Mapping orbits with low station keeping costs for constellations of satellites based on the integral over the time of the perturbing forces

Monthly Notices of the Royal Astronomical Society

et al. 2020

ABSTRACT The dwarf planet Haumea is a trans-Neptunian object that is orbited by two moons and has a recently discovered ring. The particles of this ring are near the 3:1 resonance between the spin of Haumea and the orbital motion of the particles. In this work, the ring of Haumea is investigated using Perturbation Maps. These maps show the behaviour and impact of perturbations acting over particles around Haumea. The information coming from the maps depends on the integral type for the disturbing acceleration used to build the maps. The types II and IV are used. The numerical simulations are focused in the region between 2000 and 2500 km from the centre of Haumea, which is the region where the ring was observed, considering two initial values for the 3:1 resonant angle: θres = 0° and θres = 270°. The possible stable region for the initial angle θres = 0° is larger than the stable region for the initial angle θres = 270°. Furthermore, we found that these stable regions are not continuous, indicating that there are possible gaps in the ring. Therefore, our results suggest that Haumea may not have only one single ring, but a system of rings instead. Possible transit of the particles between the ring and the region close to the orbit of Namaka is also shown.

Section: Introductionmentioning

confidence: 99%

Perturbation Maps and the ring of Haumea

Sanchez

Deienno

Monthly Notices of the Royal Astronomical Society

et al. 2020

“…A previous general study of those differences can be done using the integral of the perturbing forces acting in this system (Prado (2013), Carvalho, Moraes & Prado (2014, Lara (2016), Oliveira & Prado (2014), Oliveira, Prado & Misra (2014), Sanchez, Howell & Prado (2016), Sanchez, Prado & Yokoyama (2014), Santos et al (2015), Short et al (2016)).…”

Section: Resultsmentioning

confidence: 99%

Mapping stable direct and retrograde orbits around the triple system of asteroids (45) Eugenia

Araujo

Moraes

Monthly Notices of the Royal Astronomical Society

et al. 2017

It is well accepted that knowing the composition and the orbital evolution of asteroids may help us to understand the process of formation of the Solar System. It is also known that asteroids can represent a threat to our planet. Such important role made space missions to asteroids a very popular topic in the current astrodynamics and astronomy studies. By taking into account the increasingly interest in space missions to asteroids, especially to multiple systems, we present a study aimed to characterize the stable and unstable regions around the triple system of asteroids (45) Eugenia. The goal is to characterize unstable and stable regions of this system and compare with the system 2001 SN263 -the target of the ASTER mission. Besides, Prado (2014) used a new concept for mapping orbits considering the disturbance received by the spacecraft from all the perturbing forces individually. This method was also applied to (45) Eugenia. We present the stable and unstable regions for particles with relative inclination between 0 • and 180 • . We found that (45) Eugenia presents larger stable regions for both, prograde and retrograde cases. This is mainly because the satellites of this system are small when compared to the primary body, and because they are not so close to each other. We also present a comparison between those two triple systems, and a discussion on how these results may guide us in the planning of future missions.

“…By calculating the integral of the acceleration for one orbital period, the perturbation can be analyzed in terms of the variation of the velocity caused in the spacecraft. This integral, that is given by (6), will be called the perturbation integral (PI), which can be seen in previous works by Prado [14,15], and Oliveira and Prado [17]…”

Section: Problem Formulationmentioning

confidence: 97%

“…The formulation of the potential for the cube is given by closed equations [2,13]. The perturbation is studied with a method that measures the amount of the change made in the velocity over the time, which can be seen in more details in previous works by Prado [14,15], Sanchez et al [16], and Oliveira and Prado [17]. This methodology consists in calculating the integral of the acceleration over the time, which will be referred here as the perturbation integral and will be explained in the next sessions.…”

Section: Introductionmentioning

confidence: 99%

Mapping Orbits regarding Perturbations due to the Gravitational Field of a Cube

Venditti

Mathematical Problems in Engineering

2015

The orbital dynamics around irregular shaped bodies is an actual topic in astrodynamics, because celestial bodies are not perfect spheres. When it comes to small celestial bodies, like asteroids and comets, it is even more import to consider the nonspherical shape. The gravitational field around them may generate trajectories that are different from Keplerian orbits. Modeling an irregular body can be a hard task, especially because it is difficult to know the exact shape when observing it from the Earth, due to their small sizes and long distances. Some asteroids have been observed, but it is still a small amount compared to all existing asteroids in the Solar System. An approximation of their shape can be made as a sum of several known geometric shapes. Some three-dimensional figures have closed equations for the potential and, in this work, the formulation of a cube is considered. The results give the mappings showing the orbits that are less perturbed and then have a good potential to be used by spacecrafts that need to minimize station-keeping maneuvers. Points in the orbit that minimizes the perturbations are found and they can be used for constellations of nanosatellites.