Adding Perturbing Accelerations to J2

  • Thread starter synchhh
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In summary: The perturbing acceleration that comes into play is the thrust acting along V. However, the v vector is not explicitly defined in the equation set, so the perturbing acceleration is multiplied by the v vector before being added to the other terms.
  • #1
synchhh
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Homework Statement


I'm numerically integrating Gaussian Variational Equations on MATLAB. I have a script which, given initial values for a, e, i, Ω (RAAN), ω (argument at perigee), and θ (true anomaly), will compute the r and v vectors through numerical integration. This is done with J2 and thrust (given a value Tr, Tv, Th, radial thrust, along-V thrust, and along-h thrust per unit mass, respectively.) I'm then plotting the orbital elements obtained via GVE's and the orbital elements obtained via conversion of state vector on the same plot to ensure that they are equivalent. This needs to be done with J2 and additional perturbing accelerations.

Homework Equations


o71z3Cj.png

Note that there is a typo in Eq. (12.88). The final line reads ps but should read pw. Also, the equation I used for da/dt is as follows:

[tex]
\frac{da}{dt} = \frac{2a^2esin(\theta)}{h}p_r + \frac{2a^3\sqrt{1-e^2}}{hr}p_s
[/tex]

The Attempt at a Solution


My scripts work when I run them without including the perturbing accelerations, but including J2. The orbital elements found from conversion of state vector are equivalent to those found from integrating GVE's. I was given a function that will apply the thrust to the state vector version. The only thrust that comes into play is the thrust acting along V. The author multiplied Tv by v, and that was all. I'm not exactly sure how to apply this thrust to the GVE's, since I am given orbital elements, and as such, the v vector is not explicitly defined. Also, I'm not sure at what point the v vector comes into play in this equation set? Regardless, I've tried taking the norm of the thrust elements and adding them to J2, and I've also tried adding each component to pr, ps, and pw. I think a major problem is that I don't exactly understand what the number (0.00108263) associated with J2 is. I think that it somehow represents the effect of the oblateness of earth, but I'm not sure exactly how. How does it relate to perturbing accelerations? How could one combine the effects of J2 and perturbing accelerations? If necessary, I can provide the MATLAB files associated with this problem. Thanks for reading!
 
Last edited:
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  • #2
Not sure how to edit my post, but I think that the script that factors in the perturbing acceleration into the orbital elements found through conversion of state vector actually just uses one perturbing acceleration at a time. This is due to the problem statement, found below (#2).
W81ga7w.png
 

1. What is J2 perturbation?

J2 perturbation is a type of perturbing acceleration that affects the Earth's orbit around the Sun. It is caused by the Earth's oblateness, or its shape being slightly flattened at the poles. This results in a slightly irregular gravitational pull on objects in orbit around the Earth.

2. How does J2 perturbation affect satellite orbits?

J2 perturbation causes satellite orbits to gradually change over time. This is because the irregular gravitational pull from the Earth's oblateness causes the satellite's orbit to deviate from its original path, leading to changes in its altitude and velocity.

3. Can J2 perturbation be ignored in satellite orbit calculations?

No, J2 perturbation cannot be ignored in satellite orbit calculations. While it is a small effect compared to other perturbing accelerations, it still has a significant impact on the long-term behavior of satellite orbits. It must be included in calculations to accurately predict and maintain satellite orbits.

4. How is J2 perturbation added to satellite orbit models?

J2 perturbation is typically added to satellite orbit models by including it as a term in the equations of motion. This term takes into account the Earth's oblateness and its effect on the satellite's orbit. It can also be added as a perturbing acceleration in numerical simulations.

5. Is there a way to mitigate the effects of J2 perturbation on satellite orbits?

Yes, there are methods to mitigate the effects of J2 perturbation on satellite orbits. One approach is to periodically adjust the satellite's orbit using thrusters to counteract the effects of J2 perturbation. Another method is to design the satellite's orbit to minimize its sensitivity to J2 perturbation, such as using a higher altitude orbit.

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