It is proposed to explore the interaction of weak gravitational fields with slender elastic materials in order to assess the viability of achieving enhanced laser interferometric sensitivities for the detection of gravitational waves with frequencies between 10−4 and 1 Hz. The aim is the design of novel gravitational antennae in interplanetary orbit. The implementation of these ideas would be complimentary to existing programmes of gravitational wave research but exploiting a current niche in the frequency spectrum. The dynamics of slender structures, several km in length, are ideally suited to analysis by the simple theory of Cosserat rods. Such a description offers a clean conceptual separation of the vibrations induced by bending, shear, twist and extension and the coupling between eigen-modes due to tidal accelerations can be reliably estimated in terms of the constitutive properties of the structure. The detection of gravitational waves in the 1 Hz region would provide vital information about stochastic backgrounds in the early Universe and the relevance of supermassive black holes to the processes that lead to processes in the centre of galaxies.