Parallax: Applications by Bryan Tan (11T), Jensen Tong (11F)
Introduction
It is a hot, sunny day. While walking down Alleyn Road to grab a snack from Tesco, you turn your head to look at Dulwich College. As you walk, you notice that the metal fence posts separating the grass from the sidewalk seem to whiz past you, spending only seconds in your field of vision before disappearing behind you, while the Barry Buildings in the background barely seem to move at all, it takes you several strides before you notice any difference in its position. In the cloudless blue sky above the clock tower, you make out the outline of an airplane, flying in the opposite direction of your walk; and like the Barry Buildings, it seems to be moving very slowly across the sky. Is the fence post actually moving faster than the airplane? This familiar and obvious phenomenon is known as the parallax effect. When observing the same object from two different points on a straight line, the angle formed by the object to the two viewpoints is called the parallax angle. The parallax angle quantifies the apparent “shift” in the object’s position in the field of view of the two viewpoints (e.g. the fence post is “in front” of you at one point and “behind” you at another). Needless to say, but nevertheless shown in Fig. 1, as the distance between the object of observation and the viewpoints increases, the value of the parallax angle decreases; the further away something is, the less its position seems to change as you walk, this is why you noticed the fence posts moved “faster” than the airplane.
Beyond the parallax’s intuitive nature, lies profound applications. Because of the relationship between change in parallax angle and change in distance between two viewpoints, we can assume two constant variables and calculate the third mathematically. Thus, if the distance between two points of observation, and the parallax of the object at the same two points, then the distance between the object and the two observation points can also be known. This method of using parallax to determine distance is the reason parallax seems so intuitive. The brain can calculate a surprisingly
fig. 1: Angle Formed by Objects of Observation and Viewpoints
accurate estimate of depth, interpreting a value for an object’s parallax angle and, using the distance between the eyes, depth can be perceived. 3D computer graphics essentially simulate human vision so it is not hard to see its role in rendering complex animations. There are numerous other applications but in this article I will be particularly focusing on its use in the field of astronomy.
Stellar Parallax
Historically, the parallax method was used to calculate the Earth’s distance to different celestial objects. The position of a star in the night sky changes slightly with reference to background stars 7 at different dates, due to the Earth’s orbit around the Sun.
7 These stars are too far away to produce a measurable parallax angle themselves
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