Friday, July 03, 2009

Getting the Shot

The following is a tale of patience, perseverance, forethought, math, and celestial mechanics.

A few months ago, for an undisclosed reason, I decided that I needed a very specific photograph of Samford Hall on the Auburn campus.  This photo had to be taken from a particular angle.  It also had to be taken at night.  And, to compound matter, I decided that it would make an even more interesting picture if the moon was tucked neatly between the two towers of Samford.

To begin with, I wasn’t even sure if such a celestial alignment ever occurred.  And if it was something that occurred, when and how often?  So I began educating myself about the habits of our closest neighbor.

The moon orbits Earth about the solar elliptic (an oddity as most other moons orbit about the equator of their planet) with an inclination of around 5 degrees.  Because it orbits about the solar elliptic, the position of the moon in the sky is highly dependent on the season.  And because of the 5 degree inclination and 27.3 day orbit, the path through the sky varies quite a bit over the course of the month as well.  But, thankfully, I found a handy tool published by the US Navy that gave me the azimuth angle of sunrise, sunset and the angle of the height of the transit point, as well at the times of these occurrences.  This was enough information for me to calculate the position of the moon at any time of the night.

But being able to calculate the position of the moon at any time wasn’t what I really wanted.  I needed to know when the moon would pass through a specific spot in the sky.  So I needed to know what that position was.  Google Earth told me that the position that I was going to shoot from was 200 feet from the front steps of Samford Hall.  And Wikipedia tells me that the height of the taller spire is 170 ft.  and the roof is 154.  Simple trigonometry tells me that I need to take my picture when the moon is at a height of between 36 and 40 degrees above the horizon.  Google Earth also told me that the heading from my vantage to the left tower was 222 degrees from north, while the right tower was 230.

So that was my target.  A box in the sky bounded by those four lines. I chose the center point, 38 degrees above the horizon and 226 degrees from north.

So I plugged the navy data into a spreadsheet and began breaking the nightly lunar path down into its horizontal and vertical components.  The vertical was easy enough.  I simply took the percentage 38 was of 90 (the vertical component of transit) and applied that to the time difference between transit and moonset.  This would be the time each day that the moon would be 38 degrees above the horizon.  For the horizontal component, I first took horizontal component of the angle of transit (again, trigonometry).  I subtracted this from the azimuth of moonset. Then, if 226 fell between those two numbers (which it often didn’t), I took its percentage and applied it to the time difference between transit and moonset as well.  This gave me the time that the moon would pass through the 226 azimuth.

I calculated these figures out until the end of the year, and then began looking for nights in which these two times were very close together.  It turned out that there are 2 or 3 consecutive nights each lunar orbit with the opportunity to get a good shot.  My first opportunity came in mid May, but it was too cloudy every night to get a good shot.  My second chance came again in early June, but one night it was again to cloudy, then the next night the conjunction occurred very late at night and I couldn’t stay up because of work the next morning.

But my 3rd chance came this last week.  By my calculations, Tuesday June 30 at 10:03 PM was my best opportunity.  I went out with my camera, but discovered that my calculations were a little off.  The moon was directly behind the samford-moonSamford Bell Tower.  I waited half an hour and got a shot of the moon after it had passed to right of the tower, but this was not quite what I wanted. 

So, the next night at 11:20 I was back out there again.  And, well, you can see the results for yourself.