Calculation of distant retrograde orbits and their use for space weather forecasting

There is current renewed interest in using distant retrograde orbits (DRO) for a space weather forecasting mission, which would temporarily place spacecraft at a position near the Sun--Earth line, but closer to the Sun than the L1 point. For a continuous coverage, several spacecraft would be needed at such sub-L1 distances. With in situ observations of the magnetic field, the southward Bz < 0 field of solar coronal mass ejections (CMEs), which is not accessible remotely, could be measured hours in advance. This Bz < 0 field is a decisive factor for forecasting geomagnetic storm intensity. Here, we analyse DROs at different distances for their efficacy for a space weather forecasting mission. First, we present a simple open-source numerical framework to generate DRO trajectories, based on equations for the constrained three-body problem. This makes them easily accessible for their introduction into numerical or empirical simulations of the solar wind or CMEs. Secondly, we analyze their general characteristics, such as relationships between their minimum distance to the Sun along the Sun-Earth line and their widest longitudinal extent. Third, we combine recent progress on our understanding of the magnetic structure of CMEs with the DRO characteristics and the possible number of spacecraft, to find clues on an optimal mission configuration, at distances between 0.8 and 0.9 au from the Sun. We also identify knowledge gaps and open challenges. ESA HENON (launch 2026) and ESA SHIELD (planned for the 2030s) are bound to be the first missions to realize space weather forecasts with sub-L1 data on DROs. We here provide a baseline for future studies by combining DRO calculations with the current state of knowledge on CMEs, for space weather forecasts with strongly enhanced lead times.