Unfortunately it's not a simple formula, but rather a process.  To compute, you 
need to not only propagate the satellite orbit (as is done in a tracking 
program), but also need an algorithm to generate positions of the Sun relative 
to the Earth.  (The latter is available in a book called "Astronomical 
Algorithms" by Jean Meeus.)  You will also need to consider the diameter of 
both the Sun and the Earth.

The eclipse geometry is explained in the book "Satellite Orbits" by Montenbruck 
and Gill.  From there you need to develop a sampling method to determine entry 
and exit times.

Bear in mind that the eclipse geometry and timing is different on a 
case-by-case basis with the exception of some specialized orbits (which 
ARISSsat is not in).  

I'm sorry I couldn't offer a more satisfying answer.

73, Ken N2WWD

Sent from my iPad



On Sep 29, 2011, at 7:33 PM, <normn3...@stny.rr.com> wrote:

> Hi all!!
> How does one calculate the period and time of entry and exit of eclipse?
> I'm going to be helping a friend do an Arissat presentation for her class. 
> Due to the fact of the battery failing, this gives a 15 minute hold before 
> the power management allows transmission. So, for any chance of receiving the 
> bird, it has to  be in sunlight for 15 minutes (or so). 
> I'd prefer a mathematical formula. Echo goes through some of the same trials.
> Thanks,
> Norm
> BTW: I am an engineering student, just throw the math my way.
> 
> 
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