The private company SpaceX regularly launches satellites into geostationary orbits. SpaceX posts videos of these flights with telemetry data displaying the time from launch, altitude, and rocket speed in real time. In this paper this telemetry information is used to determine the velocity boost of the rocket as it leaves its circular parking orbit…

The "domain-coloring algorithm" allows us to visualize complex-valued functions on the plane in a single image--an alternative to before-and-after mapping diagrams. It helps us see when a function is analytic and aids in understanding contour integrals. The culmination of this article is a visual discovery and subsequent proof of the…

Comfort whilst camping overnight during outdoor pursuits is based on pain free and warm sleeping arrangements and is highly dependent on the performance of the sleeping bag and sleeping mat. In adventurous and challenging situations, performance can contribute to safety and expedition success. From the manufacturer's point of view, thermal…

In classroom science laboratories, unlike a real science laboratory, the teacher can guide students away from potential dead ends and toward data that are most likely to result in accurate conclusions. Sometimes, though, allowing students to pursue dead ends and to collect "bad" data can provide especially rich learning opportunities.…

Light refracts as it travels from one medium to another. The angle of incidence "i" and the angle of refraction "r" are related by Snell's law, sin"i" ÷ sin"r"="k," where "k" is a constant. The diagram in Fig. 1 shows a geometric representation of the formula for light passing from…

A simple mathematical formulation of Mach's principle is given based on a century of investigation into inertia, and used to check the results of Newton's famous bucket experiment.

Robust and fast methods for chemical or multiphase equilibrium calculation are routinely needed by chemical-process engineers working on sizing or simulation aspects. Yet, while industrial applications essentially require calculation tools capable of discriminating between stable and nonstable states and converging to nontrivial solutions,…

Presented here is an adaptation of George Gamow's derivation of the centripetal acceleration formula as it applies to Earth's orbiting Moon. The derivation appears in Gamows short but engaging book "Gravity", first published in 1962, and is essentially a distillation of Newton's work. While "TPT" contributors have offered several insightful…

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary,…

Fleming's right-hand rule and the right-flat-hand rule are generally applied for determining the direction of flow of induced emf/current in straight conductors. The right-hand-fingers rule is applied for coils only. The right-hand-thumb rule can be applied for either straight conductors or coils. Different rules have to be applied for different…

A new method for obtaining Russell-Saunders terms of atomic configurations is reported. This new method is significantly different from, while at the same time complementary to, previously published methods for obtaining atomic terms. This novel procedure is elicited by the method used to determine the splitting of S, P, D terms in weak ligand…

What follows are several investigations involving string musical instruments developed for and used in a "Science of Sound & Light" course. The experiments make use of a guitar, orchestral string instruments and data collection and graphing software. They are designed to provide students with concrete examples of how mathematical formulae, when…

Many students meet dipole-dipole potential energy quite early on when they are taught electrostatics or magnetostatics and it is also a very popular formula, featured in encyclopedias. We show that by a simple rewriting of the formula it becomes apparent that, for example, by reorienting the two dipoles, their attraction can become exactly twice…

The generalized second-order partial derivatives of 1/r, where r is the radial distance in three dimensions (3D), are obtained using a result of the potential theory of classical analysis. Some non-spherical-regularization alternatives to the standard spherical-regularization expression for the derivatives are derived. The utility of a…

The estimate of the time since death and, thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner's cases, especially those that involve criminal or insurance investigations. It has been known almost from the beginning of time that bodies cool after the internal…