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Help in determining orbital parameters

Help in determining orbital parameters

Help in determining orbital parameters

I have a Keplerian problem:

Given two points in space that an elliptical orbit travels through, and the time that it takes for the satellite to travel between them, how do you determine the orbit?

Specifically, I'm thinking of the equation of the ellipse as
r = -----------------------------
     1 - e * cos (theta - theta0)

But any other method of describing the orbit is just fine.
(I'm only worried about a 2D orbit for now, I'm pretty sure I could extend it on my own)

Can this be done analytically?

RE: Help in determining orbital parameters

There are 2 orbits for every such problem. The short way and the long way. The Dover Publishing book Fundamentals of Astrodynamics has a pretty good explanation and multiple methods to determine the orbit.

RE: Help in determining orbital parameters

Ok, I've checked "Fundamentals of Astrodynamics" (Bate, Mueller, White) and Battin's book ("Intro. to Mathematics and Methods of Astrodynamics").  I understand that what I'm trying to solve is called Lambert's problem or the Gauss Problem, and in general, the solution must be done numerically.

I have not, however, convinced myself of this other question's intractablity:

Given two points in an orbit and the time it takes to transverse them (and whether you're going more or less than pi radians around the ellipse), what is your velocity at the initial point?

Using the methods in these books, I can solve my problem numerically.  Battin almost implies that there is an analytic solution (see section 6.8, "Terminal Velocity Vector Diagrams") but I"m not seeing it.  Does anyone know if it exists?

RE: Help in determining orbital parameters

David Vallado gives a minimum energy transfer solution in Fundamentals of Astrodynamics and Applications (p. 428).  If you don't want to use minimum energy for whatever reason (Shorter transit times, etc.) then numerical methods are the only ones I know of.

Brian Lewis
The Aerospace Corporation

RE: Help in determining orbital parameters

If you know your velocity at your initial point then you know your orbit. You can find out all of the orbital parameters from r and v. However, the r and v are probably not the r and v you need to get to r2 in t.
With Lambert or Gauss, first you solve for the orbit, then you determine v at a point.

RE: Help in determining orbital parameters

i have to find out a transfer-ellipse between earth and any other object in space. I know the orbit of all objects. So i have startpoint at starttime and the goalpoint at arrivaltime so i habe the ime also.
I've checked out Valado and Bate,Mueller,White and it works but only with low dt or TOF (Time of Flight). The Example which is given in Bate,Mueller,White works (here: TOF 780s)
but a TOF about 3 or 4 month the orbit is far away from goalorbit(i've checked the earthorbit with TOF=1,2,3 Month and all was right but....

short TOF for better Orbitcalculation but why?

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