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The distance (900 miles) is an easy one.  Use your sextant to measure the 
diameter of the moon, and since you know the true diameter, you can calculate 
the distance to the moons center, using simple triangles similar to HP.  Use 
your sextant like a stadimeter.  As a check, you can also perform the same 
calculation using the diameter of the earth.

In terms of the RA and declination, use the earth as a nadir point and 
determine where you are relative to the star patterns shown.  Nominally, in 
celestial navigation, we use the zenith, but because it is easy to look down 
at the earth and see the star patterns, look at your nadir.  Since the star 
patterns will not shift in parallax for an orbit within the earth-moon 
system, this will provide a very reasonable RA and declination.

Finally, since we can assume you are "out of earth orbit" for 6 hours, you are 
generally pointed in the correct direction anyway.  As a result, the time to 
fire the rocket is most dependent on the distance and not so much on the RA 
and declination.

Best Regards
Brad


-----Original Message-----
From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of frankreed@HistoricalAtlas.com
Sent: Monday, July 20, 2009 7:36 AM
To: NavList@fer3.com
Subject: [NavList 9150] It's Moon-landing Monday


To celebrate the fortieth anniversary of the Apollo 11 landing on the Moon, I 
propose a navigation brain game...

You are on your way to the Moon in the year 2029, sixty years after the first 
moon landing, to begin a six-month stay as part of a team of five at the tiny 
"International Moon Base". You have been granted a twenty kilogram allowance 
for personal effects, and navigation-fanatic that you are, you have chosen to 
bring along a beautiful, well-adjusted, perfectly-aligned, traditional marine 
sextant manufactured way back in 1999. You also carry a laptop computer in a 
radiation and EMP-shielded case containing whatever databases of astronomical 
information suit your fancy (you've got at least a terabyte to spare so have 
no fear --if you can imagine it, you can load it on that laptop!). Then, just 
six hours out of Earth orbit on-course for the Moon, in a terrible accident, 
a solar flare, or an electrical fault, or just plain old gremlins wipe out 
your spacecraft's electronics leaving you no navigational capabilities, no 
automated spacecraft control, no communications with the Earth or GPS-like 
satellites or any astronauts in Earth orbit, lunar orbit, or already on the 
Moon. Life-support is functioning for a few days, and you can still fire your 
rockets and thrusters manually, but everything else is dead. So what could 
you do? You dig out your sextant from your luggage... You fire up your laptop 
with its detailed databases of astronomical data... Can you get to the Moon? 
If not to the Moon's surface, can you get yourself to within, let's say, 100 
nautical miles of some spot in lunar orbit? In short, could you become "Buck 
Bowditch in the 25th Century" and use traditional celestial navigation tools 
and skills, plus a laptop full of data and software, to save you and your 
comrades? Just to make things specific, your job is to fire your rockets at 
their standard thrust along a vector pointed at 6 hours RA and 20 degrees 
Declination (+/- 0.1 degrees in both coordinates) at an exact specified 
distance of 900 miles (+/-10 miles) from the Moon's surface on your current 
trajectory. If you do that, you will be able to rendezvous with an orbiting 
rescue spacecraft and win the game. Ready to go?? :-)

-FER
PS: The spacecraft's windows are just windows. They are not optically flat.






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