Parallax, Motion, and Angular Rate
Date: Summer 2012
I am having difficulty understanding the following observation: If you look out of the window of a fast moving train, the nearby trees, houses etc. seem to move rapidly in a direction opposite to the train's motion, but the distant objects (hill tops, the Moon, the stars etc.) seem to be stationary. In fact, since you are aware that you are moving, these distant objects seem to move with you. How is this?
Very good observations!
You describe parallax, a phenomenon where an object has an apparent position change due to a change in position of the observer. In your example, the train is moving, the tree clearly is not, but it seems to. The further away the observed object is, the less it appears to move.
The same effect may be found by: Placing your hand 6 cm from your eye. Tilt your head, observe a house about 20 m away. Completely cover-up the house using your hand at 6 cm away from your eye. Move your hand a few times to convince yourself the house is there and may be covered up. Now extend your hand to the full length(40 cm) of your arm, you will now be able to see part of the house.
The angle from your eye to the hand is very high at 6 cm. At 40 cm, the angle to the eye is substantially smaller.
Please consider the diagram above to the top right of the page.
This experiment is at very slow speed. Now imagine the same effect at 110 Km/hr... it describes the effect you observed.
The diagram comes from the Wikipedia reference above it, which has an excellent discussion concerning parallax.
PEHughes, Ph.D. Milford, NH
A person’s eyes can view direction. Because a person has two eyes, distance can also be detected. Close objects require your eyes to change direction more quickly than do distance objects. The speed at which you rotate your eyes or head when tracking an object is what provides the first impression of that object’s speed.
Dr. Ken Mellendorf
Illinois Central College
The farther away the landmark is, the slower its angular position appears to change as you move past it. This is easy to visualize by making a scale drawing.
As you, the observer X, move from the lower position to the upper position, the angle of sight to the near object Y changes much more than the angle of sight to the far object Z.
Richard E. Barrans Jr., Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming
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Update: November 2011