In the Solar System we can measure distances directly with radar ranging and space probes. However, even for the nearest stars these are not viable options and we must rely on a trigonometric method called parallax. As you might have guessed this will involve making angular measurements, so before we go on to parallax proper we will explain some things about these type of measurements.

One of the concepts we have to get used to when looking at the sky is that there is a difference between linear measurement and angular measurement. Linear measure gives the actual length of something in units like inches or meters. Angular measure gives the angle covered by an object.  We looked at linear measure in the Foundations lab.

Why does this matter when we look at the sky? When we look at the sky, we are not looking at a flat, two-dimensional surface. Most objects we see in the sky are so far away that we can't tell at a glance how far away they are or how far apart things are in space. What we can do is look in different directions and say things like, "object
A is in this part of the sky and object B is this part". What we really mean when we say that is that object A lies in a different direction compared to object B. If you imagine two straight lines, one extending from you to A and the other from you to B, then the angle those two lines make represents the angular separation between A and B (as opposed to the linear distance between A and B which would be a straight line in space connecting A and B).

To illustrate these points, consider the below photo of the Moon and an airplane.

 

Use an electronic ruler (please don't mark on the screen) and estimate the angular size of the airplane in degrees.

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Copyright 2001 C. Gino

The Moon subtends about 0.5 on the sky, as we learned in the Foundations lab. So the angular separation of the Moon and the airplane must be about three times that, or 1.5 or so. The angular size of the airplane is also easy to measure. We can measure these without worrying about how big the Moon or the airplane are in, say, km or m, or how far apart they are in space. Likewise, a point on the eastern horizon is separated from a point straight overhead by 90.

The fact that angles are used instead of linear measurements makes it better to think of the sky as an imaginary sphere on whose surface all the celestial object lie. Astronomers call this the Celestial Sphere (see the figure below). So remember to think in terms of angles when measuring distances on the Celestial Sphere. Parallax is an example of an angular measurement which you will be making in this lab.

(courtesy Lunar and Planetary Institute)