Abstract
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.
Highlights
The Kepler mission[1,2,3,4] began as a Principal Investigator (PI)-led National Aeronautics and Space Agency (NASA) Discovery-class mission (#10) that was designed to explore the structure and diversity of planetary systems
The merit function (MF) was an algorithm designed to produce numerical values for the science return given a set of inputs representing an instrument/spacecraft point design, estimates of the stellar structure of galaxy, exoplanet size and frequency distributions, and stellar and instrument noise
A comparison of the upper panels shows that the reduction of the mission duration from 4 to 3 years would result in the loss of mission capability to detect Earth-size planets in the habitable zone (HZ) of G2-dwarfs because too few transits would be observed
Summary
The Kepler mission[1,2,3,4] began as a Principal Investigator (PI)-led NASA Discovery-class mission (#10) that was designed to explore the structure and diversity of planetary systems. Models of planetary system formation[10,11,12,13] predicted the formation of many planets smaller than that of the Earth and few larger than the Earth for values of the semi-major axes near 1 Astronomical Unit (AU) Contrary to such expectations, the early ground-based observations[5,14,15] showed the presence of giant planets in short period orbits. The Kepler team employed traditional systems engineering practices of suballocating mission requirements for a given science reference case (e.g., detecting an Earth-size planet around a solar-type star) and developed comprehensive error budgets for key individual design parameters such as combined differential photometric precision.[2,16] an additional analytic framework was needed to manage the full mission complexity given additional and overlapping factors influencing science return such as the number and characteristics of observable stars, the diversity of planet sizes and orbital periods, and mission duration. A summary with a discussion of strengths and weaknesses of the MF approach is presented Sec. 8
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