Visibility Analysis of the Sun as Viewed from Multiple Spacecraft at the Sun-Earth Lagrange Points

TL;DR

The paper analyzes how placing multiple spacecraft at Sun–Earth Lagrange points L1, L4, and L5 can maximize solar visibility for on-disk and limb observations, enabling coordinated multi-view solar studies. Using CRTBP-derived periodic orbits and a grid-based solar-surface visibility framework, it quantifies visibility durations $\Psi_{ij}$ and latitude-averaged coverage $\hat{\Psi}_{i}$ under varying $\Theta_{\max}$, limb criteria, and orbit inclinations, including an oriented L4/L5 setup with angle $\alpha$ to optimize high-latitude views. It demonstrates substantial gains from multi-spacecraft configurations: on-disk visibility improves with L4/L5 placements (up to ~180% or more at high latitudes for inclined orbits), limb observations enable multi-angle constraints for magnetic-field reconstruction, and sunspot-tracking durations increase significantly, particularly at higher latitudes. These results provide quantitative guidance for designing future multi-point solar observatories and have practical implications for space-weather monitoring and planning crewed missions beyond the Earth–Moon system. Key findings include the importance of high-latitude viewing from inclined L4/L5, the value of limb-disk synergy for 3D magnetic-field studies, and the demonstrated potential to monitor solar activity with improved continuity and stereoscopic capabilities across L1, L4, and L5.

Abstract

Beyond the Sun-Earth line, spacecraft equipped with various solar telescopes are intended to be deployed at several different vantage points in the heliosphere to carry out coordinated, multi-view observations of the Sun and its dynamic activities. In this context, we investigate solar visibility by imaging instruments onboard the spacecraft orbiting the Sun-Earth Lagrange points L1, L4 and L5, respectively. An optimal arrival time for vertical periodic orbits stationed at L4 and L5 is determined based on geometric considerations that ensure maximum visibility of solar poles or higher latitudes per year. For a different set of orbits around the three Lagrange points (L1, L4 and L5), we calculate the visibility of the solar surface (i.e., observation days per year) as a function of the solar latitude. We also analyze where the solar limb viewed from one of the three Sun-Earth Lagrange points under consideration is projected onto the solar surface visible to the other two. This analysis particularly aims at determining the feasibility of studying solar eruptions, such as flares and coronal mass ejections, with coordinated observations of off-limb erupting coronal structures and their on-disk magnetic footpoints. In addition, visibility analysis of a feature (such as sunspots) on the solar surface is made for multiple spacecraft in various types of orbits with different inclinations to quantify the improvement in continuous tracking of the target feature for studying its long-term evolution from emergence, growth and to decay. A comprehensive comparison of observations from single (L1), double (L1 and L4) and multi-space missions (L1, L4 and L5) is carried out through our solar visibility analysis, and this may help us to design future space missions of constructing multiple solar observatories at the Sun-Earth Lagrange points.

Figures (17)

• Figure 1: Cartoon showing solar surface visibility with three spacecraft positioned at the Sun-Earth Lagrange points L1, L4 and L5 on the Stonyhurst heliographic coordinate system (panel a) and on the spherical surface of the Sun (panel b). The visible solar surface by an imaging instrument (with a viewing angle of $40^\circ$ toward the center of the Sun) onboard each of the spacecraft is shown in blue, red and green, respectively, for L1, L4 and L5, while the invisible region in gray. The region visible by two spacecraft is denoted in magenta for L1 and L4, while in cyan for L1 and L5. The white line represents the solar limb viewed from each of the spacecraft.
• Figure 2: Illustration of the solar radiation hemisphere that is the relative solar hemisphere from a 1 AU observer at the Earth with possessing the potential to severely affect the radiation environment at or near the Earth. It ranges from 30°E to 150°W in solar longitudes and is best observed from L4. A histogram from richardson201425 displays source longitudes of major solar proton events in the energy range of 14–-24 MeV. Highlighted are the Earth-Moon system, Hohmann transfer orbits to and from Mars, L4 and L5, and an interplanetary magnetic field line from 60°W on the Sun to the Earth modeled from an average solar wind speed in the ecliptic plane. This figure is adapted from posner2021multi.
• Figure 3: Planar Lyapunov periodic orbits at the Sun-Earth Lagrange point L1 are shown with a different set of values for the Jacobi integral.
• Figure 4: Planar and vertical Lyapunov periodic orbits at L4 are shown with a different set of values for the Jacobi integral. For the vertical periodic orbits, the one with an inclination of $14.5^\circ$ with respect to the ecliptic plane is marked in red.
• Figure 5: Definition of the heliographic inertial coordinate system (HGI) with respect to the ecliptic coordinate system (E). In panel (b), $\Theta^{t}_{ij}$ is an angle between the surface normal vector $\mathbf{n}_{ij}$ and the line-of-sight vector $\mathbf{R}_{LOS}^{t}$ at time $t$ of observations by an instrument onboard a spacecraft.