A Closer Look: Angular Size

Unlike most sciences, astronomers are generally unable to travel or to directly interact with the objects that they study, so it can be difficult to determine the distance to those sources. Among other tools, astronomers use geometry to estimate these distances.

Objects in the sky can be described by their angular size, which is how big they look, or their physical size, which is how big they are. How big an object looks depends on both how big it is and how far away it is. For instance, when looking at the Moon in the sky, it has an angular diameter of half a degree. This angular size is determined by the physical size of the Moon, and the distance to the Moon. If the Moon were twice as far away, it would look half as big, and if the Moon were twice a large, it would look twice as big. Once astronomers know an objects physical size — which they can determine through a variety of techniques — they can easily measure its angular size. Those two measurements allow them to determine how far away an object is. For instance, in this video, the students learn that the Moon appears half as wide as their pinky when held at arm's length. They also learned that when standing on the Moon, Earth appears as wide as two fingers held at arm's length. Using this knowledge, plus knowing the diameter of the Earth, they can calculate the physical size of the Moon and the distance between Earth and the Moon.

Astronomers can use parallax to determine the distance to objects in the sky. As Earth orbits the Sun, we observe nearby stars from slightly different angles. By measuring how much the position of a star appears to shift (the parallax angle), astronomers can determine the distance to that star. To understand this, close one eye and hold a finger in front of your face. Now, alternate which eye is open and which eye is closed, and you will see that it appears as if your finger is changing position. As you move your finger closer to your face, the amount of change becomes larger. Just as you can estimate the distance to your hand by the amount by which your finger appears to move, astronomers can estimate the distance to objects in the sky by measuring the apparent change in position of the objects they study during different parts of Earth's orbit.

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