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    Re: It's Moon-landing Monday
    From: Greg Rudzinski
    Date: 2009 Jul 21, 07:29 -0700

    Brad,
    
    A pair of Lubbers lines inside the spacecraft by the port hole could
    be sighted through the horizon glass of a sextant to obtain a relative
    bearing to a celestial body. This should help with thruster
    orientation.
    
    Greg
    
    On Jul 21, 5:59�am, Brad Morris  wrote:
    > Frank, you wrote:
    >
    > I was thinking of spacecraft orientation. If your rocket isn't pointed in 
    the right direction when you fire, even by a few degrees, you will not get 
    where you want to go.
    >
    > That would be an interesting exercise. �The sextant must therefore be 
    aligned to the thrust axis of the vehicle. �In other words, holding your 
    sextant in your hand and pointing it out the window (with the previously 
    agreed exercise on distance, RA and declination of the center of your 
    vehicle) does not really tell you how your vehicle is pointed! �Assuming that 
    the roll of the vehicle doesn't matter, then the vehicular pitch and yaw will 
    not be known UNLESS the sextant is referenced to the vehicle. �I am not sure 
    how we do that with our high end marine sextant!
    >
    > Best Regards
    > Brad
    >
    > -----Original Message-----
    > From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of frankr...{at}HistoricalAtlas.com
    > Sent: Tuesday, July 21, 2009 3:55 AM
    > To: NavList@fer3.com
    > Subject: [NavList 9160] Re: It's Moon-landing Monday
    >
    > Brad, you wrote:
    >
    > "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."
    >
    > Yes, that would work. The Moon would loom awfully large from 900 miles above 
    the surface. Could you measure it through the small windows typical on 
    spacecraft? You could do something similar with a couple of small, prominent 
    craters. Presumably you have detailed lunar topography (it's 2029 after all), 
    so you could ask your software to compute the exact angles between some 
    craters beneath your trajectory for the correct altitude.
    >
    > Any other ways to navigate visually??
    >
    > You added: "As a check, you can also perform the same calculation using the diameter of the earth."
    >
    > That wouldn't be accurate enough, would it? The Earth would be about two 
    degrees across seen from the Moon. Suppose I can measure its angular diameter 
    to +/-0.25 minutes of arc. That's about one five-hundredth of the diameter 
    and thus corresponds to a similar proportional error in the distance from the 
    Earth or roughly 500 miles. That is, if I measure the Earth's apparent 
    diameter as two degrees +/-0.25' then the distance away is 240,000 miles 
    +/-500 miles (off the top of my head --somebody check my math)
    >
    > "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."
    >
    > Indeed. You measure a couple of angles between stars and the Earth at known 
    GMT. We could call them "terran distances" instead of "lunar distances". Then 
    those together place you on a "ray of position" extending from the center of 
    the Earth. I will mention (again --can't resist) that you can do the same 
    thing on the surface of the Earth to fix your position by measuring lunar 
    distances at known GMT. It's space navigation on the ground.
    >
    > You concluded:
    > "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."
    >
    > I was thinking of spacecraft orientation. If your rocket isn't pointed in 
    the right direction when you fire, even by a few degrees, you will not get 
    where you want to go. In fact, the only real practical use of star sights on 
    the Apollo missions was to "align the platform" of the inertial navigation 
    system which amounts to using star sights as a 3d astro-compass. Without an 
    INS and with thrusters on manual, there's no way you could depend on the 
    pointing direction of a manned spacecraft for more than a few hours. Light 
    pressure differences on various parts of the spacecraft, slight outgassing 
    from thrusters and other components, and astronauts shifting around inside 
    would all change the spacecraft's orientation substantially. The Apollo 
    spacecraft had an auto-pilot system tied to the INS which fired thrusters 
    automatically to maintain orientation (or planned rolls). You can see a 
    dramatization of it trying to do its job after the explosion during the movie 
    "Apollo 13".
    >
    > -FER
    >
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