A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2016 Sep 26, 18:54 -0700
Mark Coady, you wrote:
"I assume this is because we are hurtling through space on our wet cosmic ball far enough to actually produce the displacement. "
The displacement is not a question of the distance travelled. It's speed. The speed of the Earth deflects the light. It's called "aberration of starlight", and it can be counted as an observable measure of the speed of light. You can measure the speed of light with sextant observations.
Aberration causes the images of stars appear to be shifted "forward" towards whatever direction on the celestial sphere the Earth is travelling towards on any day during the year. The deflection is zero for stars dead ahead along the direction of the Earth's motion and also for those dead astern. Stars in the band that is ninety degrees from there, "abeam" if we think of the Earth as a ship, are shifted towards the bow, and the amount of the deflection is equal to the Earth's speed relative to the Sun divided by the speed of light. The Earth's orbital speed is 30 km/sec while the speed of light is 300,000 km/sec. The ratio is 1/10000. This is an angle (measured as a pure number, or "in radians"). We convert that to minutes of arc by multiplying by 3438. So the deflection is just about one-third of a minute of arc or 20 arcseconds. Six months later the motion is reversed. This yields an annual range of 40 seconds of arc. If you measure the angular distances between certain pairs of stars during the year with a sextant, you can readily detect this change. For navigation purposes, it can be ignored without too much damage for standard line of position navigation. Naturally if you want tenth of a minute accuracy, like for lunars, then you need to include the aberration. It's incorporated in the normal Nautical Almanac data.
By the way, the distance that the Earth travels during the year does also shift the positions of the stars, in inverse proportion to their distances. This is the annual parallax. If we measure distances to stars in parsecs (each parsec is 3.26 lightyears or 206265 AUs), then the annual displacement in seconds of arc is just the simple inverse of the distance. A star that is 9.78 lightyears, or 3 parsecs, from the Earth has an annual parallax of one-third of a second of arc. This is beyond the worries of the celestial navigator.