Conceptual Question in Gibbs Orbit Determination

In summary, the conversation is about the Gibbs' method for orbit determination and the confusion over the direction of the S vector in the PQW coordinate system. The participants discuss the orthogonality of the PQR vectors, with P pointing towards periapsis, W pointing in the angular momentum direction, and Q pointing towards the semilatus rectum. Ultimately, it is clarified that the Q unit vector is perpendicular to both P and W, and the three r's represent measurements of position on the orbital ellipse at different points in time.
  • #1
enigma
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Hi all,

hopefully someone can help me out here:

I'm looking at the Gibbs' method for orbit determination, and I'm losing the conceptual picture in the vector calculations.

I have no problems seeing how D and N point in the W direction (PQW coordinate system), but I'll be damned if I can get a grip outside of simply swimming through the math why S: [(r2-r3)r1 + (r3-r1)r2 + (r1-r2)r3] points in the Q direction.

Anyone have any insights?

I'm reading Vallado Fundamentals of Astrodynamics and Applications section 7.5.1 if it helps.
 
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  • #2
Just a question. Are PQR supposed to be orthogonal? I ask because in celestial mechanics one often works with skew coordinate systems.

If they are orthogonal then could you show the inner product of the third one with each of the other two is zero? That would demonstrate it was in the right direction and working through the algebra might build some insight in you as to how that happens.
 
  • #3
PQW are orthogonal and tied to the orbital plane

P points toward periapsis, W points in the angular momentum direction, and Q points toward the semilatus rectum (or semiparameter depending on the book)
 
  • #4
Oh well sure then. P is aligned parallel to the major axis of the ellipse, Q is perpendicular to the plane of the ellipse (by the usual vector analysis representation of angular momentum) and R is parallel to the latus rectum which by the geometrical properties of the ellipse is perpendicular to the major axis. So there you are, orthogonal!
 
  • #5
Sorry. I misread your first post.

the three r's are three measurements of position on the orbital ellipse at three different points in time. They are not necessarily perpendicular to any of the axes except for the W axis. The Q unit vector is perpendicular to both P and W. This is not a trivial cross-product direction problem.
 

What is Gibbs orbit determination?

Gibbs orbit determination is a method used in astrodynamics to estimate the orbit of a spacecraft or celestial body. It involves using three position measurements from ground-based observers to calculate the orbit's parameters, such as the position and velocity of the object.

How does Gibbs orbit determination work?

Gibbs orbit determination uses a mathematical algorithm that takes three position measurements, along with the time at which they were taken, and calculates the orbit's parameters using Kepler's laws of motion. The method assumes that the orbit is elliptical and that the object is subject to gravitational forces from a central body.

What are the advantages of using Gibbs orbit determination?

One of the main advantages of using Gibbs orbit determination is that it only requires three position measurements, making it a relatively simple and efficient method. It also does not require any prior knowledge of the object's orbit, making it suitable for objects with unknown or highly uncertain orbits.

What are the limitations of Gibbs orbit determination?

Gibbs orbit determination assumes that the orbit is elliptical and that the object is subject to gravitational forces from a central body. This means that it may not be suitable for objects with highly non-elliptical orbits or those influenced by other forces, such as atmospheric drag. Additionally, errors in the position measurements can significantly affect the accuracy of the calculated orbit.

How is Gibbs orbit determination used in practice?

Gibbs orbit determination is used in various applications, such as tracking and predicting the orbits of satellites and space debris. It is also used in conjunction with other methods, such as least squares and Kalman filtering, to improve accuracy and mitigate limitations. Additionally, it is used in conjunction with other orbital maneuvers, such as orbit determination and orbit determination, to monitor and control spacecraft orbits.

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