Published: January 29, 2009 08:29 pm      

Here’s how to measure things

In looking at the night sky, sky gazers become acquainted with angles to describe the width of star groups, apparent distance between two bright stars, how far the moon appears above the horizon, how far Venus moves lower each hour.

The unit of angle is the degree. Most of us know that there are 360 degrees around the horizon. So between the north point of the horizon and the east point is 90 degrees. You can consider the directions along the horizon like a pie cut in four parts. One pie cut faces north, another towards east, yet another towards south and the last cut faces west.

Just as there is 90 degrees or a right angle between the compass directions, there is 90 degrees between the horizon and the top of the sky (zenith). Why can’t we instead use miles or feet to describe the spacing between objects? We use angles because we don’t have a set distance for the sky objects.

The moon and Venus are relatively close while the stars are vastly farther away. Of course, the star groups consist of stars at a number of distances away; so the distance across a group (like the Big Dipper) can’t be pinned down.

How can we measure sky angles or angular heights or widths of objects without special equipment?

We can use our hands, fingers and fist to estimate angles. If you stretch out either arm, make a fist and turn your wrist so you can see all four fingers and thumb in a horizontal direction, then the angle from edge of little finger to edge of your thumb will range from 8 to 13 degrees (depends on your hand size and arm length).

You can find your fist angle by using your fists of both hands, one after another and going from the horizon (level direction) to the top of the sky (overhead); you count how many fists it takes to cover 90 degrees. I find that 8 fists of mine will go from horizon to top of sky, so each of my fists is about 90/8 = 11 degrees across.

With a ruler, I measure that my fist is four inches across (I have small hands). The width of my index finger is .75 inch across. So the angular width of my index finger must be (.75 inches)/(4 inches) x 11 degrees = about 2 degrees. So if I extend my hand and show my index finger (a sign sports fans use to tell all that their team is No. 1), I see an angle of 2 degrees across its width.

If I stretch out my right or left hand with the thumb pointing outward and the little finger pointing the other way, the distance between is 8.5 inches; so the angle between the tip of the thumb and the tip of the little finger will be 8.5 inches/4 inches x 11 degrees = about 23 degrees.

I can check this by going from one hand stretch to another until I reach from the horizon to top of the sky. I get 4 hand stretches or 4 x 23 = 92 degrees (close to 90 degrees), confirming my hand stretch angle.

I can go outside and measure both the angular widths or heights of objects as I see them using my hands, fingers and fist. Just off my front porch in central LaVale (a few blocks north of Route 40), I find that Haystack Mountain is one fist or 11 degrees in altitude above my horizon (relative to my eye level).

I find that the utility pole down the street is 2 fists high or 22 degrees. This is also confirmed by my hand stretch, which also covers the pole length from my eye level to the top (23 degrees). The pole’s width is about one third wide as my index finger width so the pole appears to be about 2/3 degree across. For reference, both the sun and moon are about 1/3 of a degree wide.

Now to calculate angles, particularly small angles there is a formula that requires the distance and actual height or width of the object. Formula is angle in degrees = 57.3 degrees x Dimension/Distance where the dimension (either height or width) must be in the same units as distance.

For the pole mentioned earlier, its actual width is .75 feet or 9 inches (3/4 of a foot). My distance to pole is 75 feet (30 paces at 2.5 feet per pace). So by the formula, the pole’s angular width is 57.3 degrees x (0.75 feet)/(75 feet) = 0.6 degrees, not too far from 2/3 or .67 degrees.

For the proposed wind turbines, the height of the rotors will be 80 meters or about 292 feet. From a distance of a mile (5280 feet), the angle extended will be 57.3 degrees x (292 feet)/(5280 feet) = 3.2 degrees. This is about 0.3 the angle of my fist held at arm’s length.

The rotors may extend out 47.5 meters (156 feet), which at a mile distance will cover an angle of 1.7 degrees, less than the width of my index finger. Some claim that their houses will be even closer, but the final placement of the wind turbines has not been decided due to the other communication towers on Dan’s Mountain.

From three miles away, all the angles will shrink by a factor of three, making the wind turbines quite small in angle compared to your neighbors’ houses (if you live in a neighborhood, as opposed to more widely spaced residences in more affluent areas).

Our free February program at the Frostburg State Planetarium is “Tropical Skies,” showing the different view of sky sights seen near the equator, using our Planetarium Projector.

We will also have an informal tour of the current evening sky at the start. Free sky maps and 2009 Night Highlights are available to our visitors. Our programs are each Sunday at 4 p.m. and 7 p.m.

The Planetarium is in Tawes 302, a few hundred feet in back (northwest) of the Performing Arts Center whose parking area is free. Call (301) 687-7799 to request a planetarium bookmark sent to you through the mail.

Submit comments or questions to rdoyle@frostburg.edu .