How to Measure the Angular Size of the Big Dipper
Angular Sizes and Distances
In astronomy, the size and distances between objects in the sky is given as a measure of their angular distance as seen from Earth. These distances are measured in degrees and radians. The angular size of objects in the sky—stars, meteors, and the moon are usually very small; therefore, it is very convenient to represent them in degrees, arcminutes, and arcseconds.
A circumference is equal to 360°; one degree is 1/360; one arcminute is 1/21600 of a 360° circumference or 1/60 of a degree, and one arcsecond is 1/1296000 of a 360° circumference or 1/360 of one degree. To put this in perspective, the Moon has an angular size of 1/2 of a degree or 30 arcminutes which is the same as 1,800 arcseconds. The largest lunar craters have angular sizes of 2 arcminutes across.
In the next picture, the moon is drawn in perspective, as an observer on earth would see it in the sky. Since the Moon has an angular size of 1/2 degrees, it would take 180 Moons to cover the sky from the horizon to the zenith (the location in the sky just above one’s head).
One degree is shown in the picture. An arcminute is 1/60 of a degree and one arcsecond is 1/360 of a degree, and these angular measures are the ones astronomers use to measure distances in the sky.
360° Circumference; Degrees, Arcminutes, Arcseconds
Using Your Hand to Measure Angular Distances
Measuring Angular Distances with your Hand
Hipparcos satellite, launched into orbit by the European Space Agency in 1989, measured large and small angles of 118,218 stars within 20 to 30 milliarcseconds which are very small angles; however, to measure angles greater than 1/2 of a degree, you can use your own hands.
Holding your hand at arm´s length; the angular distance that you can measure with your thumb finger is one degree. With that finger you can cover two moons. Your three middle fingers cover the distance of 5°; with your fist, you can measure 10° in the sky; and the angular distance from the tip of your index finger to the tip of your pinky finger is 15°.
Angular Size of the Big Dipper
The Big Dipper
There are many sky objects that you can use to practice measuring angular sizes. One of these objects is a prominent group of stars known as the Big Dipper. The Big Dipper is a circumpolar (never sets due to its proximity to the celestial pole) asterism (a group of stars) which can be seen throughout the year. This asterism consists of seven stars; Alkaid, Mizar, Alioth, Megrez, Phecda, Dubhe, and Merak. The first three give form to the handle and the rest form the bowl.
Angular Distance Between Merak and Dubhe
Angular Distances of the Big Dipper
Now that you know what to use and the distances you can measure in the sky using your own hands, try to calculate the distances within the stars in the Big Dipper. You´ll see that the Big Dipper measures approximately 25° from Alkaid to Merak and that the angular distance from Phecda to Merak is of approximately 8°.
With your fist, you could easily measure the distance-10.3°, from Megrez to Dubhe, which is the top of the bowl and using three fingers, you may obtain the angular distances that separate the rest of the stars within this conspicuous asterism.
To easily spot the Big Dipper on any given night, try to choose a place away from any city's light pollution or use the shadow of a building or a tree to block any ambient light.
Since the Big Dipper is a circumpolar asterism (never sets below the horizon), people living in the northern latitudes of the world would be able to observe it more above in the sky and for longer periods of time than those living in the southern latitudes.
Angular Distances of stars within the Big Dipper
Alkaid to MIzar and Alcor = 6.8°
Tip of the handle
Mizar and Alcor
Mizar and alcor to Alioth = 4.4°
Alioth to Megrez = 5.5°
Part of the handle that attatches to the bowl
Megrez to Phecda = 4.5°
Left side of the bowl
Phecda to Merak = 8°
Lower part of the bowl
Merak to Dubhe = 5.5°
Right side of the bowl
Dubhe to Megrez = 19.3°
Top part of the bowl
Questions & Answers
© 2012 Jose Juan Gutierrez