What are J2 perturbations and how do they affect satellite orbits?

[Imagin_e]

Homework Statement

Hi!
I am trying to solve a problem where I need to calculate a satellite's orbit, but first I would like to ask for some clarifications from someone here that might know this stuff. I need to design an orbit so that no maneuvers (one part of the problem) are necessary to maintain it, and the hint is that there are J2 perturbation only and that the orbit is elliptical. I don't really understand this, so can someone explain what they mean with only J2 perturbations and how it is relevant here? (just asking for an explanation).

Thanks!

Homework Equations

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The Attempt at a Solution

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[gneill]

I can't help you beyond pointing out that "J2 perturbation" likely refers to the second order perturbation due to the non-spherical shape of the Earth affecting the shape of its gravitational potential. The potential function is described as a sum of terms:

$$\phi = \frac{\mu}{r}\left[ 1 - \sum_{n = 2}^\infty J_n \left(\frac{r_e}{r}\right)^n P_n sin(L)\right]$$
where:
$\mu$ = the gravitational parameter
$J_n$ = coefficients determined by experimental observation
$r_e$ = the equatorial radius of the Earth
$P_n$ = Legendre polynomilas
$L$ = geocentric latitude

If you're looking to avoid J2 perturbations then I suppose I'd look to see how the J2 term affects the potential...