# Why is the Sun influence a mere perturbation to the Moon NRHO (the orbit the Gateway should be put in the context of project Artemis)?

An article of the relevant literature Heliocentric Escape and Lunar Impact from Near Rectilinear Halo Orbits asserts: "As the spacecraft departs the immediate vicinity of the NRHO, the effects of the Sun become significant." (See block quote below).

I ask: why are those effects less significant in the NRHO vicinity, so that they can be treated just like a perturbation in the context of the CR3BP? If I calculated correctly, the Sun gravity acting on a spacecraft in the NRHO is stronger than the gravity pull of Earth on the same spacecraft.

Maybe the fact that the Earth-Moon-spacecraft system is in revolution around the Sun "generates" a centrifugal force that in part contrast the Sun gravity… I am trying to gain an intuitive physical understanding of the matter and I hope you can offer me some insights because I couldn't find them anywhere else.

edit: I quoted the article to better convey a doubt originated before reading the article itself. I try now to provide another formulation to my question to be more clear. Nasa chose the NRHO as an optimal solution for the orbit of the Gateway also because it requires low maintenance (it is fuel efficient; https://www.nasa.gov/missions/artemis/lunar-near-rectilinear-halo-orbit-gateway/). This means that the NRHO, which is a solution of the CR3BP of the Moon-Earth-System, is not heavily disrupted when considered in the context of a more realistic dynamics. I wonder how this can be the case just considering the influence of the Sun.

DYNAMICAL MODELS

In this investigation, three dynamical models are employed. The CR3BP5 provides a framework for investigation of departure dynamics and flow nearby the NRHO before and immediately after separation from the Gateway. In this regime, the primary gravitational influences on the spacecraft are the Earth and Moon, and the CR3BP is an effective approximation for the dynamics. As the spacecraft departs the immediate vicinity of the NRHO, the effects of the Sun become significant. Thus, the BCR4BP6 is employed to characterize the behavior of the departing spacecraft. The BCR4BP incorporates the influence of solar gravity on the Earth-Moon-spacecraft three-body system and offers an increase in fidelity over the CR3BP, while still offering insight into the underlying dynamical behavior in the system. Finally, an N-body model based on ephemeris data provides higher-fidelity analysis for particular mission scenarios.

5(CR3BP = circular restricted three body problem) Szebehely, Z., Theory of Orbits: The Restricted Problem of Three Bodies, Academic Press, New York, 1967.

6(BCR4BP = bi-circular restricted four body problem) Gomez, G., J. Llibre, R. Martinez, and C. Simo, Dynamics and Mission Design near Libration Points, Vol. 2. World Scientific, 2001.

• what article are you quoting? Oct 23, 2023 at 0:55
• Seems to be ntrs.nasa.gov/api/citations/20200001596/downloads/… - but that part is referencing the reasons for the dynamical models chosen in the paper. Feels like its been extracted and pondered out of context. Oct 23, 2023 at 1:14
• "So, generally speaking, the quote can be extended beyond the scope of that specific article" - no, those quotes are from "Dynamical Models" sections of the articles where the authors are speaking to why they chose to model things certain ways. Oct 23, 2023 at 1:45
• In first approximation, Earth, Moon and Spacecraft should all experience a similar gravitational acceleration toward the Sun. More precisely the accelerations would vary in relation to the mutual orbital position of those three elements. I do not know much more given that in the recent project I worked on I just assumed and studied the CR3BP (of Earth-Moon-System) related dynamic. Oct 23, 2023 at 17:15
• @Franklin The centrifugal force is "fictitous", i.e., its an artifact of the non-inertial frame. Using such a frame makes some things simpler, but they can also be a bit misleading. I have some info (with diagrams) regarding the effective potential in a rotating frame here. Oct 24, 2023 at 7:01