Re: Maximum distance to launch ground tracks

From: Bjoern Gimle (b_gimle@algonet.se)
Date: Tue May 01 2001 - 01:09:14 PDT

  • Next message: Anthony Ayiomamitis: "Re: ISS & STS"

    >
    >       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)
    
    Anthony also asked 'at what altitude is the object '- this formula is for 0
    degrees, on (see-level) horizon.
    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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