Aberration of Starlight
Published on Feb 20, 2007 at 5:30 pm.
4 Comments.
Filed under astronomy, physics.
The star Gamma Draconis (γ Dra) plays an interesting and important role in the history of astronomy. It isn’t really all that impressive of a star to look at. Gamma Draconis, also known variously as Etamin, Eltamin, or Eltanin, is magnitude 1.5, a bit brighter than Polaris. It is a red giant located about 150 light years distant. But, this star is notable because of an accidental discovery made during the early Eighteenth Century.
In most any way that you think about it, Gamma Draconis is pretty much an ordinary star. What made this star special was that it passes almost directly overhead as seen from London. It was this special position that allowed it to be instrumental in proving that the Earth goes around the Sun.
Because of its prime location, astronomers in England thought that they should be able to measure parallax with Gamma Draconis easier than with other stars. A series of zenith telescopes (telescopes that only look straight up) were constructed. The idea was to measure the position of the star as it passed overhead. As the Earth went around the Sun, the star would appear to shift back and forth in the sky. This shift is parallax. Measuring parallax was deemed key to determining that the Earth did, in fact, move around the Sun. The problem is that stars are exceedingly far away, so parallax is tiny. Conventional telescopes had enough slop in their mounts that they could not be used to make such accurate measurements. Also, measurements made through different airmasses would throw results off. So, the idea of a fixed zenith telescope to make the measurements was appealing. A number of astronomers tried this, starting with Robert Hooke, but most of their instruments were far too crude.
However, by the Eighteenth Century, technology had improved to where much better instruments could be constructed. A truly impressive zenith telescope, though, was built by Samuel Molyneux and James Bradley. Their telescope should have been able to measure an angle to a precision slightly better than one arcsecond (an arcsecond is 1/3600 of a degree). Incidentally, not knowing any better, the general assumption at that time was that all stars were about as bright as the Sun, and so given that, I compute that the brightness of Gamma Draconis would produce a distance such that it’s parallax was about 0.3 arcseconds. That gives a shift in position of 0.6 arcseconds, right at the limit of Molyneux and Bradley’s telescope. Incidentally, Gamma Draconis is actually almost 150 times brighter than the Sun, and so it is much farther away than they suspected. Its real parallax has been measured to be 0.022 arcseconds, so their instrument, as good as it was, was hopelessly insufficient for the task.
Upon making measurements, though, they found that Gamma Draconis shifted back and forth by 20 arcseconds (40 arcseconds between its farthest north and south positions!). This was vastly bigger than should have been possible. Bradley went on to construct another zenith telescope of even greater precision, capable of measuring angles to within 0.5 arcseconds (but he’d still have needed a device with ten times that capability to have any hope of detecting this star’s parallax). His new telescope could shift back and forth slightly, allowing him to measure positions of many more stars. He found that they all showed this shift of about ±20 arcseconds!
So, what gives? What was Bradley actually measuring if it wasn’t parallax? Well, to answer this, we need to realize that light travels at finite speed. It travels fast, for sure, but not instantaneous. The shift that Bradley measured was, in fact, due to the motion of the Earth, but it wasn’t parallax. Let me explain.
To make this easier, consider the case of a car sitting in a rainstorm.
Assume that it is a calm day. The rain falls straight down onto the car. An occupant of the car looks out the windshield and sees the rain falling straight down onto the car. But, what if the car is moving? The rain is still falling straight down, of course, as seen in the next picture.
But, now, the situation looks different to the driver of the car. If he were to look at a particular raindrop, it would start high in front of the car and then as it fell, it would be getting closer and closer until it hit the windshield. In other words, the rain hitting the windshield was falling straight downward, but it did not start over the car’s windshield, but rather some distance in front of it. To the driver of the car, it looks the same as if the rain were coming down at angle, as seen in the third diagram.
But, the rain is still falling straight downward, no matter how it looks to the driver! But, in order to see the rain drops that are about to hit the windshield, the driver would 
not look straight up, but would look some angle forward of straight up.
But, light also moves. So, for a stationary Earth, you’d just have to look right at the star to see it. But Earth is not stationary. It is moving, so in order to see the light of the star, you need to look slightly forward (relative to Earth’s motion) of where the star should appear to be in order to see the light of the star. As the Earth goes around the Sun, you’d see the star a tiny bit forward of where it should be. 
Then, six months later, Earth is on the far side of the Sun, going in the other direction, so the star would again appear slightly forward of where it should be, but that is now looking slightly in the other direction. The faster that the Earth moves tangentially to the star, the bigger the shift. It can be up to about 20.5 arcseconds either way. We call this shift the aberration of starlight. It is every bit as powerful a proof of Earth’s motion around the Sun as parallax, and Bradley became widely acclaimed due to his discovery.
-Astroprof
Scott on February 20, 2007 at 8:49 pm: 1
Does an aberration correction have to be applied to the position of an object that is co-moving with the observer?
Astroprof on February 20, 2007 at 9:51 pm: 2
Originally, I thought to say \”yes\” to your question. Then, I got to thinking about it a bit more.
Though my analogy to rain on a windshield is useful as a thought experiment, it is flawed in that it does not take into account special relativity. A basic premise in special relativity is that there is not really any universal prefered reference frame. So, that would mean that if the two bodies were moving in the same direction at the same speed, then it would appear as if they are stationary with respect to one another, so there\’d be no aberration.
Allan Meyer on March 14, 2007 at 11:56 pm: 3
“… if the two bodies were moving in the same direction at the same speed, then it would appear as if they are stationary with respect to one another, so there\’d be no aberration.”
DON’T NEED to invoke special relativity. This is just good old-fashioned 400 year old Galilean relativity
(G. Galilei, “Dialogo sopra i due massimi sistemi del mondo” (1632). Galileo established that an inertial frame exhibits no evidence of velocity relative to any other frame. You only need Einstein’s special relativity (Lorentz transforms) if relative velocity between observer and light source is relativistic. When the Millenium Falcon jumps to light speed, the stars streak outward from the projected flight direction, the wrong way: relativistic aberration would make them squeeze in toward the flight direction, turn blue before becoming invisible UV or x-ray sources …
See also Michelson-Morley expt. (1887), e.g. Wikipedia article
Astroprof’s Page » The first parallax measurements on June 28, 2007 at 1:01 am: 4
[…] At first, astronomers had thought all stars to be similar, so the brighter stars were presumed to be the nearer ones. But, that idea had begun to fall by the wayside by the Eighteenth Century. Astronomers realized that brightness may not correlate at all with nearness (and it largely doesn’t). Eager attempts to measure parallax inevitably resulted in failure. The stars were simply far more distant than anyone had been prepared to imagine. But, along the way, there were a lot of interesting discoveries. For example, the search for parallax led to the discovery of the aberration of starlight. […]