manual keplerian calculations
Yes, I'm that sick.
I'm working on solving the predicion problem with a pencil and paper. I've taken quite a bit of calculus, but that was quite some time ago.
Please reply directly. I'll make sure your fine words get back to the list once the details are sorted out. I'd appreciate direct email replies and I'll summarize to the list.
I have tracking software, I don't need to track via pencil and paper, I just want to know how to do it by hand.
I'm refering to the ARRL book AMatuer Satellite Handbook (Davidoff)
I'm starting with the Keplerian data for AO-7 from Keplerian Bulletin 78, ARLK078.
The epoch time is Oct 10, 2008 at 15:45:01.72Z
I attached the kep file for AO-7 for reference.
Any reference to values is about AO-7 from that Keplerian Update.
Here are my questions:
First to get the terms and understanding correct -- the Mean Anomoly is listed as 320.9603 deg.
Is this the value of E that is used on page 12-4 to 12-5, and I quote:
"In an eliptical orbit, time from perigree, t is given by:
t = ( T / 2pi) * (E - e *sin(E)) [ eq 12.10 ]
where the angle E, known as the eccentric anomaly, is defined by the associated equations:
E = 2 * arctan( sqrt( (1-e)/(1+e)) * tan ( (theta)/2 ) + (360deg * n)
n = 0 when -pi <= theta <= pi or 1 when pi < theta <= (3pi)"
OK, so it says E (the eccentric anomaly) is a function of theta and eccentricity.
Eccentricy of the orbit is in the Keps.
Let's just assume I'm trying to compute the lat/long of AO-7 at the epoch.
Is the RAAN in the Keps the longitude of the satellite at the epoch?
Is the mean anomaly the longitude of the satellite at the epoch?
I need the value of E to compute the value of t for this reason:
(skip ahead to page 12-18 from the Handbook mentioned above)
Finding latitude of the satellite, phi, at perigree is:
phi(p) = arcsin( sin(i) * sin(w) )
where i = inclination, w = angle between the ascending node and perigree.
Using equation 12.23, to find that latitude of the SSP:
phi(t) = arcsin ( sin(i) * sin( phi(t) + w) ) [Eq. 12.23 ]
Is that a misprint? the value of phi(t) depends on phi(t) ?
The gap here I'm trying to understand is, computing t (the elapsed time since the ascending node) so I can plug it into the formula for latitude [ phi as a function of t, phi(t) ]
Summary of questions:
Which data from the kep do I use to compute t based on equation 12.10
What does RAAN and Mean Anomaly mean at the Epoch?
Is the bird at latitude zero at epoch?
Computing a from Keplers laws, a = 31.25 * T^(2/3).
Is this T the Anomalistic Period?
Using that value of a, and eccentricity e, I can compute
w_dot = 4.97 * (Req/a)^(3.5) * (5 * cos^2(i) -1)/ ((1-e^2)^2) [eq 12.13a]
How does w_dot relate to ang of apogee from the kep data?
Thanks,
-jeff
W7BRS
ps. Again, reply directly -- this sort of question can make enough spam on the DL to last you through Festivus.
----- Original Message ----- From: "Jeff Wandling W7BRS" jw@w7brs.com
ps. Again, reply directly -- this sort of question can make enough spam on the DL to last you through Festivus.
A very good starting point is Dr Kelso's work on http://celestrak.com/
And there's plenty (!) of C++ code out there which implements the algorithms, so (worst case) you could figure things from the code.
Simon Brown, HB9DRV www.ham-radio-deluxe.com
Simon (HB9DRV) wrote:
Bit of a digression, but you know what we need, one of these days, is an open source code library for satellite tracking -- ideally cross-platform for both *nix/Windows. This is something that would get use outside of the amateur community.
cathrynham wrote:
What does gpredict use? It seems to work, so it would be a good start. I wish I knew more about how to calculate the predictions...
Gordon
On Mon, 13 Oct 2008 19:04:13 +0100 Gordon JC Pearce MM3YEQ gordonjcp@gjcp.net wrote:
Gpredict uses sgp4/sdp4 C-code by 5B4AZ, see http://5b4az.chronos.org.uk/pages/norad.html , which is a translation of Kelso's pascal code into ANSI C. I have made certain modifications and optimisations to improve efficiency when tracking a large number of satellites simultaneously but the algorithms are the same. For gpredict it is built and linked as a static library but it is only a matter of linker options to build a shared library (the windows version does indeed use DLL). The code itself is re-entrant.
I have also seen C++ implementations, which might be more suitable for C++ applications. I believe the tracking code from Ham Radio Deluxe is also available as GPL; don't know about its portability though.
73 Alex OZ9AEC
I'm sure the HRD could be out in a nicely coded C++ library using GCC.
Simon Brown, HB9DRV www.ham-radio-deluxe.com
----- Original Message ----- From: "Alexandru Csete" alexc@phys.au.dk
In English: I'm sure the HRD code could be compiled into a nice Linux library.
Simon Brown, HB9DRV www.ham-radio-deluxe.com
----- Original Message ----- From: "Simon (HB9DRV)" simon@hb9drv.ch
I'm sure the HRD could be out in a nicely coded C++ library using GCC.
To all so far, Thanks. I think I'll take the question back and keep studying the problem.
http://5b4az.chronos.org.uk/pages/norad.html , which is a translation of Kelso's pascal code into ANSI C. [...]
Getting a little far away from the question. Re-interpreting source code is one way to verify that the software design solution used by the author of the code predicts the tracking. I can probably (and did already actually) run this code and generate tracking data. The formulae in the code are suspiciously close to the handbook, but there was a lot of reorganization of the equations to the point I had to replace the brain-fuse. Glad there are spares handy.
I'm sure Dr. Kelso, et al. code is just peachy.
It's not quite what I'm after. I need to use the formulae in the handbook to arrive at the same answer.
If I stumble across an email reply that addresses the questions regarding the formulae in the handbook, I'll summarize. I may trip over the answer myself if I keep re-reading the handbook.
Thanks again,
-jeff W7BRS
Jeff Wandling W7BRS wrote:
To all so far, Thanks. I think I'll take the question back and keep studying the problem.
Get your hands on Vallado's Fundamentals of Astrodynamics and Applications either at the university library or buy your own. If you are at all serious about understanding what is going on it's a bargain even though it has a textbook price.
-Joe KM1P
----- Original Message ----- From: "cathrynham" cathrynm@junglevision.com
The Windows DLL I use is available in source code, it's not really Windows-specific as it's just number crunching. It handles satellites and the Sun, Moon and maybe another planet.
To my surprise (!) I haven't put it on my new website, an error I can correct :-)
Simon Brown, HB9DRV www.ham-radio-deluxe.com
participants (6)
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Alexandru Csete
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cathrynham
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Gordon JC Pearce MM3YEQ
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Jeff Wandling W7BRS
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Joe Fitzgerald
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Simon (HB9DRV)