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## Quiz of the Month (January 2008)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```   a = 69o
b = 109.5o
c = 111o
d = 70.5o

Notes.

With the notation of the figure,

2x + 2y + 39 = 180    (Triangle)
So        x + y = 70.5
But   x + y + b = 180  (Straight line at P)
So            b = 109.5
Hence d = 180 - 109.5 = 70.5 (Cyclic quad.)
(etc.)

{Notice that x and y cannot be found individually.}

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#### THIS MONTH'S QUIZ

Assume that Earth and Mars both move at constant speed in circular orbits in the same plane around the Sun as centre. The radius of Earth's orbit is 93,000,000 ml, and of Mars' orbit is 142,000,000 ml. The Earth completes one orbit in 365 days, and Mars does so in 687 days.

1. Find the speed of each of these planets in their orbits, in miles per second.

2. Mars was at opposition (i.e. the centres of Sun, Earth and Mars, in that order, lay on a straight line) on 24th December 2007. On what date will the next opposition occur?

3. On what date will Mars next be at quadrature (i.e. as seen from Earth, the direction of Mars is at right angles to the direction of the Sun)?

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