Problem $2(30$ points$)$: You are doing a first$-$order analysis on a new satellite in an elliptical orbit $(e=0\mathrm{.}2)$ with perigee at an altitude of $700$ km $.$ Considering only secular $J_2$ effects,

$($a$)$ Is it possible to design an orbit such that the effects of ${}^{}$ counteract ${}^{}($i$.$e$.,{}^{}=-{}^{})?$ This condition would ensure that the longitude of periapsis $(+)$ is constant.

$($b$)$ Is this condition feasible for any other values of perigee altitude?

Note: For both parts explain the process you followed to arrive to your conclusion and provide supporting evidence $($derivations$,$ plots, data, etc.$).$