Exoplanet imaging along a time-varying focal line using tethered spacecraft

Abstract

The design of a tethered spacecraft to image exoplanets using the solar gravitational lens (SGL) is investigated. This mission would require the spacecraft to travel to a distance of at least 547 AU from the sun, where the semi-infinite focal line of the SGL begins, and rasterize pixel by pixel the exoplanet image, which could have a diameter on the order of 1 km. In addition, the spacecraft would need to perform trajectory control to stay within the time-varying focal line, which moves due to, among other factors, the orbit of the exoplanet about its parent star. Rotating tethered spacecraft provide an interesting potential mission architecture, as they do not require thrust to achieve coverage of the roughly 1 km image, reserving it instead only to perform center of mass trajectory control. Equations of motion are derived for collinear configurations with two and three subsatellites, and tether retrieval and deployment laws are developed that take into account the geometry of the Archimedean spiral—ideal for imaging or interferometry applications. Trajectory control schemes with one and two thrusters in the case of two subsatellites and three thrusters in the case of three subsatellites are considered. In addition, the vibrational behavior of the viscoelastic tethers is analyzed. Simulations are carried out for realistic conditions in an example mission to image a hypothetical Earth-like exoplanet. The results reveal some inherent challenges of covering the entire image plane with two subsatellites, which the three-subsatellite configuration addresses. Results also show that no vibration control is necessary as the vibration amplitude is negligible. Estimates of the total imaging time are 2.5 months for a two-subsatellite spacecraft and 16.8 days for a three-subsatellite configuration.