Navigating stellar wobbles for imaging with the solar gravitational lens

The solar gravitational lens (SGL) offers unique capabilities for direct high-resolution imaging of faint, distant objects, such as exoplanets. For that purpose, in the near future, a spacecraft carrying a meter-class telescope with a solar coronagraph would be placed in the focal region of the SGL. That region begins at ~547~astronomical units from the Sun and occupies the immediate vicinity of the target-specific primary optical axis -- the line that connects the center of the target and that of the Sun. Clearly, this axis is not at rest. It undergoes complex motion as the exoplanet orbits its host star, as that star moves with respect to the Sun, and even as the Sun itself moves with respect to the solar system's barycenter due to the gravitational pull of planets in our solar system. Although less prominent, other motions exist. An image of an extended object is projected by the SGL into an image plane and moves within that plane, responding to the motion of the optical axis. To sample the image, a telescope must always be on the move, following the projection, with precise knowledge of its own position with respect to the image. We consider the dominant motions that determine the position of the focal line as a function of time. We evaluate the needed navigational capability for the telescope to conduct a multiyear exoplanet imaging mission in the focal region for the SGL. We show that even in a rather conservative case, when an Earth-like exoplanet is in our immediate stellar neighborhood at ~10 light years, the motion of the image is characterized by a small total acceleration that is driven primarily by the orbital motion of the exoplanet (estimated to be at the level of 6 um/s^2, decreasing inversely with distance to a target) and by the reflex motion of our Sun (target independent, staying at ~0.2 um/s^2). Such a small acceleration can be maintained for the entire ~10-year duration of a prospective imaging mission with modern electric micropropulsion systems. We conclude that the required navigation in the SGL's focal region, although complex, can be accurately modeled and is achievable with realistic, available propulsion technology.