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    Re: Apollo spacecraft sextant
    From: Frank Reed CT
    Date: 2004 May 3, 16:43 EDT
    I wrote:
    "The actor playing Lovell mentions sighting Antares and Sirius."

    Trevor K replied:
    "I don't understand what navigational information that would provide.
    Antares is 230 light years away from us, or some 70 parsec. "

    Hmm. If I were on a boat and I said to you "I've taken some sights of Antares and Sirius", would you assume I was measuring their parallax? No, of course not. So I don't see what's leading you to think that here.

    The astronauts could measure ordinary altitudes above the Earth's horizon (limb). They could also measure angles relative to the fixed axes of the spacecraft to get an accurate orientation of the vehicle which would then be used to update the inertial guidance system. Orientation is critical (and probably a better use for an onboard sextant than straight position-finding). Most spacecraft keep track of their orientation with inertial systems (gyroscopes), but these drift and on a long enough mission --longer than the Apollo missions apparently-- you would need to update the angles. You would also need to reset the angles from scratch if the system went into "gimbal lock".

    And asked:
    "Would sight-reduction of the latter type of observations have to follow
    notions analogous to ..." etc.

    Let's be clear, they don't use sextants to navigate spacecraft. But if you want to indulge in some "what if", you could certainly invent procedures that would work throughout the Solar System. This would require an almanac with heliocentric coordinates for all of the planets, but that's no problem (the Nautical Almanac from the 1780s included heliocentric latitudes and longitudes, for some odd reason, but not distances). There's one case in practice that I can think of where an unmanned spacecraft was designed to do some fully autonomous navigation as an experiment. It's called "Deep Space 1". If I remember correctly, they did just the sort of thing you would expect --measuring the positions of the planets against the background of the fixed stars. This was done photographically, and that's probably more sensible than using a sextant for any system you might design today.

    But how about some indulgent speculation. We want "purist" space-borne celestial navigation (no cheating with radio signals!)... I can measure the angles between various extremely distant objects (the "fixed" stars) and various nearby objects whose positions are known for every instant of time from almanac data. To make it specific, suppose I measure the angle between the star Antares and the Earth's near limb. I then add the Earth's semidiameter (which I can measure or more likely calculate from an assumed position). Now I have the center-to-center angle between the Earth and Antares. Let's suppose it's 120 degrees (an observer on the Earth at sea level directly beneath my location would measure an altitude of 30 degrees). Instead of a circle of position, this sight gives us a "cone" of position. The cone's vertex is at the Earth's center and it extends out to infinity as a two-dimensional surface (in 3d space). You're somewhere on that cone. If I take another sight, I get another cone and those two cones cross in two lines radiating outward from the Earth's center. Assuming I can toss out one of the lines by inspection (same as in terrestrial celestial navigation with two stars), I still need to get my position along that infinitely long line radiating up from the surface fix. To do that, you would need a cone with a different vertex. In other words, we need to measure a star's angular distance from some other Solar System object. For greatest accuracy, this should be a nearby object. So if you're navigating in the general vicinity of the Earth-Moon system, you would probably shoot a lunar (!) [with traditional lunars, the fact that you are on the Earth's surface and the Earth's diameter is known allows you to subtract out the effects of horizontal parallax, but this type of sight turns that procedure on its head --the measured parallax tells us how far we are from the center of the Earth]. If you're halfway from the Earth to Mars, you could use Venus, or the Sun, or Mars itself. And since we can safely assume we have a telescope with decent light-gathering power, you would also have a near endless choice of asteroids which would provide excellent spread in angles.

    The math involved in clearing sights like the above is not especially difficult, but I think it's beyond the usefulness of the discussion --unless one of you is building an interplanetary spacecraft in your backyard, in which case I would be happy to sign on as navigator.

    Have laptop, will travel.

    Frank E. Reed
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
    [ ] Clavius Base, Moon
       
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