Angular Measurement
When measuring positions, distances, or sizes in the sky, it is helpful to think of ourselves as inside a
large sphere. When we measure the distance between two celestial objects – like stars – or the size of a
celestial object – like a planet – it is measured as an angle (see figure below). Angular distance and size
is measured in “degrees of arc” with the vertex of the angle at the center of the sphere. Fractional
values of “degrees of arc” are measured in arcminutes and arcseconds. One arcminute (written 1’) is
equivalent to 1/60 of a degree and one arcsecond (written 1”) is equivalent to 1/60 of an arcminute or
1/3600 of a degree.
Angular
Distance/Size
Angular
Distance
Angular
Size
Angular measurement can be used to describe the distance between two celestial objects such as stars or the size
of a celestial object like a planet.
Prepared by the Center for History of Physics at AIP
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Name: ________________________________
Date: _______________
Measuring the Big Dipper
In the field, you can use your hand to estimate the angular distance between and size of celestial objects
like the Big Dipper!
The North Star (Polaris)
The Pointer Stars in
the Big Dipper
always point to the
North Star
7
2
Mizar
1
Alkaid
3
Dubhe
4
Megrez
6
Alioth
The Big Dipper (Ursa Major)
5
Phecda
Prepared by the Center for History of Physics at AIP
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Merak
1. Find the Big Dipper in the sky using the North Star. Remember that the two stars at the edge of
the Big Dipper always point to the North Star (see above illustration).
2. Hold your arm outstretched to the sky. Your eyes will be the center of the celestial sphere. As a
guide, the angular size (diameter) of the moon is approximately 30° (see below).
Use the following chart to estimate the distance between the different stars in the Big Dipper:
Pinky finger width
Three middle fingers together (Ring
finger, middle finger, and pointer finger)
Back of your fist
Pinky and pointer finger in a “Y” shape
Pinky and thumb in a “Y” shape (Hang
Loose sign)
1 degree of arc
5 degrees of arc
10 degrees of arc
15 degrees of arc
25 degrees of arc
Fill in the different distances on the above illustration of the Big Dipper. Fill in the following
distances in degrees, arcminutes, and arcseconds. Remember the following conversion:
1° (Degree of arc) = 60 Arcminutes = 360 Arcseconds
Alkaid  Dubhe = ________ Degrees = ________ Arcminutes = __________ Arcseconds
Merak  Polaris = ________ Degrees = ________ Arcminutes = __________ Arcseconds
Alkaid  Polaris = ________ Degrees = ________ Arcminutes = __________ Arcseconds
Check how accurate you are with the below diagram. Remember, these are just estimates, so if
you are off by a few degrees, don’t worry.
~5°
Prepared by the Center for History of Physics at AIP
~30
arcminutes
or 1/2°
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