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Tisserand's parameter is an "almost" conserved quantity in the CR3BP, even after flybys (useful for identifying asteroids).

$$T_P = \dfrac{a_p}{a}+2\sqrt{\dfrac{a}{a_p}(1-e^2)}\cos(i)$$

It does however assume that the orbit of the perturbing body is circular, something that's only approximately true for a planet like, say, Jupiter.

Is there a better way of accounting for the slight eccentricity of the perturbing planet that assuming it to be 0? I don't expect a correcting term to be great, just if there's anything that's better than the default of ignoring it.

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