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AST 3722C  Spring 2008
Homework #1. Due before class on January 22.
(Not January 15 as originally on this paper.)
Instructions: Solve each problem below. Where math is involved, and unless otherwise
indicated, show your work.
1.
[1 point]
Chapter 7 Problem 5, pages 5556. This is practice in using the spherical
trig formulae.
2.
[1 point]
Chapter 7 Problem 9, page 58. A realworld problem! (Sort of.)
3.
[3 points]
You and a friend start a journey toward the North Pole. You start from the
same latitude – i.e. 60
◦
N – but you start from diﬀerent longitudes. You start in Quebec at
a longitude of 75
◦
W. Your friend starts in Sweden at a longitude of 15
◦
E. You both travel
northward at exactly the same rate over the tundra and ice, so that you are always at the
same latitude. Let
φ
be your latitude at any given moment.
(a) Derive the greatcircle angular distance
θ
between you and your friend as a function
of
φ
.
(b) Assume the small sphericaltriangle approximation works all along your journey and
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 Spring '09
 Fernandez
 Astronomy

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