Several space-based climate engineering methods, including shading the Earth with a particle ring for active cooling, or the use of orbital reectors to increase the total insolation of Mars for climate warming have been considered to modify planetary climates in a controller manner. In this study, solar reectors on polar orbits are proposed to intervene in the Earth's climate system, involving near circular polar orbits normal to the ecliptic plane of the Earth. Similarly, a family of displaced polar orbits (non-Keplerian orbits) are also characterized to mitigate future natural climate variability, producing a modest global temperature increase, again to compensate for possible future cooling. These include deposition of aerosols in the stratosphere from large volcanic events. The two-body problem is considered, taking into account the eects of solar radiation pressure and the Earth's J 2 oblateness perturbation.
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 .
Assume that a group of two or more satellites are ying close a given nominal trajectory around Earth-Moon triangular point, in such a way that, there is some freedom in the selection of the geometry of the constellation. We are interested in avoiding large variations of the mutual distances between spacecraft and controlling the conguration of the formation. Previous studies about triangular libration points have determined the existence of regions of zero relative radial acceleration with respect to the nominal trajectory that prevent from the expansion or contraction of the formation. In this work, we carry out two dierent control strategies for a formation near a given nominal trajectory around L4: a bang-o-bang control and a minimum weighted total ∆V consumption. This study involves a linear approximation of the equations of motion relative to the bounded solutions around the triangular libration point, and it considers dierent geometrical possibilities in the zero drift regions. To investigate the inuence of the gravitational force of the Sun, the Bicircular Four Body Problem is studied. According to the results obtained, some suggestions on the design of the geometric conguration in the formation are given.
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