True Masses of Radial-Velocity Exoplanets
We explore the science power of space telescopes used to estimate the true masses of known radial-velocity exoplanets by means of astrometry on direct images. We translate a desired mass accuracy (+/10% in our example) into a minimum goal for the signal-to-noise ratio, which implies a minimum exposure time. When the planet is near a node, the mass measurement becomes difficult if not impossible, because the apparent separation becomes decoupled from the inclination angle of the orbit. The combination of this nodal effect with considerations of solar and anti-solar pointing restrictions, photometric and obscurational completeness, and image blurring due to orbital motion, severely limits the observing opportunities, often to only brief intervals in a five-year mission. We compare the science power of four missions, two with external star shades, EXO-S and WFIRST-S, and two with internal coronagraphs, EXO-C and WFIRST-C. The star shades out-perform the coronagraph in this science program by about a factor of three. For both coronagraphs, the input catalog includes 16 RV planets, of which EXO-C could possibly observe 10, of which 6 would have a 90% guarantee of success. Of the same 16 planets, WFIRST-C could possibly observe 12, of which 9 are guaranteed. For both star-shade missions, the input catalog includes 55 planets, of which EXO-S could possibly observe 37, of which 20 are guaranteed. Of the same 55, WFIRST-S could possibly observe 45, of which 30 are guaranteed. The longer spectroscopic exposure times should be easily accommodated for the RV planets with guaranteed success.