# NavList:

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

**Re: Raw data for bubble**

**From:**Bill Noyce

**Date:**2007 Mar 12, 22:15 -0400

I'll take a shot at answering some of Bill's questions... The "magic number" 0.2724 isn't an angle, it's simply the ratio moon_radius / earth_radius SD is the angular distance of the moon's radius as seen from the earth, and similarly HP=SD/0.2724 is the angular distance of the earth's radius as seen from the moon, which is another way of describing the parallax of the moon at the horizon. When we're on the line from the center of the earth to the moon, parallax is zero (and Ho=90 degrees). For intermediate cases, cos(Ho) represents how far from that centerline we are, and thus how much of the HP to include. Augmentation reaches a maximum of about 0.3' and is caused simply by being closer to the moon when it's overhead because the earth is a sphere. The ideal formula would involve tangents, and the ratio of the earth's radius to the moon's orbital distance, but this ratio is so small we can approximate tan(x)=x (when x is in radians). sin(Ho) represents how much closer to the moon we are than the center of the earth is; it's zero when the moon is on the horizon, and 1 when it's overhead. So the formula ends up something like aug = tiny_number*sin(Ho)*SD, where tiny_number is something like 0.005 For most practical purposes, you can cut a lot of corners, and simply say Ho(degrees) augmentation <10 . . . . . . 0.0' 10-30 . . . . . 0.1' 30-56 . . . . . 0.2' 56-90 . . . . . 0.3' This neglects the fact that augmentation will be slightly more when SD is greater, or less when SD is less. I believe that this kind of "constant augmentation" is built into the "moon correction" tables in the NA. I'm pretty sure the NA doesn't try to account for the effect of oblateness. It would affect parallax a tiny bit, and augmentation an entirely negligible amount, I believe. -- Bill N. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---