Science merit function for the Kepler mission

The Kepler mission was a National Aeronautics and Space Agency (NASA) Discovery-class mission designed to continuously monitor the brightness of at least 100,000 stars to determine the frequency of Earth-size and larger planets orbiting other stars. Once the Kepler proposal was chosen for a flight opportunity, it was necessary to optimize the design to accomplish the ambitious goals specified in the proposal and still stay within the available resources. To maximize the science return from the mission, a merit function (MF) was constructed that relates the science value (as determined by the PI and the Science Team) to the chosen mission characteristics and to models of the planetary and stellar systems. This MF served several purposes; predicting possible science results of the proposed mission, evaluating the effects of varying the values of the mission parameters to increase the science return or to reduce the mission costs, and supporting quantitative risk assessments. The MF was also valuable for the purposes of advocating the mission by illustrating its expected capability. During later stages of implementation, it was used to keep management informed of the changing mission capability and support rapid design tradeoffs when mission down-sizing was necessary. The MF consisted of models of the stellar environment, assumed exoplanet characteristics and distributions, detection sensitivity to key design parameters, and equations that related the science value to the predicted number and distributions of detected exoplanet. A description of the MF model and representative results are presented. Examples of sensitivity analyses that supported design decisions and risk assessments are provided to illustrate the potential broader utility of this approach to other complex science-driven space missions.