A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2020 Nov 28, 09:40 -0800
You don't need these corrections if you have some basic information available. First find the planet's parallax. You want its "horizontal parallax" or parallax at the horizon. This is identical to the semi-diameter of the Earth as seen from that planet on any given date. You can use the Sun as a starting point. Its h.p. is 9 seconds of arc or 0.15'. Next compare the distance of the planet to the distance to the Sun. The distance to the Sun is 1 AU so you want the distance to the planet on the date in question in AUs. Then for that planet the h.p. is 0.15' / dist (dist in AU). This is very simple: if a planet is twice as far away as the Sun, then its parallax is half as large. If it's half the distance to the Sun, then its parallax is double the Sun's. And so on in proportion. Nothing more than that.
With the planet's horizontal parallax in hand, you can calculate the parallax in altitude just as you would for the Moon. It's h.p. × cos(alt). And since parallax lowers the planet's position, that correction is always additive.
Do we have to worry about parallax for other planets? Consider Jupiter. Its distance ranges from 4.2 AU to 6.2 AU. Therefore its parallax is always less than 0.04 minutes of arc which is negligible even for the most careful work in celestial navigation. But suppose you decide to shoot a sight of the planet Mercury... Then you might worry, just a little, about parallax. But who shoots Mercury anyway?