Navigating stellar wobbles for imaging with the solar gravitational lens
  The solar gravitational lens (SGL) offers unique capabilities for
high-resolution imaging of faint, distant objects, such as exoplanets. 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 vicinity of the
target-specific primary optical axis - the line that connects the center of the
target and that of the Sun. This axis 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. 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 follow 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. We show that even in a rather conservative case, when an
Earth-like exoplanet is in our stellar neighborhood at $\sim10$ light years,
the motion of the image is characterized by a small total acceleration $\sim
6.1\,\mu {\rm m/s}^2$ that is driven primarily by the orbital motion of the
exoplanet and by the reflex motion of our Sun. We discuss how the amplified
light of the host star allows establishing a local reference frame thus
relaxing navigational requirements. We conclude that the required navigation in
the SGL's focal region, although complex, can be accurately modeled and a $\sim
10$-year imaging mission is achievable with the already available propulsion
technology.
