Radial velocity measurements have proven a powerful tool for finding planets in short-period orbits around other stars. In this paper we develop an analytical expression relating the sensitivity to a periodic signal to the duration and accuracy of a given set of data. The effects of windowing and the sensitivity to periods longer than the total length of observations are explored. We show that current observations are not yet long or accurate enough to make unambiguous detection of planets with the same mass and period as Jupiter. However, if measurements are continued at the current levels of accuracy (5 m s-1) for a decade, then planets of Jovian mass and brown dwarfs will either be detected or ruled out for orbits with periods less than ~15 yr. As specific examples, we outline the performance of our technique on large-amplitude and large-eccentricity radial velocity signals recently discussed in the literature, and we delineate the region explored by the measurements of 14 single stars made over a 12 yr period by Walker et al. Had any of these stars shown motion like that caused by the exoplanets recently detected, it would have been easily detected. The data set interesting limits on the presence of brown dwarfs at orbital radii of 5-10 AU. The most significant features in the Walker et al. data are apparent long-term velocity trends in 36 UMa and β Vir, consistent with super planets of mass of 2 MJ in a 10 yr period, or 20-30 MJ in a 50 yr period. If the data are free of long-term systematic errors, the probability of just one of the 14 stars showing this signal by chance is about 15%. Finally, we suggest an observing strategy for future large radial velocity surveys that, if implemented, will allow coverage of the largest range of parameter space with the smallest amount of observing time per star. We suggest that about 10-15 measurements be made of each star in the first 2 yr of the survey, then 2-3 measurements yr-1 thereafter, provided no (or slow) variation is observed. More frequent observations would of course be indicated if such variations were present.
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机译：径向速度测量已被证明是寻找其他恒星周围短周期轨道上的行星的有力工具。在本文中，我们开发了一种解析表达式，将周期性信号的灵敏度与给定数据集的持续时间和准确性相关联。探索了窗口效应和对比观测总长度更长的时间段的敏感性。我们表明，目前的观测还不够长或不够准确，无法对与木星相同质量和周期的行星进行明确的探测。但是，如果以目前的精度水平（5 m s-1）进行测量十年，那么将发现木星质量行星和褐矮星，或者将其排除在小于15年周期的轨道上。作为具体示例，我们概述了我们的技术在文献中最近讨论的大振幅和大偏心径向速度信号上的性能，并通过Walker等人在12年内对14个单颗恒星的测量来描绘了该区域。等如果这些恒星中的任何一颗表现出像最近发现的系外行星所引起的运动，那将很容易被发现。该数据对在轨道半径为5-10 AU的褐矮星的存在设置了有趣的限制。 Walker等人中最重要的功能。数据是36 UMa和βVir的明显长期速度趋势，与10年内质量为2 MJ的超级行星或50年内质量为20-30 MJ的超级行星相一致。如果数据没有长期的系统误差，则仅14个恒星之一偶然显示此信号的概率约为15％。最后，我们为未来的大型径向速度调查提出了一种观测策略，如果实施该策略，则可以覆盖最大范围的参数空间，并且每颗恒星的观测时间最少。我们建议在调查的前2年中对每颗恒星进行约10-15次测量，然后在没有观察到（或缓慢）变化的情况下对yr-1进行2-3次测量。如果存在这种变化，当然会指出更频繁的观察结果。
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