Observing from the Equator

Part 1 - Why is dusk (twilight) so brief near the equator?

Twilight ends (and night darkness begins) when the sun is anywhere from about 12 to 18 degrees below the horizon.  At the equator the sun sets perpendicular to the horizon.  Therefore, it makes its fastest beeline from dusk to darkness there.  As you move to higher latitudes, the path of the sun becomes more and more tilted with the horizon so it takes longer for the sun to reach that magic 12-18 degree mark below the horizon.  If you have ever taken a tropical cruise (or artic cruise) , this phenomena becomes very apparent.

Part 2 - If you live on the equator, every day is 12 hours of daylight and 12 hours of night.  (OK, there are some strange atmospheric effects that make this not exactly true but we can ignore them.)  It has everything to do with the path that the sun takes in the course of a day.  If you have already learned the Stellarium program, you can observe this for yourself.  Your job is to explain what aspects about this daily path can help you rationalize why this 12/12 cycle exists each and every day on the equator.

It all comes down to the last answer.  Think of the path that the sun makes across the sky on any given day.  Because the sun moves perpendicular to the horizon, it makes a perfect semicircle in the sky during the day.  Being half a circle, it stands to reason that the length of daylight would also be half of 24 hours.  So the sun is above the horizon 12 hours and below the horizon 12 hours. 

I will also take a different answer.  Some students use the argument of symmetry to justify the 12 hour day at the equator.  It goes something like this:  Pick a point on the earth that is NORTH of the equator (say 43 degrees North) and pick some day that is not an equinox (say June 21).  This example is the first day of summer in Milwaukee.  Given this data, the daylight will be much longer than 12 hours.  However, if you look at the same location SOUTH of the equator, they will be experiencing the first day of winter and have a day experiencing much shorter than 12 hours of daylight.  The average daylight of these two locations will be 12 hours and the average LOCATION is exactly at the equator. 

Note: A lot of students say the sun always rises due east (and sets due west) every day at the equator.  NO!  You can see this for yourself in Stellarium.  On the first day of summer the sun rises in the north-east and sets in the north-west.  The difference is the path that it takes throughout the day.  The sun rises (and sets) perpendicular to the horizon every day at the equator.

Part 3 - Describe the moon phases as viewed from the equator.  Also, do the same if you were even further south (such as Australia).  By this, I mean how are things different from, say, an observer in Milwaukee.

This has everything to do with YOUR orientation in space.  A person at the north pole is upside-down with respect to a person at the south pole.  You therefore see everything a bit different compared to other observers.  Personal note:  Many years ago I was going through the phases of the moon with my class and showing pictures along with the discussion.  One student stopped me and corrected me that I had my pictures backwards.  The heavy Australian accent quickly made me realize that I was "northern hemisphere bias".   A person in the southern hemisphere observes the phases progress different from us.

Part 4 - Describe a day and a year at the equator if the earth had a tilt of 90 degrees instead of 23½ degrees.

The planet Uranus is almost like this.  It orbits on its side.  The north pole is in perpetual daylight for half the year and perpetual darkness the other half of the year.  If you lived at the Earth's equator you would still have a 12 hour day and 12 hour night but the sun would rise and set at all different places on the horizon throughout the year.  At one extreme, the sun would spend the whole day at the northern horizon (summer solstice), in 3 months it would rise due east, go through zenith and set due west (equinox). and in another 3 months it would spend the whole day at the southern horizon (winter solstice). 

You can see this for yourself.  Use Stellarium to place yourself on Uranus and then at the equator of that planet.  Go to the time 2/1/2050 and watch a day close to an equinox.  Then watch a solstice on 2/1/2070.  Remember the tilt is ALMOST 90 degrees. 

Note:  It is interesting that the north pole will experience 6 months of day and 6 months of night no matter what the tilt angle (unless it is zero ... in which case the sun would always be on the horizon).  What would change is the size of the Artic Circle (and Antarctic Circle).  If the tilt were 43 degrees (latitude of Milwaukee), on the first day of summer we would enjoy 24 hours of sunlight with the sun skimming the northern horizon at midnight.