A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 Apr 3, 12:39 -0700
John Howard, you wrote:
"If the speed of light was important for navigation almanacs how would you figure the position of a star that is 2000 light-years away?"
It's a funny thing. We don't need to worry about the positions of the stars as delayed by light travel time because the average effect of that delay just drops out: it's some angular position change but it doesn't matter. We see the stars where we see them (see PS). That's the average effect. And as the Solar System coasts along through space for endless millennia, the position changes due to light travel time delays are immaterial. We do, however, worry about the change in the position due to the variable delay caused by the earth's motion around the Sun. This variable delay is equivalent to what we call aberration of starlight. And it amounts to a 20-arsecond periodic wobble in the stars' positions over the course of the year depending on the geometric details. Note that aberration is not normally described in terms of light delay, but it's certainly possible to calculate it that way. That's a common feature of relativity: time and distance and the synchronization of events are all intertwined.
For the planets in the Solar System, the positions are more obviously affected by light delay. We see Jupiter "where it was" when light left it. The positional offsets are generally less than the 20 arcseconds we see from stellar aberration. This is really very easy to calculate, and iteration is only necessary for exceedingly high precision work. It's important to understand that there are different ways of presenting the data, and it's quite possible to acquire the JPL data with the appropriate delays for an observer on earth already calculated into the positions. For celestial navigation and other applications for observers on the surface of the Earth, that's preferred. On the other hand if you're plotting trajectories of interplanetary spacecraft, you generally want to do that correction yourself for the locations of a set of observers who may be in different locations in the Solar System.
PS: How do we know our entire Galaxy isn't rocketing through the Universe at some tremendous speed, like 10% of the speed of light? Well, actually, it is. Speed is entirely dependent on the observer's point of view. If I jump in my interstellar spacecraft and accelerate away from Earth to a speed of 10% of c relative to Earth, then I can equally well say that the entire Milky Way Galaxy is travelling relative to me at a speed of 10% of c (with some small local variations impressed on top of that average speed). But that's not really what we mean by the question. There is an overall intergalactic "soup" out there. the galaxies we see at great distances show a consistent relative expansion of the distances between any pair proportional to distance, but how do we know that our Galaxy doesn't have its own unique velocity relative to that intergalactic "soup"? The simplest way to see this is by looking at Doppler effects of light from individual galaxies. And these show no specific large velocity (though there is a small one). But there's a secondary effect: the distribution of the galaxies across the sky would be impacted by light-delay (equiv. to aberration of starlight) if we were zipping along at some large percentage of the speed of light and assuming that there is no coincidental natural variation in the distribution of galaxies. Galaxies "dead ahead" in our motion through the Universe would be more densely packed, thanks to aberration, while those astern would be more thinly distributed. We don't see that variation in apparent density, and that is yet another bit of evidence that the Milky Way has no substantial speed relative to the "cosmological rest frame" (that intergalactic soup and more specifically the original soup created by the Big Bang). So aberration can, in fact, affect the positions of the stars in the night sky in a permanent way, independent of our annual motion around the Sun, but in the real world, relative speeds are so low that there is no observational effect.