The increasing concern regarding potential close encounters between Earth and high-risk asteroids necessitates real-time monitoring and proximity detection of these celestial bodies. This paper addresses the challenge of designing relative motion orbits and spacecraft transfer in large elliptical orbits by employing the complete analytical solution. By exploiting the periodic properties of this analytical solution, the paper presents innovative designs and classifications of geometrical configurations for relative motion orbits of actively observing spacecraft. Additionally, an orbit transfer method for impulsive manoeuvring spacecraft is proposed, enabling efficient planning considering both the longest observation time and optimal fuel consumption. The research uncovers the kinetic mechanism governing the relative motion of tracking spacecraft orbits, revealing insights essential for achieving long-duration and efficient close observation missions of target asteroids.