Use a Python notebook to solve this astronomy problem:

You have been granted a total of 60 hours of telescope time at the Keck Observatory to use their high-resolution spectrograph to obtain precision radial velocities of stars with transits from some ground-based survey. Your observations will occur in 2-hour intervals starting either at 19:00 or ending at 06:00. The 30 observing blocks you get will be randomly distributed over a four-month interval, and it is even possible that you can get both the start and end of a given night. Each observation takes 15 minutes, including time to point the telescope. How many observations can you get over the whole run, assuming that theres a 25% chance that the weather is bad? Your observations have an accuracy of 10 m s1, and the radial velocity amplitude can be anywhere from 5 to 40 m s1. Expected periods range from 5 to 15 days. Generate artificial radial velocity curves to teach yourself how many data points you need for each star in order to find the period to an accuracy of 5%, meaning that the width of the main peak in the power spectrum has a full width at half maximum that is 5% of the period. Does this number depend on the period or amplitude you expect for example, do you need more points when the period is long or if the amplitude is low? Come up with a strategy to sample these stars, assuming that the periods are equally likely over the expected range and the amplitudes can be any value, so that you will get at least the minimum number of observations you need for a good radial velocity. How big a sample of stars can you select for this project? You will have to be clever with the various ways to generate random numbers in numpy.