Physics

It is a common practice to fix a vertical gnomon and study the moving shadow cast by it. This shows our local solar time and gives us a hint regarding the season in which we perform the observation. The moving shadow can also tell us our latitude with high precision. In this paper we propose to exchange the roles and while keeping the shadows fixed on the ground we will move the gnomon. This lets us understand in a simple way the relevance of the tropical lines of latitude and the behavior of shadows in different locations. We then put these ideas into practice using sticks and threads during a solstice on two sites located on opposite sides of the Tropic of Capricorn.

Radiation pressure afforded by natural broadband sunlight upon a transmissive diffractive sail is theoretically and numerically investigated. A grating period of one micrometer is found to convert 83% of the solar black body spectrum into sailcraft momentum. Non-optimized orbit-raising trajectories for diffractive and reflective sails are compared. Potential advantages of diffractive sails are also described.

Motivated by MacKenzie's observation of a negative force couple near to impact, this paper explores a model for how the golf club moves near to impact. It assumes the golf club is moving as the distal arm of a double pendulum. At impact the club head is moving straight down the target line, at its maximum speed, on a path with a specified radius of curvature. From this model the forces and torques required to move the club near to impact are calculated. The negative couple near to impact is a robust feature of this model, balancing the torque associated with the force that drives the center of mass of the golf club. The negative couple allows the golfer to maintain a larger radius of curvature of the path of the club head as it moves through impact. Because the negative couple can also serve to reduce the rotational speed of the club, the presence of a negative couple at impact in the golf swing manifests a trade between distance and direction.

Despite a previous description of his state as a stable fixed point, just past midnight this morning Mr. Boddy was murdered again. In fact, over 70 years Mr. Boddy has been reported murdered 10 6 times, while there exist no documented attempts at intervention. Using variational data assimilation, we train a model of Mr. Boddy's dynamics on the time series of observed murders, to forecast future murders. The parameters to be estimated include instrument, location, and murderer. We find that a successful estimation requires three additional elements. First, to minimize the effects of selection bias, generous ranges are placed on parameter searches, permitting values such as the Cliff, the Poisoned Apple, and the Wife. Second, motive, which was not considered relevant to previous murders, is added as a parameter. Third, Mr. Boddy's little-known asthmatic condition is considered as an alternative cause of death. Following this morning's event, the next local murder is forecast for 17:19:03 EDT this afternoon, with a standard deviation of seven hours, at The Kitchen at 4330 Katonah Avenue, Bronx, NY, 10470, with either the Lead Pipe or the Lead Bust of Washington Irving. The motive is: Case of Mistaken Identity, and there was no convergence upon a murderer. Testing of the procedure's predictive power will involve catching the D train to 205th Street and a few transfers over to Katonah Avenue, and sitting around waiting with our eyes peeled. We discuss the problem of identifying a global solution - that is, the best reason for murder on a landscape riddled with pretty-decent reasons. We also discuss the procedure's assumption of Gaussian-distributed errors, which will under-predict rare events. This under-representation of highly improbable events may be offset by the fact that the training data, after all, consists of multiple murders of a single person.

Various paradoxes about the relativity theory have been developed since the birth of this theory. Each paradox somewhat shows people's query about the relativity theory, and solving of each paradox demonstrates the correctness of relativity theory once again. In this paper, four paradoxes about the special theory of relativity are brought forward: displacement paradox, electromagnetic transformation paradox, Doppler paradox and magnetic force paradox. We hope some researchers can reasonably explain these paradoxes, and then knowledge of the relativity theory will become more abundant.

A century after observing the deflection of light emitted by distant stars during the solar eclipse of 1919, it is interesting to know the concepts emerged from the experiment and the theoretical and observational consequences for modern cosmology and astrophysics. In addition to confirming Einstein's gravitational theory, its greatest legacy was the construction of a new research area to cosmos science dubbed gravitational lensing. The formation and magnification of multiple images (mirages) by the gravitational field of a compact or extended lens are among the most striking phenomena of nature. This article presents a pedagogical view of the first genuine gravitational lens effect, the double quasar QSO 0957 + 561. We also describe the formation of rings, giant arcs, arclets and multiple Supernova images. It is also surprising that the Hubble constant and the amount of dark matter in the Universe can be measured by the same technique. Finally, the lensing of gravitational waves, a possible but still not yet detected effect, is also briefly discussed.

It is customary to employ a semi-spherical scale model to describe the apparent path of the Sun across the sky, whether it be its diurnal motion or its variation throughout the year. A flat surface and three bent semi-rigid wires (representing the three solar arcs during solstices and equinoxes) will do the job. On the other hand, since very early times, there have been famous armillary spheres built and employed by the most outstanding astronomers for the description of the celestial movements. In those instruments, many of them now considered true works of art, Earth lies in the center of the cosmos and the observer looks at the whole "from the outside." Of course, both devices, the scale model of the sky and the armillary sphere, serve to represent the movement of the Sun, and in this paper we propose to show their equivalence by a simple construction. Knowing the basics underlying the operation of the armillary sphere will give us confidence to use it as a teaching resource in school.

One reason that the planet Neptune will be remembered for, is to do with the fact that it was the first planet whose existence was postulated before being observed. This was based on analysing deviations in Uranus' orbit. The present study gives a brief account of the history behind the discovery of Neptune, looking at the same, through the conflicting lenses of France and Britain. With this context established, the study then investigates deviations in Uranus' orbit (experimentally found to range from 10,100 km to 21,276,000 km), under a host of different conditions and orientations of the perturbing body (Neptune/Jupiter). This was accomplished using Universe Sandbox 2, which is a physics-based simulation software, presented on the gaming platform, Steam. The paper then examines what these deviations correspond to, as viewed from Earth, finding that the deviation angle ranges between 0.04 arc-seconds and 3.22 arc-seconds. The paper in this way, demonstrates how using games like Universe Sandbox 2, can aid in approaching problems that would be considered difficult to visualize using a purely mathematical approach.

A new lease on life was given to ESA's International Gamma-ray Astrophysics Laboratory, because of its unique capability to identify electromagnetic counterparts to sources of gravitational waves and ultra-high energy neutrinos.

The shadow is a separated feature in the satellite images specially high resolution images. It may be looked as a problem when it causes a loss in the ground ray response to the shaded area, and may be, from other view, considered as an indication to the height of the bodies or buildings, when it hidden due to top view of the satellite image usually. The location of the object on the earth affects its shadow length, direction and darkness. The ostensible sun path in the sky also affects the shadow length and direction, it is depending on the change of the rotation axis of planet about its center during the year. And it is clear that the shadow is changing with the sun transmission in the day times. The sun location needs complex equations, because there are several angles describing its location with taking into consideration the location of the shaded body on the earth spatially the latitude, and the shadow direction and length depend on the sun location so it need more equations. Some engineering purposes, and some engineers and designer can not process these complex astronomy equations every time they need to calculate the shadow effect on the urban region or garden for examples, or other architectural purposes, it is unpractical process to estimate the shadow direction and length for civil from these equation. So, we derived in this study a high accurate empirical Gaussian equation to find shadow length percent in the limits of the study area depends on single parameter which is the number of day during the year, and calculating the percent of shadow, so we can calculate the shadow length percent accurately in any day number by the suggested equation after knowing the real building height.