A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 Apr 4, 09:29 -0700
Rafal, you wrote:
"The goal is to use JPL ephemeresis as it is used currently to generate NA"
Yes, that's a reasonable goal, and by doing so, you are able to assert that any products you develop are built on the same data as the official Nautical Almanac. You can't say "as good as" the NA until you have some level of quality-control in place, but it's a start. A small note: you're spelling it wrong. The word is "ephemeris" and in English technical language, the preferred plural (strictly a matter of tech culture --not a law!) is "ephemerides". Whether you pronounce the plural as an anglicized word like "e-FEM-a-rides" (rhymes with tides) or as a semi-classical Greek word like "e-fe-MER-a-deez" is also a matter of tech culture.
You also wrote:
"As these data provides me information about position of objects in Solar system at time t. But due to finite value of speed of light I cannot see these objects at the same moment, but after some time interval dt."
There's been some confusion about the meaning of that time variable, t, by the way. It's not the view "from the Sun" or "at the Sun". It's a time coordinate for observers at rest with respect to the Solar System's center of mass at large enough distance from the Sun so that there is no gravitational time dilation. You could imagine a time coordinate set up by observers in the Oort Cloud. That's effectively equivalent to the time used in Solar System integrations. Positions of objects in this time coordinate are really just like positions in traditional Newtonian physics at some time, t. It's an "omniscient" t with no attention paid to signal delays. If light travelled at an infinite speed, we would see objects at time t at their positions at time t. If an explosion occurred at time t1 on Earth and also at time t1 on Mars, different observers in spacecraft in the inner Solar System would see those synchronized explosions at different times, and only observers equidistant from Mars and Earth (on a plane halfway between them) would see or otherwise detect the explosions at the same time of observation, t2.
To account for the actual speed of light, for the level of precision in the Nautical Almanac and similar sources is not complicated and requires far less accuracy than you may be imagining, and iteration is not necessary. It's important to remember that we're worried about angular positions, not time-domain phenomena like the positions of planetary moons. The typical shift in angular position for the entire travel time of light from Saturn to the Earth, e.g., is about a quarter of an arc minute or 15 seconds of arc. If you want accuracy to an arcsecond (so that the finished product can be safely assumed accurate to 6 arcseconds or a tenth of a minute of arc), then your computation of the effect of light travel time only needs to be accurate to +/-8% or so, and that's a low bar to pass. For such low grade estimations, it's entirely sufficient to model the Solar System as a simple clock five hands (the Earth plus four navigational planets). Each planet is on the end of a hand of the clock with a length equal to the mean distance from the Sun, a, and each hand revolves around the center of the clock at an angular proportional to the inverse of the planet's orbital period (which by Kepler III is proportional to a^(3/2)). It's a mathematical "orrery". That's more than accurate enough to work out the small changes in position during the light travel time from each observed planet to the observer's own planet.
Another option: try Aldo Vitagliano's SOLEX application which has options to output data in a variety of formats and can (if I remember correctly) incorporate the light delay correction automatically. I have used this for several projects.