Perturbations in Cislunar Space; Perturbation Sources (Part I)

In the concept of cislunar exploration, these sets of space forces have played crucial roles in the flight characteristics of a spacecraft bound for a cislunar mission. Perturbations often refer to changes or deviations in the flight path of a spacecraft from a pre-determined trajectory due to exterior forces or effects that are not accounted for while computing simple two-body mechanics of the space mission. Within the Earth-Moon system, perturbations play significant roles due to the complex gravitational influences and environmental effects of this region.

Perturbations in the Earth-Moon system often arise from a variety of sources. Because of the gravity influence of both the Earth and the moon, the first source usually develops from third-body effects, as they become crucial. The two body dynamics majorly assess the gravity behavior of the spacecraft to the nearby celestial object (Earth or moon, depending on the proximity to the spacecraft). The third-body effect arises from the influence of the second celestial object in the cislunar system. This means a spacecraft near Earth still experiences the influence of gravity from the moon, no matter how small. Similarly, the spacecraft near the lunar sphere of influence still experiences gravity influences from the Earth.

Furthermore, perturbations also arise from gravity influences from non-spherical fields. It is obvious that both the Earth and the moon deviate gradually from perfect spherical shapes. This results in an irregular distribution of mass across their shapes, often characterized by spherical harmonics, which usually affect the trajectory of spacecraft. This trajectory change predominantly obtains its root cause from the Earth's oblateness (often called the J2 effect) as well as the mass concentrations of the moon. Additionally, the giant Sun, despite its far distance, has its non-negligible input in the Earth-Moon system. Photon emissions from the sun exert pressure on the traveling spacecraft, particularly in the cislunar space where Earth's shadowing effect is less pronounced. The extent of the solar radiation pressure effect on the spacecraft largely depends on the surface properties of the spacecraft, its orientation, and its net distance from the sun. In addition, lunar and Earth atmospheric drag, though minimal, may influence low-attitude orbits near the moon or Earth.

In continuation, perturbations have also been traced to relativistic effects, all stemming from Einstein's general relativity theory, and taking significant dominance in high-precision orbital dynamics. These relativistic effects could be from the Dilation of Gravity Time (time running slower in fields of stronger gravitational influence, which has to be accounted for, especially within the cislunar space, particularly near the Earth or the Moon), or from the relativistic correction of orbits (where the curvature of spacetime around massive bodies can alter the trajectory of a spacecraft). Though relativistic effects are less pronounced compared to low-Earth orbits, they can affect navigation in cislunar space, particularly for long-duration missions.

Another unavoidable cause of perturbations in cislunar space is the action of tidal forces. These forces arise from the gravitational gradient across a spacecraft due to a nearby massive celestial object, causing differential acceleration between different parts of the spacecraft. Tidal forces can be perceived in a variety of ways, such as a spacecraft experiencing varying gravity pull on its near and far sides relative to the Earth, the Moon, or even the Sun, posing a possibility of altering the spacecraft's trajectory or even the structural stability and robustness of the spacecraft, in some extreme cases. Tidal forces can cause trajectory alterations, as they dominate the Earth-Moon system. On approaching the Moon, smaller gravitational gradients result in weaker tidal forces compared to Earth. Tidal effects also affect resonances in cislunar space, particularly in orbits near the Lagrange points of the Earth-Moon system.

Lastly, and very significantly, Electromagnetic effects on spacecraft motion cannot be ignored. Electromagnetic effects usually result from interactions with the charged space environment and magnetic fields. The Earth’s magnetic field extends into high orbits in cislunar space, although it is weaker at those points, compared to low Earth orbit (LEO). On the other hand, the Moon’s crustal magnetic fields are localized but can still influence small spacecraft near its surface. Electromagnetic effects could also emanate from Plasma interactions. The spacecraft interacts with charged particles in the solar wind and Earth’s magnetosphere, thus, differential charging can occur on different spacecraft surfaces, leading to electrostatic discharges. Also, if a spacecraft has an electric charge and moves through a magnetic field, it experiences what is termed a Lorentz force that can also alter its trajectory. Consequently, the transition between Earth’s magnetosphere and interplanetary space subjects traveling spacecraft to variance in plasma densities and magnetic fields. Also, prolonged exposure to these induced solar winds causes charging, potentially affecting onboard electronics and sensitive instruments. In some cases, for highly charged spacecraft, the Lorentz force can begin as a small but transcend into a cumulative perturbation.

Perturbations are highly significant factors that must be adequately considered in planning cislunar missions, as they could completely sweep a spacecraft off course. In some cases, some perturbative forces need to be iterated on motion during mission analysis, as they may be only induced and observable as the spacecraft moves. Analysis and provision for perturbative effects on a spacecraft will see the spacecraft maintain course during the phases of the in-space maneuvers with minimal disruptive effects.