Long Abstract:

An external occulter (or starshade, or star-visor) flying in formation tens of thousands of kilometres from a space telescope is a candidate architecture proposed for the discovery and study of terrestrial-analogue planets around nearby stars.  This astronomical technique offers the potential for direct imaging of extrasolar planetary systems as well as the capability of spectroscopic discrimination and study of planetary surfaces, atmospheres, and the debris disk remnants of planetary system formation.  External occultation solves many optical problems such as suppressing scattered and diffracted light from the target star, allowing a large outer-working-angle, and providing good throughput of the exoplanet signal.  

Near-term candidate missions to employ free-flying external occultation leverage the Earth-Sun-L2 and Earth-fallaway solar orbits for placement of the telescope and occulter.  In 2006 a proposal to fly an external occulter ~ 20,000 kilometres from the James Webb Space Telescope (JWST) to discover exoplanet candidates around the nearest stars was submitted for a NASA Discovery mission.  Although not selected for funding, its characteristics have much in common with other near-term missions of interest.  Optimizing science retrievable within the inherent constraints of the environment is crucial to assessing mission feasibility and the proper architecting of it.

However, drawbacks of this architecture are that the occulter takes from days to weeks to slew between targets, formation-keeping between the craft is required as well as good inter-target navigation techniques, and a large antisun-exclusion zone limits when high-contrast observations of most target stars may occur.  In order to offset these shortcomings, proper mission design must be considered.  In this paper, for likely near-term free-flying external occulter missions, the theoretical inter-relationship between critical mission design parameters is presented along with computer simulations for comparison.  Navigation and formation-keeping are discussed in this context.  Science quality metrics are also discussed in terms of the astrodynamical relationships, and the potential impact on mission completeness goals is demonstrated from the simulations.

Navigation for inter-target transits and formation keeping during observations are critical elements in performing free-flying external occulter missions.  Many navigation techniques have been proposed, however in this paper, a distinction between inertial and non-inertial techniques is highlighted which may offer an alternative way of approaching the problem.

Formation-keeping of an external occulter within a few metres across the line-of-sight is roughly equivalent to maintaining alignment of a long strand of spaghetti at a distance of a few tens of kilometres.  However, this problem is in many ways easier than formation-keeping required for the Terrestrial Planet Finder Interferometer (TPF-I) mission which requires sub-wavelength optical path control with high-speed, simultaneous metrologization of multiple free-flying optical benches.  The free-flying occulter does not rely on large-angle beam combination, so alignment tolerances are vastly relaxed and metrology can be performed at a more leisurely pace by leveraging inherent advantages of the telescope-occulter-target geometry.  Nevertheless, the geometry between telescope, occulter, and nearby gravitational sources, and other ambient forces, shear the formation on timescales of many hundreds of seconds which requires correction.  The magnitudes and scaling are discussed in terms of mission scope and requirements at a first-order level in this paper.  Questions about extension toward a more accurate astrodynamic model are posed.

Using techniques drawn from statistical-mechanics in conjunction with physical kinematic and dynamic arguments for a randomly distributed set of targets, one may derive theoretical scaling relationships between free-flying external occulter mission parameters such as telescope-occulter range, number of targets, mean number of observations per target, specific impulse, transit strategies, occulter spacecraft mass, propulsive power, and mission duration.  However, circumstances for likely science missions
produce variation from the ideal model in ways that may be important for mission and vehicle design.  Application of the ideal- and computer-models to guide mission designers in their exploration of parameter space and optimization of such missions is discussed.