# 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: Sextant double reflection: angles halved
From: Richard Toohey
Date: 2021 Feb 16, 06:51 -0500
Hmmm. Your first proof made perfect sense to me. I considered the starlight’s reflections as course changes. The starlight was initially on course 140 let’s say. Then the light changed course to 210 (a positive course change of 2N) before coming back to its final heading of 090 ( a turn back to the left or negative 2U).

So, in my mind, both of your proofs work.

And I guess my approach removes the positive/negative labels all together!

On Mon, Feb 15, 2021 at 10:32 PM David Pike <NoReply_DavidPike@fer3.com> wrote:

David - I sent my proof a bit ago, but damn, yours is about 10 times simpler!  Love it!

Except I was too slick.  You have to consider direction of bending.  A better argument is:

Letting clockwise be positive, starlight is bent (180-2v) - (180-2u) = Minus Theta, so Theta = 2(v-u)

For triangle ABC, (90-v) + (90+u) + Phi = 180, or Phi =  v-u,  so Theta = 2 Phi.  Got there in the end. Sorry.  DaveP

View and reply to this message

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)