How square is Pegasus?

The Great Square of Pegasus:
How square is it?

10. Measuring: Use your astrolabe, quadrant and cross-staff to measure (pick the tool which you think is best for the task)... ...the two diagonals of the Great Square, (is it really a square?)

I chose to use the cross-staff for this task. Measurements were made from 18:30 to 19:00 on Saturday February 1st 2019 at the Edmund G. Kline dark sky site near Deer Trail Colorado.

Pegasus is about finished for this time of year and sets in the West early in the evening. From my home location with light polluted suburban skies this would be tough, especially with Pegasus setting into the Denver lights. The Kline site is 60 miles east of town. I'm normally out there at least once during the New Moon, so I brought along my cross-staff. Although there's still a "light dome" over Denver, the four stars of the Great Square were easily visible at the end of twilight.

The activity calls for measuring the two diagonals of the square. I made these measurements, and in addition made four measurements around the sides of the square.

Here is a table of my observations. The cross-staff reading is converted to the measured angle of separation using the math described in the cross-staff section. The Stellarium values were derived using the Angle Tool plugin and are reasonably accurate, probably to within a quarter of a degree.

	Cross-staff scale / reading	Angle of Separation computation	Stellarium says:
Alpheratz - Markab (diagonal)	E / 45.8 cm	21.27^o	20.42^o
Algenib - Scheat (diagonal)	E / 44.8 cm	21.73^o	20.59^o
Alpheratz - Scheat	E / 66.6 cm	14.72^o	14.19^o
Alpheratz - Algenib	E / 66.6 cm	14.72^o	13.98^o
Scheat - Markab	E / 76.5 cm	12.83^o	12.87^o
Algenib - Markab	E / 55.5 cm	17.62^o	16.56^o

My answer is "no". The Great Square is not really square. Finding equal diagonals would not prove a square. You can have infinite quadrangles other than squares with equal diagonals. But you cannot have a single square with unequal diagonals. So finding unequal diagonals will disprove a square. Also, a square would have four sides of equal length which is clearly not the case in Pegasus.

Once again I am really impressed with the accuracy of the measurments from the cross-staff. It has been working really great for my Sun-Venus and Venus-Jupiter measurements. Stars are much dimmer than solar system objects and present new challenges. I'm certain that my technique will improve with practice.

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