Periodic orbits for space-based reflectors in the circular restricted three-body problem

Abstract

The use of space-based orbital reflectors to increase the total insolation of the Earth has been considered with potential applications in night-side illumination, electric power generation and climate engineering. Previous studies have demonstrated that families of displaced Earth-centered and artificial halo orbits may be generated using continuous propulsion, e.g. solar sails. In this work, a three-body analysis is performed by using the Circular Restricted Three Body Problem (CRTBP), such that, the space mirror attitude reflects sunlight in the direction of Earth's center, increasing the total insolation. Using the Lindstedt-Poincaré and differential corrector method, a family of halo orbits at artificial Sun-Earth L 2 points are found. It is shown that the third order approximation does not yield real solutions after the reflector acceleration exceeds 0.245 mm s −2 , i.e. the analytical expressions for the in-and out-of-plane amplitudes yield imaginary values. Thus, a larger solar reflector acceleration is required to obtain periodic orbits closer to the Earth. Derived using a two-body approach and applying the differential corrector method, a family of displaced periodic orbits close to the Earth are therefore found, with a solar reflector acceleration of 2.686 mm s −2 .

Solar sail cooperative formation flying around L2-type artificial equilibrium points

“…According to Refs. [24,51], there exists a large family of halo orbits when the sail attitude is maintained fixed in the rotating reference frame T . In the following analysis, the nominal trajectory will be obtained under the condition n ≡ r s , that is, with the assumption that the solar sail normal vector always lies along the Sun-sail line.…”

Periodic orbits for the perturbed planar circular restricted 3–body problem

“…For instance this theorem can be applied to the models of the perturbed circular restricted 3-body problem by zonal harmonic coefficients, oblateness, triaxial, and radiation pressure effects because these models have a first integral. If the circular restricted 3-body problem with a small perturbation has not a first integral the multipliers of the circular periodic orbits cannot be used for knowing if such orbits can be extended, this is the case of planar circular restricted 3-body problem with a solar sail [43].…”

“…In this section the previous results of Theorems 3.1 and 3.2 will be applied to two perturbed planar circular restricted 3-body problems. In the first application the perturbed problem has a first integral [2], and the second one does not have a first integral [43]. 4.1.…”

“…Planar circular restricted 3-body problem with solar sail perturbation. In this case the equations of motion with reflecting the solar sail reflector (see [38] and [43]) arer + 2n ∧ṙ = ∇V + a,…”

On the Periodic Solutions for the Perturbed Spatial Quantized Hill Problem

“…Some of these systems have applications in space missions for spacecrafts in the planet-Moons systems (such as the Earth-Moon system). Further, this problem has application in stellar systems, to study the behavior of exoplanets in the proximity of one or both objects of a binary star system [16][17][18].…”