Angular Size

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Learning Goals: аThe goal of this lab is understand how an object's distance, physical size, and angular size relate to one another, and to learn how astronomers use this relationship to determine the sizes of distant objects.

Challenge:

Using only the provided materials and your understanding of angular size, your team will develop a method for estimating the diameter of the Old Capital building's dome.

Resources: аWorksheetGoogle Mapsmeter sticks, tape measure, rulers, calculators, paper, pens

Terminology:а small-angle formulapercent error formula

Tutorials: аnone


Background:

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 if you're mathematically-inclined). 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.

Humans have evolved binocular vision to help us make these distance guesses for things that might affect our survival, such as bears or lions. We also compare sizes of known objects, such as buildings and trees, when they are near the object in question. In astronomy, distances are more uncertain and objects that appear close in the sky may be many light-years apart. Thus, our basic measurement of size in astronomy is angular size.

In order to learn the true physical size of an object, one must find the distance to the object by some independent method. Converseley, if the physical size of an object is known this can be combined with its apparent angular size to determine its distance. In both cases the desired quantity can be calculated from the others using theаsmall-angle formula.

hands angular

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 outstreched 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.

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