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    Re: Mars Tables
    From: Bruce Hamilton
    Date: 2008 May 28, 18:48 -0700

    Well, as I suspected between Geoffrey's theodolite and Frank's
    reasoning, the problem is almost solved.  Now we need someone to write
    up a grant application.
    Luis could certainly make the Starpilot work for Mars. Can you picture
    the new key? Welcome to Starpilot, please select your planet.
    Field trip anyone?
    
    
    frankreed@HistoricalAtlas.net wrote:
    > Bruce Hamilton, you wrote:
    > "This is the one place in the world I can ask this question and not get
    > laughed at, and probably get an answer."
    >
    > LOL. I'm definitely laughing, but laughing with you!
    >
    > You asked:
    > "Has any one worked out tables for celestial navigation on Mars?"
    >
    > Well, let's see... The stars are in the same positions, so no problem there.
    > You would have to adjust the annual precession for "Martian" values, and
    > there is essentially no nutation. The annual aberration would be nearly the
    > same, though smaller in magnitude (about 16 arcseconds instead of 20, and
    > somewhat variable)  The standard, widely available JPL ephemeride solutions
    > are accurate enough in 3d space that we could easily compute the SHA and Dec
    > of the Sun and the navigational planets (Venus, EARTH, Jupiter, and Saturn).
    > The variability in delta-T that we have on Earth would be much smaller on
    > Mars.
    >
    > Of course, the spherical triangle math doesn't change, so you could use HO
    > 229, if you want. One small thing to keep in mind: in terms of linear
    > distances, celestial navigation is twice as accurate on Mars because one
    > minute of arc difference in a star's altitude corresponds to about 3000 feet
    > on Mars instead of one nautical mile as on Earth (if you want, you could
    > define a "Martian nautical mile" with that shorter length). This is a
    > specific case of the general principle that the accuracy of celestial
    > navigation (by altitudes from the horizon, or equivalently zenith distances
    > from the vertical) decreases as the radius of curvature of the surface
    > increases. So it's less accurate on Earth, more accurate on Mars, and really
    > accurate (in terms of distance on the ground per minute of arc change in
    > altitude) on a small spherical asteroid. Similarly, on one planet, if the
    > local radius of curvature is greater, which implies a flatter portion of the
    > planet, then the accuracy of celestial goes down. Note that the "surface"
    > whose curvature is being measured is really the surface of the geoid. If you
    > have an asteroid shaped something like a diverging lense, concave on both
    > sides, the geoid would be flat on both sides, and then celestial
    > observations could not distinguish positions at all (except by small changes
    > in parallax of objects which are nearby).
    >
    > The density of the Martian air is less than 1% of that on the Earth, so
    > above about ten degrees altitude you could ignore refraction for standard
    > sextant observations (I say "about" because of the difference in atmospheric
    > composition).
    >
    > Finally, we get to Phobos and Deimos. Lunar distance observations would give
    > quite accurate time on Mars, though in some latitudes the moons are always
    > below the horizon. The positions of the Martian moons are known to high
    > accuracy, but this is a case where ultra-high accuracy would pay back great
    > benefits. The moons potentially offer the easiest and most accurate method
    > of finding one's position on Mars. Since many bright stars can be seen in
    > daylight, this could be done without a sextant. You would photograph Phobos
    > or Deimos among the background stars, measure its RA and Dec and then from
    > its known 3d position in space (assuming the Universal Time is already
    > known), you would draw a ray which would intersect the surface of Mars at
    > your location. That would give you a very accurate latitude and longitude on
    > Mars. So we would essentially be using lunar distances to get a position fix
    > without any need to determine a local vertical... where have I heard that
    > before???
    >
    > For the foreseeable future, on Mars, it seems to me that "air traffic
    > control" is probably a better approach to position-finding. In other words,
    > you emit a signal trackable from orbit, and "they" keep track of your
    > position and beam it back to you. We've seen some nice examples of this in
    > the past few days as the Mars Reconnaissance Orbiter has photographed the
    > Phoenix lander descending under its parachute (SPECTACULAR! Coolest thing
    > I've seen in months!) and then its landing site complete with ancillary
    > components. And from that we know the exact position of Phoenix on Mars.
    >
    >  -FER
    >
    >
    >
    > >
    >
    >
    
    
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