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We describe a strategy for scheduling astrometric observations to minimizethe number required to determine the mutual orbits of binary transneptuniansystems. The method is illustrated by application to Hubble Space Telescopeobservations of (42355) Typhon-Echidna, revealing that Typhon and Echidna orbitone another with a period of 18.971 +/- 0.006 days and a semimajor axis of 1628+/- 29 km, implying a system mass of (9.49 +/- 0.52) x 10^17 kg. Theeccentricity of the orbit is 0.526 +/- 0.015. Combined with a radiometric sizedetermined from Spitzer Space Telescope data and the assumption that Typhon andEchidna both have the same albedo, we estimate that their radii are 76 +14/-16and 42 +8/-9 km, respectively. These numbers give an average bulk density ofonly 0.44 +0.44/-0.17 g cm^-3, consistent with very low bulk densities recentlyreported for two other small transneptunian binaries.

(42355) Typhon-Echidna: Scheduling Observations for Binary Orbit Determination