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| Geodesics (more thoughts) |
by Unicorn |
2006-11-19 12:55:59 |
Please click here to see what I'm talking about.
The question raised in another words is:
" What is the relation between latitude and logitude for a "small"
circle ? "
A great circle contains center of globe, but a small circle is the
intersection by a plane eccentric to the sphere center.
The area of interest to you is bounded by four great circles, two
longitudes and two great circles of different inclination with same
points on equator. [ One small circle inside four great circles ! ]
<Br.
Sorry, my response below was incomplete. While the range in latitude
is easy to find as given, the range occupied by longitude can be found
by the following procedure.I give now the rest.
Let the ellipse projection of the small circle on the equitorial plane
have semi major axis a , semi minor axis b and distance to center c .
It is easy to calculate a,b,c in any given case. Then the limits of
longitude are given by plus or minus ArcTan[a/Sqrt[c^2-b^2] ]. ( c>b )
This corrosponds to the sketch you have provided where the pole is
outside the small circle. When the circle contains pole inside of it,
then, there are no limiting longitudes.
The exact relation is still not given,hope this helps. Otherwise, I
could send a Mathematica code for it .
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[ Reply ] |
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hey | by DennisMV | 2003-04-25 15:23:24 |
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