Re: Maximum distance to launch ground tracks

From: Anthony Ayiomamitis (anthony@perseus.gr)
Date: Tue May 01 2001 - 03:18:38 PDT

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    > >
    > >       If you are using the calculator within Windows, for example, you
    > will see a
    > > button for COS and also another for INV. If you want the arccos, ie. the
    > inverse of
    > > the cosine, enter your value, hit the INV box to check it off and then hit
    > COS.
    > >
    > Mathematically, arccos returns a value in radians = 180 degrees / PI() =
    > 57.29578
    > The formula given assumes it is returned in degrees, which is the default in
    > Windows' Calc, but not in Excel and other programming systems - be careful
    > about that (also you should select menu View / Scientific to SEE the
    > functions - in Standard cos and arccos can be used by TYPING o and io)
    
    Bjoern,
    
          Thanks for pointing out that the calculator must be in "View/Scientific" mode as
    I forgot to mention that bit of trivia. I always have it in that mode and it is
    something that I inadvertently took for granted.
    
    > Anthony also asked 'at what altitude is the object '- this formula is for 0
    > degrees, on (see-level) horizon.
    
           I am not the one who asked but the reply and content are what really matter ....
    :-)
    
    Anthony.
    
    > To find the ground range for another value, use the same formula for another
    > Earth radius, then subtract the distance corresponding to the elevation you
    > want (a).
    > With R=6371 km and a in degrees:
    >
    > DIST = R * {arccos[cos(a)*R/(R+HEIGHT)]  /  57.29578}  - a * R / 57.29578
    >
    > assuming your calculator works completely in degrees. If using radians, use
    > DIST = R * arccos[cos(a / 57.29578)*R/(R+HEIGHT)]   - a * R / 57.29578
    >
    > With HEIGHT = 200 km, this gives for
    > a=0    DIST=1576
    > a=5    DIST =1113
    > a=10  DIST = 810 ...
    > a=85  DIST =   17
    >
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