# NavList:

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

Message:αβγ
Message:abc
 Add Images & Files Posting Code: Name: Email:
Re: How to pre-calculate for negative altitudes?
From: Frank Reed
Date: 2017 Oct 23, 07:22 -0700

It's just the usual spherical triangle "cosine formula" solved for hour angle:

HA = cos-1[sin(h) / cos(Dec) / cos(Lat) - tan(Dec) · tan(Lat)].

This comes from:

sin(h) = sin(Dec) · sin(Lat) + cos(Dec) · cos(Lat) · cos(HA),
or re-arranged:
cos(HA) = [sin(h) - sin(Dec) · sin(Lat)] / [cos(Dec) · cos(Lat)].

Plug in -0.833° for h, and you will recover the hour angle for standard sunrise/sunset tables. Convert that angle to hours and minutes, apply equation of time and zone correction, and you'll find exactly the times as normally published for sunrise and sunset. As I noted in an earlier message, these times are a convenient fiction.

You say that you want to generate the "correct" tables using -51' for the altitude, setting h = -0.850° above. Even if there is some sense in which this is a "correct" number, and I don't think there is, your tables won't have much merit unless you travel back in time. There are no sailors adrift in lifeboats in the year 2017. There aren't even lifeboats anymore! :) Of course, calculating for entertainment --calcutainment!-- is good, clean fun, no matter what. :) And maybe you do have a time machine?? I've been working on one myself. It also includes a pocket-sized gravitational wave detector... ;)

Frank Reed

Browse Files

Drop Files

### Join NavList

 Name: (please, no nicknames or handles) Email:
 Do you want to receive all group messages by email? Yes No
You can also join by posting. Your first on-topic post automatically makes you a member.

### Posting Code

Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.
 Email:

### Email Settings

 Posting Code:

### Custom Index

 Subject: Author: Start date: (yyyymm dd) End date: (yyyymm dd)