A weak spring is connected at one end to a rotor turning at constant angular velocity. The spring extends to a stretched length as determined by the spring mass, rest length, spring constant, rotor radius and rotor angular velocity. When released from the rotor, the inner end of the spring pulls away as expected, causing a wave to travel down the spring as it collapses. During this time interval, the outer end of the spring continues to move along its original circular path in uniform circular motion, as if the spring were still connected to the rotor. This is analogous to the effect of a hanging Slinky released from rest whose bottom end remains at a fixed position above the ground until a wave from the top of the Slinky reaches the bottom of the Slinky. Values from a numerical model and measurements from video analysis show that upon release the inner end travels along a circle of similar radius as the outer end. The effect appears as a series of alternating semi-circles. In addition, the simulation and data agree that (1) the spring extension and drag angle increase with the angular velocity of the rotor; (2) the droop angle decreases with angular velocity of the rotor; (3) the collapse time and bend angle of the collapsing spring are independent of the angular velocity.
A bridge rectifier is a diamond-shaped configuration of diodes that serves to convert alternating current (AC) into direct current (DC). In our world of AC outlets and DC electronics, they are ubiquitous. Of course, most bridge rectifiers are built with regular diodes, not the light-emitting variety, because LEDs have a number of disadvantages. For educational purposes, however, an LED-based rectifier is ideal because it allows students to literally see the rectifier operating. Here I'll discuss the practical aspects of building a full AC adapter incorporating an LED-based rectifier and ideas on how to use it in class.
In July 2007, we observed a stellar occultation by Pluto from three sites in New Zealand and Australia. From these occultation observations, we find that Pluto's atmospheric pressure is still at the increased level measured in 2002 and 2006 with a pressure at a radius of 1275 km of 2.09 +/- 0.09 mu bar. One of the sites, Mt. John Observatory, was similar to 70 km from the shadow center and we recorded the first central-flash occultation by Pluto. We carried out a dual-wavelength observation from this site with two different cameras using filtered high-time resolution observations in the visible from the one-meter telescope at Mt. John Observatory. From our central-flash observations, we find the elliptical shape that best matches the data corresponds to a nearly prolate atmosphere with an ellipticity of 0.09. The flux observed in the central-flash data can be fit equally well with either a haze layer or a thermal gradient in the altitudes probed by the occultation. However, the star light contributing to the central-flash occultation for the haze layer model would pass through a radius of 1130 km from Pluto's center. Given our current best estimate of Pluto's surface radius is greater than 1151 km (Tholen, D.J., Buie, M.W. [1997]. Bulk properties of Pluto and Charon. In: Stern, S.A., Tholen, D.J. (Eds.), Pluto and Charon. The University of Arizona Press), we prefer the thermal gradient solution or a combination of haze and thermal gradient to explain the occultation light curves. (C) 2014 Elsevier Inc. All rights reserved.
The PHOT (Portable High-Speed Occultation Telescope) systems were developed for the specific purpose of observing stellar occultations by solar system objects. Stellar occultations have unique observing constraints: they may only be observable from certain parts of the globe; they often require a rapid observing cadence; and they require accurate time-stamp information for each exposure. The PHOT systems consist of 14 inch telescopes, CCD cameras, camera mounting plates, GPS-based time standards, and data acquisition computers. The PHOT systems are similar in principle to the POETS systems (Portable Occultation, Eclipse, and Transit Systems), with the main differences being (1) different CCD cameras with slightly different specifications and (2) a standalone custom-built time standard used by PHOT, whereas POETS uses a commercial time standard that is controlled from a computer. Since 2005, PHOT systems have been deployed on over two-dozen occasions to sites in the US, Mexico, Chile, Namibia, South Africa, France, Austria, Switzerland, Australia, and New Zealand, mounted on portable 14 inch telescopes or on larger stationary telescopes. Occultation light curves acquired from the 3.9 m AAT (Anglo-Australian Telescope) have produced photometric signal-to-noise ratios (S/N) of 333 per scale height for a stellar occultation by Pluto. In this article we describe the seven PHOT subsystems in detail (telescopes, cameras, timers, and data stations) and present S/N estimates for actual and predicted occultations as functions of star brightness, telescope aperture, and frame rate.
Pluto occultations are historically rare events, having been observed in 1988, 2002, 2006, and, as Pluto moves into the crowded Galactic plane, on several occasions in 2007. Here we present six results from our observations of the 2006 June 12 event from several sites in Australia and New Zealand. First, we show that Pluto's 2006 bulk atmospheric column abundance, as in 2002, is over twice the value measured in 1988, implying that nitrogen frost on Pluto's surface is 1.2–1.7 K warmer in 2006 than 1988 despite a 9% drop in incident solar flux. We measure a half-light shadow radius of 1216 ± 8.6 km in 2006, nominally larger than published values of 1213 ± 16 km measured in 2002. Given the current error bars, this latest half-light radius cannot discriminate between continued atmospheric growth or shrinkage, but it rules out several of the volatile transport scenarios modeled by Hansen & Paige. Second, we resolve spikes in the occultation light curve that are similar to those seen in 2002 and model the vertical temperature fluctuations that cause them. Third, we show that Pluto's upper atmosphere appears to hold a steady temperature of ∼100 K, as predicted from the methane thermostat model, even at latitudes where the methane thermostat is inoperative. This implies that energy transport rates are faster than radiational cooling rates. Fourth, this occultation has provided the first significant detection of a non-isothermal temperature gradient in Pluto's upper atmosphere also reported by Elliot et al., possibly the result of CO gas in Pluto's upper atmosphere. Fifth, we show that a haze-only explanation for Pluto's light curve is extremely unlikely; a thermal inversion is necessary to explain the observed light curve. And sixth, we derive an upper limit for the haze optical depth of 0.0023 in the zenith direction at average CCD wavelengths.