Reading Paper on Earth Occultation Technique

[yucheng]

TL;DR

I was reading a paper and I need help with the derivations of the equations for occultation timing. Where were these equations first derived?

The Burst and Transient Source Experiment Earth Occultation Technique​

https://www.semanticscholar.org/pap...hman/b4e57f91de6fec73fa680bcd7d6efbdf0de10bee

In **Appendix B**, the authors derive the equations for the occultation times. However, it appears that many steps were left out. I suspect that these equations were first derived elsewhere. Do you happen to know where? I have tried looking into the citations in the last paragraph of the **Introduction**, but to no avail (maybe I did not look carefully enough?) It might possibly be located in the Proceedings to the Gamma Ray Observatory Science Workshop...

Thanks in advance!

P.S. I am just trying my luck here {:-)

 

[Baluncore]

Appendix B seems fairly complete to me. It assumes the Earth is a sphere and that seen from a satellite the Earth hides a circular area of sky. Since the position of the satellite relative to the Earth is known, the centre of the circular occultation is known. The height of the satellite decides the angular diameter of the occultation. The target, at an infinite range, effectively crosses the circle along a chord that probably never passes through the centre of the circle.

It is Appendix C that I find less complete. Since the WGS84 ellipsoid for the Earth is then being considered, I would use Starlink, or SLALIB: A Positional Astronomy Library;
http://www.ascl.net/1403.025
https://github.com/Starlink/starlink

Your observatory organisation probably has a license for a fully maintained version of the software system.