Sun-Earth Systems Research Articles

Low-energy Earth–Moon transfers via Theory of Functional Connections and homotopy

Numerous missions leverage the weak stability boundary in the Earth–Moon–Sun system to achieve a safe and cost-effective access to the lunar environment. These transfers are envisaged to play a significant role in upcoming missions. This paper proposes a novel method to design low-energy transfers by combining the recent Theory of Functional Connections with a homotopic continuation approach. Planar patched transfer legs within the Earth–Moon and Sun–Earth systems are continued into higher-fidelity models. Eventually, the full Earth–Moon transfer is adjusted to conform to the dynamics of the planar Earth–Moon Sun-perturbed, bi-circular restricted four-body problem. The novelty lies in the avoidance of any propagation during the continuation process and final convergence. This formulation is beneficial when an extensive grid search is performed, automatically generating over 2000 low-energy transfers. Subsequently, these are optimized through a standard direct transcription and multiple shooting algorithm. This work illustrates that two-impulse low-energy transfers modeled in chaotic dynamic environments can be effectively formulated in Theory of Functional Connections, hence simplifying their overall design process. Moreover, its synergy with a homotopic continuation approach is demonstrated.

Exploration and Maintenance of Homeomorphic Orbit Revs in the Elliptic Restricted Three-Body Problem

A novel station-keeping strategy leveraging periodic revolutions of homeomorphic orbits in the Elliptic Restricted Three-Body Problem within the pulsating frame is presented. A systemic approach founded on arc-length continuation is presented for the discovery, computation, and classification of periodic revolutions that morph from their traditional circular restricted three-body counterparts to build an a priori dataset. The dataset is comprehensive in covering all possible geometric architectures of the restricted problem. Shape similarity is quantified using Hausdorff distance and works as a filter for the station-keeping algorithm in relation to appropriate target conditions. Finally, an efficient scheme to quantify impulsive orbit maintenance maneuvers that minimize the total fuel cost is presented. The proposed approach is salient in its generic applicability across any elliptic three-body system and any periodic orbit family. Finally, average annual station-keeping costs using the described methodology are quantified for selected “orbits of interest” in the cis-lunar and the Sun–Earth systems. The robustness and efficacy of the approach instill confidence in its applicability for realistic mission design scenarios.

Non-linear dynamics of a test particle near the Lagrange points L4 and L5 (Earth-Moon and Sun-Earth case)

The two-bodies problem can be fully solved, and was solved by Kepler (1609) and Newton (1687). The general three-body problem is often given as an example of a mathematical problem that ‘can’t be solved’. So, there is no general analytical solution. This problem can be significant and a special case of this problem is the Circular Restricted Three-Body Problem (CRTBP), which can be applied to the Earth-Moon system with a spacecraft, the Sun-Earth system with an asteroid, etc. In this paper, let’s focus on the motion of a test particle near the triangular Lagrange points L4 and L5 in the Earth-Moon and the Sun-Earth systems. Studying the movement of an object around these points is especially important for space mission design. To generate a trajectory around these points, the non-linear equations of motion for the circular restricted three-body problem were numerically integrated into MATLAB® 2023 software and the results are presented in the plane (x, y) and the phase plane (x, vx) and (y, vy). By numerical orbit integration, it is possible to investigate what happens when the displacement is relatively large or short from the Lagrange points. Then the small astronomical body may vibrate around these points. The results in this paper are shown in the rotating and inertia axes. Various initial positions near the Lagrange points and velocities are used to produce various paths the test particle can take. The same examples of numerical studies of trajectories associated with Lagrange points are shown in the inertial and the rotating coordinates system and are discussed. From the results of the numerical tests performed in MATLAB® 2023, it is possible to saw that there are different types of periodic, quasi-periodic, and chaotic orbits

Five-impulse low-energy earth-moon transfer using manifolds

The libration points in the Earth-Moon and Sun-Earth systems are widely regarded as cost-effective gateways into interstellar space. The associated manifold tubes have been utilized by numerous researchers in the development of transfers between distinct systems. In this paper, a five-impulse transfer method, based on the manifold, has been proposed for designing the low-energy transfer trajectory for the Earth-Moon system. The Sun-Earth-Moon-Spacecraft four-body problem is decomposed into two circular restricted three-body problems: Sun-Earth-Spacecraft and Earth-Moon-Spacecraft. Moreover, a time parameter is employed to describe the positional relationship between the Sun-Earth and Earth-Moon systems, thereby facilitating their conversion. A phase angle is utilized to characterize the position of the Poincare section, and multiple orbital elements, such as orbital altitude and inclination, are considered in the constraints. To solve the design of multi-constrained transfer trajectories, sequential differential correction algorithms are proposed. The results demonstrate that this method can be used to create compliant low-energy transfer trajectories for various combinations of time parameters and phase angles. Additionally, excellent velocity increments and time-of-flight metrics can be found within a single Sun-Earth-Moon conjunction cycle. In parallel, the method is validated by reconstructing transfer trajectories in a bicircular restricted four-body problem model (BCR4BP) of the Sun-Earth/Moon system.

Evolution of Periodic Orbits in the Sun-Jupiter and Sun-Earth Systems

Objective: The periodic orbits around smaller and larger primaries are studied in the Sun-Jupiter and Sun-Earth systems, considering smaller primary as an oblate spheroid. Methods: We used the Poincare surface section method to find the periodic orbits and discussed the differences between these orbits with and without oblateness. Findings: Different trajectories are drawn with the change of Jacobi constant and radiation pressure. Size variations, location, and eccentricity of an orbit around smaller primary are observed due to oblateness effect of the Jupiter and Earth. Oblateness of the smaller primary and radian pressure of the bigger primary have a significant effect on eccentricity, orbit shape, size, and position in phase space. Novelty : Small solar system bodies, such as asteroids and comets in the Sun-Jupiter and Sun-Earth systems, can be explored using periodic orbits. Perturbation caused by oblateness of the smaller primary must be understood and addressed during human exploration missions. Keywords: Circular Restricted Three Body Problem; Poincare Surface Sections; Jacobi Constant; Radiation Factor; Oblateness; Trajectories; Resonance

Maurya Receives 2019 Sunanda and Santimay Basu International Early Career Award in Sun–Earth Systems Science

Ajeet Kumar Maurya received the 2019 Sunanda and Santimay Basu International Early Career Award in Sun–Earth Systems Science at AGU’s Fall Meeting 2019, held 9–13 December in San Francisco, Calif. The award recognizes “work that shows promise of making outstanding contributions to research in Sun–Earth systems science and furthers the understanding of plasma physical processes and their applications for the benefit of society.”

Thomas Receives 2019 Basu U.S. Early Career Award for Research Excellence in Sun–Earth Systems Science

Evan G. Thomas received the 2019 Basu U.S. Early Career Award for Research Excellence in Sun–Earth Systems Science at AGU’s Fall Meeting 2019, held 9–13 December in San Francisco, Calif. The award is given annually to one early career scientist (no more than 3 years postdegree) from the United States in recognition of “significant work that shows promise of making outstanding contributions to research in Sun–Earth systems science and furthers the understanding of plasma physical processes and their applications for the benefit of society.”

Missions to Earth and Mars using a lunar launch facility

Many space agencies are working on solutions for manned operations on the Moon, both on its surface and in cislunar space. In such a scenario, with stable human presence, a launch facility would be needed and launch vehicles could take advantage of the benefits of the lunar environment. In the present paper missions to Earth (to a geostationary orbit) and to Mars (to an areostationary orbit), from a lunar launch facility, has been studied. The trajectories are analysed by using an ephemeris model, taking into account four attractive bodies (Earth, Moon, Sun and Mars). In the first phase of the two missions, the launcher places the spacecraft on a circular lunar orbit by using liquid, solid or hybrid propulsion systems. The latter solution is analysed assuming in situ propellant production using aluminum and oxygen, elements in which the moon is very rich. In the second phase of both the missions, a minimum energy trajectory is studied, which, exploiting the Luni-Solar perturbations, allows the spacecraft to escape the gravitational field of the Moon. In the mission to Earth, this manoeuver puts the spacecraft on a very high and inclined elliptical orbit. The last phase involves a circularization manoeuvre towards the GEO and transfers are studied for two different initial inclinations, using an electric engine. In the mission to Mars, the escape impulse is used to leave both the Earth-Moon and Sun-Earth systems. The interplanetary phase is analysed for several transfer final times and considering an electric engine with variable specific impulse. Finally, the performance of a lunar launch facility is compared to that of a traditional Earth facility, showing great advantages are obtained in terms of payload ratio.

Katamzi-Joseph Receives 2018 Sunanda and Santimay Basu (International) Early Career Award in Sun–Earth Systems Science

Zama T. Katamzi-Joseph will receive the 2018 Sunanda and Santimay Basu (International) Early Career Award in Sun–Earth Systems Science at AGU’s Fall Meeting 2018, to be held 10–14 December in Washington, D. C. The award recognizes “outstanding contributions to research in Sun–Earth systems science that further the understanding of both plasma physical processes and their applications for the benefit of society.”

Stawarz Receives 2018 Basu United States Early Career Award for Research Excellence in Sun–Earth Systems Science

Julia Stawarz will receive the 2018 Basu United States Early Career Award for Research Excellence in Sun–Earth Systems Science at AGU’s Fall Meeting 2018, to be held 10–14 December in Washington, D. C. This award is given annually to “one early career scientist (no more than 3 years post-degree) from the United States in recognition of significant work that shows the focus and promise of making outstanding contributions to research in Sun–Earth systems science that further the understanding of both plasma physical processes and their applications for the benefit of society.”

Shi Receives 2017 Basu Early Career Award in Sun–Earth Systems Science

Quanqi Shi will receive the 2017 Sunanda and Santimay Basu Early Career Award in Sun–Earth Systems Science. He will present a talk and will be formally presented with the award at the 2017 American Geophysical Union Fall Meeting, to be held 11–15 December in New Orleans, La. This award recognizes “outstanding contributions to research in Sun–Earth systems science that further the understanding of both plasma physical processes and their applications for the benefit of society.”

Blum Receives 2017 Basu United States Early Career Award for Research Excellence in Sun–Earth Systems Science

Lauren Blum will receive the 2017 Basu United States Early Career Award for Research Excellence in Sun–Earth Systems Science at the 2017 American Geophysical Union Fall Meeting, to be held 11–15 December in New Orleans, La. This award is given annually to “one early career scientist (no more than 3 years post-degree) from the United States in recognition of significant work that shows the focus and promise of making outstanding contributions to research in Sun–Earth systems science that further the understanding of both plasma physical processes and their applications for the benefit of society.”

Simulation of Low Thrust Spacecraft Guided Motion for a Number of Missions in the Solar System

Models of spacecraft guided motion in the gravitational fields of different configurations were developed. Parameterization of the optimal control laws for all the trajectory segments of the spacecraft moving in the N-body gravitational field was realized. The dependence patterns of control laws on mission purposes were determined. The simulation of the number of missions in the Solar system was performed: low Earth orbit – L1 and L2 of the Earth-Moon and the Sun-Earth systems, L1 – L2 and L2 – L1 of the Earth-Moon and the Sun-Earth systems, low Earth orbit – asteroid Eros, low Earth orbit – Venus, low Earth orbit – Mars. Moreover, the Venus gravity assist maneuver was considered.

Komar Receives 2016 Basu United States Early Career Award for Research Excellence in Sun-Earth Systems Science

Colin Komar will receive the 2016 Basu United States Early Career Award for Research Excellence in Sun-Earth Systems Science at the 2016 American Geophysical Union Fall Meeting, to be held 12–16 December in San Francisco, Calif. This award is given annually to one early-career scientist (no more than 3 years post-degree) from the United States in recognition of significant work that shows the focus and promise of making outstanding contributions to research in Sun-Earth systems science that further the understanding of both plasma physical processes and their applications for the benefit of society.

Olwendo Receives 2016 Basu Early Career Award in Sun-Earth Systems Science

Joseph Olwendo will receive the Sunanda and Santimay Basu Early Career Award in Sun-Earth Systems Science. He will present a talk and will be formally presented with the award at the 2016 American Geophysical Union Fall Meeting, to be held 12–16 December in San Francisco, Calif.

Analysis of Effect of Oblateness of Smaller Primary on the Evolution of Periodic Orbits

Evolution of periodic orbits in Sun-Mars and Sun-Earth systems are analyzed using Poincare surface of section technique and the effects of oblateness of smaller primary on these orbits are considered. It is observed that oblateness of smaller primary has substantial effect on period, orbit’s shape, size and their position in the phase space. Since these orbits can be used for the design of low energy transfer trajectories, so perturbations due to planetary oblateness has to be understood and should be taken care of during trajectory design. In this paper, detailed stability analysis of periodic orbit having three loops is given for A2 = 0.0001.

Analysis of Effect of Solar Radiation Pressure of Bigger Primary on the Evolution of Periodic Orbits

Evolution of periodic orbits in Sun-Mars and Sun-Earth systems are analyzed using Poincare surface of section technique and the effects of solar radiation pressure of bigger primary and actual oblateness of smaller primary on these orbits areconsidered. It is observed that solar radiation pressure of bigger primary has substantial effect on period, orbit’s shape, size and their position in the phase space. Since these orbits can be used for the design of low energy transfer trajectories, so perturbations due to solar radiation pressure has to be understood and should be taken care of during trajectory design. It is also verified that stability of such orbits are negligible so they can be used as transfer orbit. For each pair of solar radiation pressure q and Jacobi constant C we get two separatrices where stability of island becomes zero. In this paper, detailed stability analysis of periodic orbit having two loops is given when q = 0.9845.

Duly Receives 2015 Basu United States Early Career Award for Research Excellence in Sun-Earth Systems Science

Timothy Duly will receive the 2015 Basu United States Early Career Award for Research Excellence in Sun-Earth Systems Science at the 2015 American Geophysical Union Fall Meeting, to be held 14–18 December in San Francisco, Calif. This award is given annually to one early-career scientist (no more than 3 years postdegree) from the United States in recognition of significant work that shows the focus and promise of making outstanding contributions to research in Sun-Earth systems science that further the understanding of both plasma physical processes and their applications for the benefit of society.

Jiang Receives 2015 Basu Early Career Award in Sun-Earth Systems Science

Chaowei Jiang will receive the Sunanda and Santimay Basu Early Career Award in Sun-Earth Systems Science. He will present a talk and will be formally presented with the award at the 2015 American Geophysical Union Fall Meeting, to be held 14–18 December in San Francisco, Calif.

Bosco Receives 2014 Basu Early Career Award in Sun-Earth Systems Science

John Bosco has been awarded the Sunanda and Santimay Basu Early Career Award in Sun-Earth Systems Science. He presented a talk and was formally presented with the award at the 2014 American Geophysical Union Fall Meeting, held 15–19 December in San Francisco, Calif.