just to one side of
Jupiter), and the distance Jupiter to Earth is 600 M Km. Their relative velocity
at that point is around 20 Km/s, multiply that by 300 is 6,000 Km/s, so the
disc of visibility at that distance is 356,000 Km in diameter, which easily
covers the Earth. As the disc of visibility is traveling across the Earth at
6,000 Km/s, at any point on Earth the occultation could be seen for approximately
60 seconds.

 Emboldened because my head is not yet spinning, I am
carrying on with the calculations.

If Callisto occulted Io when both were on the near side of
Jupiter as seen from Earth, they would be 1.6 M Km apart and their relative
velocity would be 9 Km/s as they are now traveling in the same direction, so
the occultation would last much longer. The zone of visibility would be
correspondingly larger at 450,000 Km, but its speed across the earth much
slower at 3,375 Km/s. This gives a viewing time of 133 seconds from any point
on Earth.

My head is now spinning. Somebody please do their own calculations to check mine, as I am still not 100% sure on them. You can then either berate or applaud me depending on the outcome. I have deliberately not shown the calculations or methodology as anyone else repeating my work might make the same mistake as I did (if I did!).Tom Hollings.

----Original Message----

From: rmmloeffen at gmail.com

Date: 05/08/2017 11:32

To: "General Physics and Natural Philosophy discussion list"<physics at tuks.nl>

Subj: Re: [Physics] Fw: Occultations and eclipses

Carl and Tom.
Thank you for your efforts in this "head hurting" discussion. I hope we will have more of these disputes.
It's rather quite lately around here.And Arend: Still alive and searching?

Ruud Loeffen.
On Fri, Aug 4, 2017 at 2:38 AM, carmam at tiscali.co.uk <carmam at tiscali.co.uk> wrote:
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.

_______________________________________________

Physics mailing list

Physics at tuks.nl

http://mail.tuks.nl/cgi-bin/mailman/listinfo/physics

-- 
Ruud LoeffenPaardestraat326131HC Sittardhttp://www.human-DNA.org

_______________________________________________
Physics mailing list
Physics at tuks.nl
http://mail.tuks.nl/cgi-bin/mailman/listinfo/physics

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.tuks.nl/pipermail/physics/attachments/20170805/04db7331/attachment.html>