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Wikipedia has this to say about the discovery of the aberration of light:

In 1728, while unsuccessfully attempting to measure the parallax of Eltanin, James Bradley discovered the aberration of light resulting from the movement of the Earth. Bradley's discovery confirmed Copernicus' theory that the Earth revolved around the Sun.

http://en.wikipedia.org/wiki/Gamma_Draconis

If parallax was a known phenomenon at the time, what was the theory at the time that caused parallax? Other than the motion of Earth around the Sun, what else could account for parallax?

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The phenomenon of parallax itself is simply the result of different views of one's surroundings observed from different locations. For binocular vision, we get a different view of our environment from each eye simultaneously, and the visual cortex of our brains learns very early on how to process the two distinct images into an appearance of a three-dimensional image. (Actual physical interaction with the objects in the environment is also important in "educating" the visual cortex about distances to objects. We generally accomplish this during infancy.)

In the case of astronomical parallax, celestial objects are generally so distant that the two (or more) different views must be obtained at different times from different positions of the Earth on its orbit. (The exception is the Moon, which is close enough to show parallax in simultaneous observations from well-separated points on the Earth. As an example, this is why occultations of stars by the Moon are not seen by all observers on the otherwise proper side of the Earth.)

To note the presence of astronomical parallax, it is necessary to have very precise measurements of the direction in which the object is seen, relative to a much more distant "background". The fact that this is not observed with the naked-eye was used until the 18th Century as an argument against the motion of the Earth about the Sun, since (obviously) the planets and stars would show parallax if the Earth were not simply stationary at the center of the Universe.

One difficulty in measuring parallax for stars is that, as we now know, the change in observed direction, even at diametrically opposite locations on the Earth's orbit, is at most a bit over one second of arc (1/3600 of a degree) for the closest stars and generally hundredths of a second or less for most of the visible stars. But even to discern that requires being able to compare the observed directions of the stars at different times. In the age before photography, this required having precise charting of the stars on the sky, which was the result of a tremendous effort in the centuries after the first use of telescopes in astronomy. It wasn't until 1838 that the first sufficiently accurate observations of stellar parallax were accomplished.

By comparison, the aberration of starlight due to the Earth's motion is an effect about twenty times larger than the largest stellar parallaxes, so it was became possible to detect that by 1725.

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Thank you for the very informative answer. You do discuss why aberration is easier to detect than parallax, which answers another (unasked) question of mine, but the core question is not addressed: Why was Bradley trying to measure parallax if it had not been discovered yet? And if it had been discovered (or suspected), yet the Earth was supposedly stationary (because Bradley's discovery proved that it wasn't), then what would explain the parallax? –  dotancohen Apr 15 '13 at 5:18
    
It was understood that stellar parallaxes should be seen if the Earth were in fact in motion, but they are too small to observe by eye and require telescope observation and precise comparison to verify. The heliocentric model of the solar system was not widely accepted during the 17th Century and Newton's mechanics alone was not considered adequate support for it (Aristotle's physics was only finally discarded by "natural philosophers" by the late 18th Century). Galileo's observations of moons orbiting Jupiter was also not regarded as sufficient evidence (continued)... –  RecklessReckoner Apr 15 '13 at 6:04
    
since mere telescopic observation was not considered a reliable means of investigating nature by most philosophers of the time. Bradley and others needed to find a proponderance of acceptable physical evidence in order to show convincingly the inadequacies of the "Aristotlean view" of the cosmos. This was a very difficult transition for the way of thinking about the physical universe and took more than two centuries after the death of Copernicus to achieve. (Consider the continuing resistance of some people to the "Darwinian view" of the history of living things on Earth.) –  RecklessReckoner Apr 15 '13 at 6:10
    
I see, thanks. Therefore Bradley's discovery of aberration was the final bit of needed evidence? –  dotancohen Apr 15 '13 at 7:06
    
That I don't know off-hand. Harvard was the first university to teach the heliocentric model as the "accepted" one by the mid-18th Century, but the preponderance of evidence wasn't really achieved (to the point where scientific doubt was effectively eliminated) until the middle of the following century, after stellar parallax was satisfactorily measured and the Foucault pendulum was demonstrated. Scientific "truths" are really arrived at only by showing that a particular viewpoint is supported by observations far better than any others proposed; we never really know what The World truly is. –  RecklessReckoner Apr 15 '13 at 8:13

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