# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Venus, Jupiter, and the Moon**

**From:**Dave Walden

**Date:**2008 Dec 22, 06:16 -0800

Here's another solution. As a reminder, this 'no altitude' method relies on the effect of the moon's parallax, not its motion relative to the stars. Previous posts have described solutions of the intersecting cones and sphere problem by various methods. This post will describe the "Nothing But Frank" method, with no close initial position required. As Frank points out, we know the ground point of the moon, 74W, 22S. Since we have observed lunar distances, the moon must be above the horizon, so we must be in the hemisphere centered on the moon's GP. (Since in our case, the other two bodies are so close, not much is to be gained by consideration of the hemispheres where they are visible.) Let's take the GP as our starting point. We'll set up Frank's calculator with the GP as the lat and long, and the observed Jupiter distance. We first fix the long and iterate to look for the lat were the LD error is zero. If we're really lucky, there will be such a point at the moon's GP long. But this is unlikely. We'll use a "hill climbing" algorithm. Imagine while hiking at night you approach a hill and want to go to the summit which you can't see. Your plan is to approach the hill along a north-south line and continue as long as you ascend. When you reach a crest and are about to descend, you stop, turn 90deg right and take a step. If you're going up, proceed, it you're going down, stop turn back, then turn left and proceed on the east-west line. When you reach another crest, repeat. When right and left both lead you down, you're at the summit. Works for hills of "reasonable" shape and no "local" maxima. We proceed, using Frank's calculator, moving along the 74W north-south line, find a local minima (ok, we're using a "valley descending" algorithm.) We find a minimum at 60S. We then proceed east 'til we find another minimum at 20E. We go north to 43S and call this close enough. The first figure plots LD error vs. lat on the 74W line. The second shows the LD error on a lat-long grid with circles proportional to the LD error. Once we've gotten to the right neighborhood, we can move along lat or long lines finding the LD error equal zero points. Plotting 4-5 of these gives up the shape of the Jupiter curve. We proceed in the same manner for Venus (not forgetting to reset the observed LD). Where these curves intersect, we have a good approximate position and proceed as Frank describes. The last figure shows a view of the earth from the moon. The GP of the moon is at the center of the earth's disk. The curved lines result from plotting the LD error zero points we found above. The points at the ends of the lines from the earth's disk are the points in space (at a distance of 60 earth radii from the moon) were the center to center LD would be zero. I.e. the planet would lie directly behind the moon. Circles around the point represent lines on which the observed lunar distance would be constant. The arc segments we have drawn are constant LD lines on the earth's surface (they are the intersections of the cones of constant LD with the surface of the earth.) --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---