**
=EQUALS= **

**A CLUB OF
INVESTIGATION AND DISCOVERY**

**
OCTOBER 2011 MEETING ANNOUNCEMENT**

**
TUESDAY, October 18**

6:00 - 7:00

OLATHE EAST HIGH SCHOOL, Room 507

14545 West 127th Street, Olathe, KS

**THE FALL SEASON AND
THE SOLAR SYSTEM - DIGITALLY EXAMINED!**

**A CHALLENGE TO YOU**

**The LEVEL 1 booklet
is below - try to do one of the five assignments. They do not take much
time.**

**THE MATH TEST IS
ABOVE - try to do problems 1, 2, 3, 10, and 20. THESE ARE ALL DOABLE!**

**We will also talk
about PRIME NUMBERS, and the infinite projects that come from being able to find
them.**

**
THE ORBIT PROBLEM**

**Assume the moon
has an orbit of 20 days. That is, after 20 days, it returns to the
horizon.**

After 20 days, we see, though the moon has completed one full cycle (a SIDEREAL MONTH [that's the word I was searching for last night]), it is not in line with the earth and the sun. This is because the earth, too, is moving. This is why the SYNODIC month is longer than the SIDEREAL month.

What does this look like after 21 days?

21 days and we're still not at the synodic month. An astronomical "Tortoise and the Hare" Game! Does the moon fall in line at 22 days?

Yes! In fact, it overshot our extended line! So if, here the sidereal month is 20 days, the synodic month is between 21 and 22 days.

*
But what is it exactly?*

We can see it's when angles α and β are equal.

But* when* are they equal?

This is Problem #2 in the "Tough Test" booklet. And can we confirm, using this method, the sidereal and synodic periods of our actual moon?