Saturday, October 4, 2014

Three Methods to Measure the Elevation of Objects on the Horizon

As I was planning my view of the lunar eclipse on October 8, 2014, I was wondering if I'd be able to see the moon in total eclipse at 6:25am above the treeline. I wanted to share three methods I use for determining the elevation of objects on the horizon when planning for astronomical events.

Let's use the roofline of my neighbor's house as an example of all 3 of these techniques...

1. "At Arms Length" Method

I learned about this when I first started observing the night sky. It's the easiest and quickest technique, but the least accurate. To measure objects using this technique, all you have to do is hold your hand out at arms length and judge distances relative to your hand proportions. The proportions usually mentioned are:
  • 1° = Pinky fingernail
  • 5° = Index, middle, and ring fingers on one hand
  • 10° = Width of fist
  • 15° = Distance between pinky and index fingers in "I love you" sign language, or "rock and roll" hand gesture
  • 25° = Distance between tip of thumb and tip of pinky in "hang loose" or "shaka" hand gesture.
This technique becomes more difficult when you don't have a clear view of the horizon, like in the photo below, but it's great for quick estimates.

measure elevation of horizon
Three fingers above the horizon estimates 5° to the top of the tree
2. Lookup Previous Photo Timestamp

For this method you need two pieces of information, the photo timestamp from a previous photo, and the identity of one of the objects in the photo. Then you can look it up using software like Stellarium to see what the elevation of the object was at that time. This is, of course, pretty useless out in the field - but it can be a very accurate way of planning ahead for future trips.

Of course, if you have a perfectly clear horizon, you can always just look up the rise or set time of the object you are interested in (e.g. moonrise is easy enough to find online).  But if you have objects obstructing the horizon, such as this roofline, it can be harder to tell - so the timestamp method comes in handy.

Using this photo and looking up the elevation of the moon at that exact time, I can tell that the Moon was elevated 4°45' above the horizon.

measure elevation of moon
Using the exact photo timestamp from this image, I looked up the elevation of the moon in Stellarium (below)

measure elevation of moon
Elevation of the center of the moon at this time was 4°45'

3. Theodolite

A theodolite is a "precision instrument for measuring angles in the horizontal and vertical planes." Guess what, there's an app for that! The Theodolite app is amazing, and can help you measure the elevation of objects on the horizon in real time looking through the phone like augmented reality. You can even export photos that include cross-hairs and measurements. I also included a screenshot in this to show the in-app view.

way to measure elevation
In-app screenshot

how to measure elevation
Theodolite app estimates the roofline is 5.6° which is 5°36'
So here are the results, all pretty good estimates. Theodolite wins for convenience!
  • At arms length method = "less than 5°"
  • Photo timestamp method = 4°45' to the center of the moon
  • Theodolite = 5°36' to the roofline

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