Resources: Worksheet (PDF)Worksheet (docx)

Terminology: Equatorial Coordinate SystemEclipticRight AscensionDeclination, AltitudeAzimuthMeridianThe Horizontal Coordinate SystemSmall-Angle FormulaStellar ParallaxPercent Error Formula

1, 5, 10, 15, and 25 degrees of the sky can be estimated by outstretched pinky, 3 fingers, fist, pinky-pointer, and pinky-thumb.

Whenever you look at an object, you are measuring its angular size - the amount of space it takes up in your field of view in degrees, minutes, and seconds (or radians). You can't directly measure an object's size in centimeters or inches unless you walk up to it and use a ruler. You know that faraway objects look small and nearby objects look big, so your brain puts together an object's angular size with your guess as to its distance to give you an idea of its actual size.

Complex and precise instruments exist and can be constructed for measuring the angular size of objects, but a set of rough measurement tools can be found at the end of most people's arms. Because humans are built to mostly the same proportions, if you hold your arms outstretched with your palms facing forward, your hands will have about the same angular size in your field of vision regardless of whether you are tall, short, big or small. Your fingers and knuckles can be used to make rough measurements of angular sizes and distances on the sky as shown in the diagram to the right. Other useful angular size rulers exist as well. For example, the moon is almost exactly one-half degree in extent as viewed from the surface of the Earth.

Learning Goals: The goal of this lab is for students to familiarize themselves with the celestial sphere, and get experience estimating angles using (literal) rules of thumb, and work on estimating distances using parallax.