An Adaptive Scheduling Tool to Optimize Measurements to Reach a Scientific Objective: Methodology and Application to Measurements of Stellar Orbits in the Galactic Center

In various fields of physics and astronomy, access to experimental facilities or to telescopes is becoming more and more competitive and limited. It therefore becomes important to optimize the type of measurements and their scheduling to reach a given scientific objective and to increase the chances of success of a scientific project. In this communication, extending the work of Ford and of Loredo et al., we present an efficient adaptive scheduling tool aimed at prioritizing measurements in order to reach a scientific goal. The algorithm, based on the Fisher matrix, can be applied to a wide class of measurements. We present this algorithm in detail and discuss some practicalities such as systematic errors or measurement losses due to contingencies (such as weather, experimental failure, ...). As an illustration, we consider measurements of the short-period star S0-2 in our Galactic Center (GC). We show that the radial velocity measurements at the two turning points of the radial velocity curve are more powerful for detecting the gravitational redshift than measurements at the maximal relativistic signal. We also explicitly present the methodology that was used to plan measurements in order to detect the relativistic redshift considering systematics and possible measurement losses. For the future, we identify the astrometric turning points to be highly sensitive to the relativistic advance of the periastron. Finally, we also identify measurements particularly sensitive to the distance to our GC: the radial velocities around periastron and the astrometric measurements just before closest approach and at the maximal R.A. astrometric turning point.