A satellite of mass \(m_{\text {sat }}\) is in an elliptical orbit around a star of mass \(m_{\text {star }} \gg m_{\text {sat }}\). If the mechanical energy of the starsatellite system is \(E_{\text {mech }}\) and the magnitude of the angular momentum of the satellite about the star is \(L\), what are the semimajor axis \(a\) and the eccentricity \(e\) of the satellite's orbit?