# 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

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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