  Detection of Jupiter mass companions to nearby solar type stars with precise
radial velocity measurements is now routine, and Doppler surveys are moving
towards lower velocity amplitudes. The detection of several Neptune-mass
planets with orbital periods less than a week has been reported. The drive
toward the search for close-in Earth-mass planets is on the agenda. Successful
detection or meaningful upper limits will place important constraints on the
process of planet formation. In this paper, we quantify the statistics of
detection of low-mass planets in-close orbits, showing how the detection
threshold depends on the number and timing of the observations. In particular,
we consider the case of a low-mass planet close to but not on the 2:1 mean
motion resonance with a hot jupiter. This scenario is a likely product of the
core-accretion hypothesis for planet formation coupled with migration of
jupiters in the protoplanetary disk. It is also advantageous for detection
because the orbital period is well-constrained. Detection of few Earth mass
rocky cores will require ~ 1 m/s velocity precision, and most importantly, a
much better understanding of stellar radial velocity jitter.
