In the study of astronomy and astrophysics, it is essential to observe the distant stars and other exotic celestial objects – and we do so using telescopes. But a telescope can cover only a small area of the sky at a time, i.e. it has a limited field of view as compared to the vastness of the sky it is trying to cover. And a problem astronomers face is trying to find an efficient method of finding a moving object in the sky with their telescopes in a limited amount of time. This is the essence of the scheduling problem.

The scheduling problem deals with finding algorithms to maximize the probability of finding an astrophysical object being searched for in a section of the sky using one or more telescopes. In a certain section of the sky (a “patch”), there is an associated probability distribution for finding the object, and it adds up to 100%. Typical patches sizes are of the order of hundreds of square degrees, while 1-2 mm telescope have a FOV (field of view) in the order of a tenth of a square degree. Therefore, to take images, or to “scan” the entire patch could require thousands of exposures (an exposure is the process of taking an image with a telescope). Each exposure takes some time to gather enough light to form an image, and therefore to scan the entire patch could take an extremely long time.

However, the patch itself is not visible for very long due to a number of reasons. Firstly, images can only be taken at nighttime, since the Sun outshines the distant light of any objects we may want to observe during the day. The second problem, and the one that we shall be concerning ourselves with, is the fact that the patch seems to move through the sky as the Earth is rotating. Therefore, the patch, which we shall assume is rectangular in shape, sinks below the horizon and out of view slowly. Therefore, the scheduling problem is to find an optimal schedule for scanning regions of the patch using the telescope(s) so that the probability covered is maximized.

For this, we must first “grid” the entire patch, i.e. make it a matrix of smaller tiles, which represent the area covered in one image, which is the same as the area of the FOV of the telescope. Once this 2-D matrix is ready, we can assign a probability to each tile and generate algorithms which create an observation schedule that maximizes the total scanned probability.

For the purposes of this simulation, three sample patches have been provided below, with the option of running the SeAr or GrAr on them. This simulation will show you the difference in the schedules generated for the two algorithms.

**Choose on of the five options, and a random grid will be generated. **