QUESTION: How did Bradley allow for the effect of the earth's rotation about its own axis? The star's posiotn is apparently moving due to this. Three months later the earth's tilt with respect to the plane of the ecliptic will also have an angular effect. Just fixing a telescope to a chimney doesn't sound to be enough!
from an optical physicist who has never been perticularly interested in Astronomy!
ANSWER: Bradley didn't have to consider the rotation of the Earth, because his telescope could only make "transit" observations (that is, while a star was near the celestial meridian), and during transit observations the aberration of starlight is affected only by the observer's motion toward or away from the star, not his transverse motion. And since the rotation of the Earth is exactly transverse at the time a star is transiting, it does not affect the stellar aberration at all.
However, even if he'd had a telescope that could point in other directions, he really wouldn't have had to consider that problem, because at his latitude the Earth's rotational velocity is nearly 100 times smaller than our orbital motion, which is the cause of stellar aberration (of course, since his experiment was the first proof of our orbital motion, he couldn't have know that ratio; but everyone who thought the Earth was moving presumed that its orbital motion must be much faster than its rotation). And there is no way that the technology of his day could have produced measurements accurate enough to notice such a small effect. (That is, in fact, why he attached the telescope to his chimney; by "fixing" it along a north-south arc, it could measure positions much more accurately than any more movable telescope.)
Still, in the unlikely event that he could have observed the effect of our rotation, there are easy ways to get around the problem (as far as I am aware, they were originally used by Tycho Brahe, primarily to deal with atmospheric refraction, which increases the apparent altitudes of stars). Namely, if you observe a celestial body at some angle to the east of the meridian as it rises, you also try to observe it at the same angle to the west of the meridian as it sets. Any errors due to its being east or west of the meridian are more or less equal and in opposite directions, so taking an average of the measured positions cancels out any such errors.
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QUESTION: Many thanks for your reply but I'm still confused as to what he actually measured. A telescope just points up into the sky. Did he measure something else to get a datum? Did he use a given time? The transit gives him a time but that means he can only measure difference orthogonal to that. I can just see that putting crosswires on a star in January, leaving everything fixed and observing again in April is going to show a difference in the vertical N-S direction but you say he knew the effect formed an ellipse.
So I'm not suggesting he could measure the effects of the earth's rotation as your reply seems to be aswering. I'm wanting to know how he could measure anything without a fixed datum to compare it with. I can see that parallax is clearly measureable because very distant stars can be assumed to show no change and therefore provide a datum against which the angle of nearer stars will change.
Can you tell me what measurements would have comprised his raw data?
The measurements themselves were very simple. It happened that Beta Draconis, a fairly bright star, passes almost exactly overhead at the latitude of Bradley's residence, so he mounted a telescope to his chimney at an essentially vertical angle, allowing it to observe the star passing through its field of view each night (about 4 minutes earlier each night, due to the difference between our rotation period and the length of the day).
If Beta Draconis were close enough to measure its parallax, its north-south position would have gradually varied during the course of the year, in a manner consistent with the Earth's moving from one side of our orbit to the other, creating a parallactic effect. But instead, it drifted north and south in a completely different way. At first Bradley thought there might be some error in the mounting of the telescope, but could find no fault in its construction. Over the course of a year he saw the star gradually move southward (when it should have been moving northward), then northward (when it should have been moving southward), then southward again, until after a year it was back where it started, and began to repeat the incomprehensibly "incorrect" motion again.
In other words, all Bradley had to do was to measure (relative to the normal position of the star, presumably using a guide wire mounted in the focal plane of the field of view) the north-south position of the star as it passed nearly overhead. Theoretically, he could also have measured the east-west motion by using a clock to measure any deviations in exactly when the star passed overhead compared to an absolutely uniform timing; but clocks of the day were not accurate enough to make such precise measurements, so only the north-south motion was actually measured.
There is an excellent discussion of Bradley's career with a detailed discussion of the method of observation of Beta Draconis and its results at http://www.cadsas.com/books/greatastronomers/page-11.html
(about a third of the way down the page). It provides a far more detailed discussion of the results, but the answer above is a reasonable summary of the technique.