Intervening in Earth’s climate system through space-based solar reflectors

Abstract

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.

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

“…Thus, the differential corrector method permits to find a new set of displaced orbits in the Sun-Earth-reflector CRTBP. Previous works have only obtained this kind of orbits in the twobody problem, assuming fixed solar acceleration vector directed along the Sun-line, as was described previously ([Dankowicz(1994)], [McInnes(1999)], [McInnes(2010b)], [Bewick et al(2011)], [Salazar et al(2016a)]). Although linear stable circular polar orbits could be generated with any displacement z p in the two-body scenario, as shown in Fig.…”

“…The motion of a solar space reflector in the Sun-Earth system can be approximated by the equations of the CRTBP [Szebehely (1967)]. In this approach, there exist five natural equilibrium points, known as Lagrangian points.…”

“…solar sails, orbiting reflectors to increase the amount of sunlight ( [McInnes & Simmons(1992)], [Dankowicz(1994)], [McInnes(1999)], [McInnes(2010b)], [Bewick et al(2011)], [Salazar et al(2016a)]). These are basically polar circular orbits, displaced behind Earth along the Sun-Earth line due to the solar radiation force exerted on the space mirror surface, as shown in Fig.…”

“…Analytical and numerical L 2 halo orbits for a solar reflector are obtained using the Lindstedt-Poincaré and differential corrector methods [Thurman & Workfolk (1996)], respectively. Analytical solutions are derived from a third order Taylor series expansion about artificial L 2 point, while the differential corrector method uses as first guess the third order solution ([Szebehely (1967)], [McInnes(1999)], [Baoyin & McInnes(2006)], [Baig & McInnes(2009)], [Salazar et al(2016b)]). The analytical results yield imaginary solutions after the reflector acceleration exceeds 0.245 mm s −2 , i.e.…”

“…Since solar radiation force greatly affects the reflector orbits about Earth [Salazar et al(2016a)], a family of non-Keplerian polar orbits for solar reflectors can be generated managing the reflector orientation, so that the solar radiation pressure applies a force on the mirror surface, dislocating the polar orbit from the Earth's center to behind it along the Sun-Earth line [McInnes & Simmons(1992)]. A two-body analysis, i.e.…”