Orbit Determination Issue (Method of Gauss, in Escobal's text)

In summary, the author is having difficulty solving an equation for H_i from Escobal's Methods of Orbit Determination guide but does not have the data to solve it himself.
  • #1
tjcafitz
1
0
So I'm coding up some initial orbit determination stuff in MATLAB (for personal education; I love this stuff), and I am using 'Methods of Orbit Determination' by Escobal as a guide. I already got Vallado's code to work, now I'm just comparing other methods. I'm having an issue with one of his equations, though. Obviously, the method is angles-only, but one of the givens Escobal requires is H_i, and in his nomenclature section he says that H is the "Altitude of satellite measured normal to adopted ellipsoid". So its the altitude, which is an unknown since we don't have the orbit. I don't even have range data. Am I interpreting this part wrong? The reason I care about that variable is that my values for the X, Y, and Z vectors are off, which gives me a small slatn range value, which gives me the incorrect final value. the set of equations is:
G1(i) = a_e/sqrt(1-(2*f-f^2)*sin(phi)^2) + H ;
G2(i) = (1-f)^2*a_e/sqrt(1-(2*f-f^2)*sin(phi)^2) + H ;
X(i) = -G1(i)*cosd(phi)*cosd(theta(i)) ;
Y(i) = -G1(i)*cosd(phi)*sind(theta(i)) ;
Z(i) = -G2(i)*sind(phi) ;

Any ideas/help would be greatly appreciated.
 
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  • #2
I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
 
  • #3
tjcafitz said:
So I'm coding up some initial orbit determination stuff in MATLAB (for personal education; I love this stuff), and I am using 'Methods of Orbit Determination' by Escobal as a guide. I already got Vallado's code to work, now I'm just comparing other methods. I'm having an issue with one of his equations, though. Obviously, the method is angles-only, but one of the givens Escobal requires is H_i, and in his nomenclature section he says that H is the "Altitude of satellite measured normal to adopted ellipsoid". So its the altitude, which is an unknown since we don't have the orbit. I don't even have range data. Am I interpreting this part wrong? The reason I care about that variable is that my values for the X, Y, and Z vectors are off, which gives me a small slatn range value, which gives me the incorrect final value. the set of equations is:
G1(i) = a_e/sqrt(1-(2*f-f^2)*sin(phi)^2) + H ;
G2(i) = (1-f)^2*a_e/sqrt(1-(2*f-f^2)*sin(phi)^2) + H ;
X(i) = -G1(i)*cosd(phi)*cosd(theta(i)) ;
Y(i) = -G1(i)*cosd(phi)*sind(theta(i)) ;
Z(i) = -G2(i)*sind(phi) ;

Any ideas/help would be greatly appreciated.
Hi!

Do you have Vallado's code maybe? I would really like to take a look at it :)
Thanks!
 

1. What is the Method of Gauss and how does it relate to orbit determination?

The Method of Gauss is a mathematical algorithm used to determine the orbit of an object around a central body, such as a planet or star. It is based on the principles of celestial mechanics and uses the observed positions of the object over time to calculate its orbit parameters.

2. What is the significance of the Method of Gauss in space exploration?

The Method of Gauss is a fundamental tool for orbit determination in space exploration. It allows scientists and engineers to accurately predict the trajectory of spacecraft and other objects in space, which is essential for successful missions and safe operations.

3. How does the Method of Gauss differ from other methods of orbit determination?

The Method of Gauss is different from other methods of orbit determination in that it takes into account the gravitational influence of multiple bodies on an object's orbit. This makes it more accurate for calculating trajectories in complex systems, such as the Earth-Moon-Sun system.

4. What are the advantages and limitations of using the Method of Gauss for orbit determination?

The main advantage of the Method of Gauss is its accuracy in predicting the trajectory of objects in complex systems. However, it requires precise and frequent observations of the object's position, which can be challenging to obtain in certain situations. It also assumes a two-body problem, which may not always be accurate in real-world scenarios.

5. How has the Method of Gauss evolved over time?

The Method of Gauss has evolved significantly since its initial development in the early 19th century. It has been refined and expanded upon by scientists and mathematicians, and new techniques and technologies have been incorporated to improve its accuracy and applicability. Today, it remains a fundamental tool for orbit determination in space exploration and continues to be refined and improved upon by scientists.

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