Simulated Jupiter signal observed with a precision of 5 and 2 m s⁻¹. Solid lines are best‐fit Keplerians to the simulated data sets. With measurement precision of 5 m s⁻¹, an unreliable 2 σ detection is obtained with no information on the orbital eccentricity. With precision of 2 m s⁻¹, a solid 5 σ detection is made, and the eccentricity is determined to within ±0.05.