Distance-Based Short-Periodic Semimajor Axis Corrections in Satellite Relative Motion

Earth’s oblateness effects on the long-term evolution of satellite relative motion have been extensively studied in recent decades. However, much less attention has been given to the effect of sectoral and tesseral harmonics on the inter-satellite distance growth. This subtle effect becomes increasingly important in modern missions, involving large constellations of satellites, characterized by strict safety and fuel-use constraints. In this context, the current work provides a comprehensive modeling of short-periodic (SP) terms, emanating from the tesseral and sectoral harmonics, and their effect on the averaged inter-satellite distance. The averaged distance is utilized as a metric for quantifying the long-term effects of the gravitational harmonics on the relative drift. It is proven that differential sectoral and tesseral perturbations induce a secular inter-satellite drift due to SP terms related to the semimajor axis. These SP terms can be utilized as periodic corrections, mapping between mean and osculating orbital elements, thus mitigating the anticipated drift. A method that formulates the differential drift effects for a geopotential of arbitrary order is developed, and the dominant drivers of inter-satellite drift are detected. These drivers are then modeled in numerical simulations, showing that incorporating SP corrections of the semimajor axes can significantly mitigate the inter-satellite distance drift, thereby facilitating safe and efficient operation in, e.g., large satellite constellations.