The solar eclipse and its relation with higree months

The solar eclipse occurs at short time before the crescent birth moment when the moon near any one of moon orbit nodes It is important to determine the synchronic month which is used to find Higree date. The 'rules' of eclipses are: Y= ± 0.997 of Earth radius , the solar eclipse is central and 0.997 < |Y| < 1.026 the umbra cone touch the surface of the Earth, where Y is the least distance from the axis of the moon's shadow to the center of the Earth in units of the equatorial radius of the Earth. A new model have been designed, depend on the horizontal coordinates of the sun, moon, the distances Earth-Moon (rm), Earth-sun (rs) and |Y| to determine the date and times of total solar eclipse and the geographical coordinates of spot shadow as well as the shadow diameter and the variations with time. The results are compared with Almanac and others programs are gets a good agreements and the results show the area of eclipse shadow inversely proportional with rm /rs .The Higree month which must be begin after the solar eclipse and the relation were discussed hear.

On static equilibrium of a hemispheroid

In the course of a coffee-table conversation with my friends regarding the nature of static equilibrium of different solid objects the situation involving a uniform hemisphere came up. Intuition (and perhaps experience) tells that a uniform hemisphere as shown in Figure 1 resting on a flat surface will be at stable equilibrium, and so will an oblate hemispheroid as shown in Figure 2. Things get complicated when we move to a prolate hemispheroid like the one shown in Figure 3, for the nature of its equilibrium is less obvious. The intuition does come to mind though that if the prolate hemispheroid is made indefinitely taller, keeping its equatorial radius fixed, then the equilibrium should eventually become unstable. Intrigued, we decided to probe into the matter quantitatively.

Uranus after Voyager 2 and the Origin of the Solar System

The discoveries made by the Voyager 2 spacecraft at Uranus in January 1986 are discussed in the light of the modern Laplacian theory for the formation of the solar system. Various accounts of this theory, which has as its basis the concept of supersonic convective turbulence, have been presented at previous meetings of the ASA (Prentice 1977, 1979, 1981a). The most important confirmation by Voyager was the discovery of 2 new satellite groups near orbital radii 2½ RUand 3½ RU(RU= Uranus’ equatorial radius = 26, 200 km), as first predicted in 1977. The discovery that the densities of the Uranian satellites are consistent with these bodies having condensed in a single compositional class, consisting of anhydrous rock, NH3ice and CH4.6H2O clathrate hydrate in normal solar proportions, confirms the hypothesis that the chemistry of all planetary/regular satellite systems are accounted for by a single choice of the turbulence parameter, namely β = 0.107 ±0.001. The implication of the Voyager data for the origin of comets is also discussed.

Magnetohydrodynamic flow in a container due to the discharge of an electric current from a finite size electrode

In this paper we consider the Stokes flow field generated in a hemispheroidal container by the axisymmetric discharge of an electric current. The current is discharged from a circular electrode which is at the centre of the equatorial plane of the spheroid. The electrode is assumed to be at a constant potential. The equatorial radius of the spheroid is a and that of the electrode is k , the annulus k ≼ r ≼ a being a free surface. For a given container depth it is shown that as k increases the intensity of the flow field decreases and when the depth of the container is comparable to k the intensity of the flow field is only a small fraction of that associated with the point electrode case. As one might expect, the vorticity has a singularity at the rim of the electrode. When the width of the annulus forming the free surface is small, relative to the radius of the electrode, an eddy is formed about the rim of the electrode. As the annulus increases the eddy decreases in size until it eventually disappears.