
The Ringed Planets
When I was a kid, Saturn was the ringed planet. But today, we know that all of the outer planets have rings. The James Webb Space Telescope has now imaged each of them in infrared revealing their distinctive structures, including Jupiter‘s very faint ring (located by the arrow and dashed curve). The planet images below…

Simplest Chaos
The motion of one of the simplest dynamical systems, a torqued, damped, nonlinear pendulum, can be infinitely complicated. Consider a simple pendulum of length and mass rigidly connected to an axle of radius wrapped by a rope that hangs down one side with a mass climbing up and down it, as in the attached animation.…

Vampire Ein Stein
Just a couple of months after announcing the remarkable discovery of a single shape that forces a nonperiodic tiling of the plane, Smith, Myers, Kaplan, and GoodmanStrauss have announced an improved aperiodic monotile or ein stein. (Ein stein is “one stone” in German.) The hat and turtle shapes tile the plane only nonperiodically, but with their…

The Temperature of the Vacuum
Quantum field theory predicts that the temperature of empty space should depend on the observer’s motion, increasing proportionally with acceleration. Here I attempt an accessible introduction to this striking effect, related to Hawking radiation and discovered independently by Fulling, Davies, and Unruh, assuming only sophomorelevel physics (including hyperbolic functions) with some assistance from Mathematica. Hyperbolic…

A Century of Compton Scattering
One hundred years ago today the Physical Review published research on light scattering electrons that would earn its author, Wooster graduate Arthur Compton, a Physics Nobel Prize. By relativistically conserving spacetime momentum, as in the diagram below, and treating light as particles now called photons, Compton discovered that deflecting an electron through an angle stretches…

We Are Going
After half a century confined to lowEarth orbit, and as soon as late next year, humans will once again leave Earth and voyage to Moon. The reality of this exciting adventure crystallized earlier this month when NASA announced the diverse and inspiring Artemis II crew: Clockwise from left in the photo below are Christina Koch,…

Behold, an Ein Stein!
This academic year has been thrilling: first nuclear fusion breakeven, now an ein stein! Last week, a preprint at arxiv.org by David Smith et al. announced an “ein stein”, or one stone, a shape that forces a non periodic tiling of the plane, ending a halfcentury quest by many researchers, including me. A retiree and…

Generalizing Coulomb’s Law
The forces between two electric charges in arbitrary motion are complicated by velocity, acceleration, and timedelay effects. The forces need not even lie along the line joining the two charges! Suppose a source charge is at position with velocity and acceleration , and a test charge is at position with velocity and acceleration . Let…

Triple EVA
Since the mid 1960s, all space walks or extravehicular activities (EVAs) have involved just one or two astronauts — except once. In May 1992, on the STS49 mission, the crew of the space shuttle Endeavour was attempting to rescue a stranded communications satellite, Intelsat 603. After repeated twoperson EVAs failed to capture the satellite, NASA and the…

5Color Theorem
On 1852 October 23, Francis Guthrie noticed that he needed only 4 colors to color the counties of England so no two bordering counties shared the same color. This works for any map, but only in 1976, and with the aid of a computer, did Kenneth Appel and Wolfgang Haken finally prove the 4color theorem. Here I outline…
Thanks, Mark! I enjoy reading your posts as well.