Rendezvous missions to temporarily captured near Earth asteroids

Abstract

Missions to rendezvous with or capture an asteroid present significant interest both from a geophysical and safety point of view. They are key to the understanding of our solar system are as well stepping stones for interplanetary human flight. In this paper, we focus on a rendezvous mission with 2006RH 120 , an asteroid classified as a Temporarily Captured Orbiter (TCO). TCOs form a new population of near Earth objects presenting many advantages toward that goal. Prior to the mission, we consider the spacecraft hibernating on a Halo orbit around the Earth-Moon's L 2 libration point. The objective is to design a transfer for the spacecraft from the parking orbit to rendezvous with 2006RH 120 while minimizing the fuel consumption. Our transfers use indirect methods, based on the Pontryagin Maximum Principle, combined with continuation techniques and a direct method to address the sensitivity of the initialization. We demonstrate that a rendezvous mission with 2006RH 120 can be accomplished with low delta-v. This exploratory work can be seen as a first step to identify good candidates for a rendezvous on a given TCO trajectory.

Recent Advances in Celestial and Space Mechanics

“…The final mass of the spaceraft for the best overall rendezvous is m f ≈ 280.855 kg which corresponds to a ∆V ≈ 496.43m/s, where we compute ∆V such that m f = m 0 e − ∆V Ispg 0 . Notice that in [5] we have obtained a better transfer corresponding to a ∆V of 203.6m/s, however for this mission the rendezvous would take place on June 26th 2006 and the duration would be about 415 days which requires to detect and launch the mission about 14 months before June 1st 2006 creating an unrrealistic scenario. Note that the spacecraft performs only one revolution around the Earth in the inertial reference frame.…”

“…We denote by ξ = (q, m) the state and by f (t, ξ , u) the controlled Sun perturbed CR3BP dynamics (3) including the mass evolution (5). The optimal control problem is now written as follows:…”

“…We first assume the spacecraft hibernating on a periodic orbit awaiting detection of a TCO. Motivated by the successful Artemis mission and prior numerical simulations on the rendezvous transfer [5], we chose the hibernating orbit to be a Halo orbit around the Earth-Moon L 2 libration point with a z-excursion of 5000 km. This orbit is similar to the ones successfully used for the Artemis mission [6,7].…”

“…In order to solve the optimization problems associated with our mission, we use indirect shooting methods [3,4,5,12]. The main difficulty of these methods is the initialization of the algorithm and existence of numerous local minima.…”

“…The reason to impose this control structure is twofold. First, preliminary calculations on a set of random TCOs with a free control structure for a similar control problem in [5] pro-vided results mimicking impulse transfers with at most three impulses. In extremely rare instances adding a fourth switching or more would reduce the cost.…”