Regularized luni-solar gravity dynamics on resident space objects
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https://doi.org/10.1007/s42064-020-0085-6
Regularized luni-solar gravity dynamics on resident space objects Harishkumar Sellamuthu1 (), Ram Krishan Sharma2 1. Agnikul Cosmos Private Limited, Indian Institute of Technology Madras, Chennai 600036, India 2. Department of Aerospace Engineering, Karunya Institute of Technology and Sciences, Coimbatore 641114, India
ABSTRACT
KEYWORDS
Resident space object population in highly elliptical high perigee altitude (> 600 km)
luni-solar perturbations
orbits is significantly affected by luni-solar gravity. Using regularization, an analytical orbit
regularization
theory with luni-solar gravity effects as third-body perturbations in terms of Kustaanheimo–
Kustaanheimo–Stiefel (KS) transformation
Stiefel regular elements is developed. Numerical tests with different cases resulted in good accuracy for both short- and long-term orbit propagations. It is observed that the luni-solar perturbations affect the accuracy of the analytical solution seasonally. The analytical theory
Research Article
is tested with the observed orbital parameters of the few objects in highly elliptical orbits.
Received: 18 December 2019
The analytical evolution of osculating perigee altitude is found to be concurrent with observed
Accepted: 9 May 2020
data. Solar perturbation, when compared with lunar perturbation, is established to be
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dominant over such orbits.
1
Introduction
Gravitational forces, other than central mass, exerting perturbations on orbital motion are one of the prominent dynamics in celestial mechanics, aptly named third-body perturbations. The lunar motion under the attraction of the Sun is a fundamental model to study the third-body gravity effects [1]. Luni-solar gravity effects are a driving factor behind the orbital motion of resident space object (RSO). Other perturbations on RSO motion are non-spherical gravity of the Earth, atmospheric drag, and solar radiation pressure. RSO in highly elliptical orbit (HEO) (perigee altitude hp > 600 km) in the exoatmospheric region has longer orbital lifetimes, relative to RSO in low perigee HEO, by averting the natural decay due to atmospheric drag. Nodal regression and apsidal precession of the orbit are caused by the oblateness of the Earth namely J2 . Luni-solar perturbations primarily maintain semi-major axis a and vary the eccentricity e causing the oscillation of the perigee altitude hp . The short-periodic of the oscillation is driven by the mean motion of the Sun and the Moon [2]. The initial phases of the short-period oscillation are sensitive to the initial angles of the Sun and the Moon with respect to the RSO orbital plane. The conjunction probability of HEO RSO
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2020
increases as they pass between the high spatial density regions of low Earth orbit (LEO) and geosynchronous orbit (GEO). Furthermore, higher risks also warrant highly dynamical ground operation environment to carry out precise analyses for collision avoidance during the launch phase, critical conjunction
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