Technical Notes

This note has its genesis with a discussion among a few friends over coffee. Shortly after the vernal equinox one year, the question arose: what is the nature of the periodic change in daylight at some latitude on earth? Is it sinusoidal? Well, we knew it could not be a sine wave since above the arctic circle there are portions of the year during which there are twentyfour hours of either daylight or night. But, for most latitudes, is it reasonably estimated by a simple periodic function?

This paper is divided into three sections. The first section focuses on modeling the dynamics of a pandemic. The model embeds several parameters, which we estimate in order to explore the nature of the dynamics of a pandemic. We explore the timing of a generic shelter-in- place order to control growth of infection. In section 2 we use real data from Santa Clara County, CA to identify system parameters and validate the model. In section 3 we use the validated model for Santa Clara County to examine strategies for scaling back the shelter-in-place order, predicting the future of the pandemic.

This paper is excerpted from the preceding paper, but with most of the mathematics removed. It focuses on the conclusions of the study.

These notes began with my interest in exploring the orbital mechanics of the James Webb Telescope. My research, however, uncovered a number of interesting facts regarding the project including: the complexity of the project, the energy-saving positioning of the instrument, and the strange oscillations of the planned orbit.This note documents positioning the telescope near the L2 Lagrange Point; it develops the non-linear differential equations for the orbit. It remains unfinished.