Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe escape velocity for a limited material distribution in a gravity field
سرعة الإفلات في حقل جاذبية توزيعة مادية محدودة
819
0 4
0
(
0
)
Created by
Shamra Editor
Ask ChatGPT about the research
ينظر هذا البحث في سرعة الإفلات في حقل جاذبيّة توزيعة ماديّة محدودة , و ما يستلزم ذلك من النّظر في قانون نيوتن في الجاذبيّة, و في متّجه حقل الجاذبيّة لتوزيعة ماديّة محدودة في نقطة معيّنة, و في دالّة الكمون و الطّاقة الكامنة, حيث أثبتنا أنّ الطّاقة الكامنة في اللانهاية معدومة , و استلزم البحث أيضا دراسة تابع هاملتون, و أوجدنا سرعة إفلات نقطة ماديّة من سطح كرة إنْ كانت حركة النّقطة الماديّة شاقوليّة, أو كانت حركة النّقطة الماديّة أفقيّة ,أو كانت حركة النّقطة مائلة, و أوجدنا سرعة إفلات نقطة ماديّة من قرص في الحالتين الشاقوليّة و المائلة, و انتهى البحث إلى إيجاد سرعة إفلات نقطة ماديّة من حلقة في الحالتين الشاقوليّة و المائلة, و تبين في النهاية أنّ سرعة الافلات من الحلقة تتطابق مع تلك التي نحصل عليها في حالة الكرة.
This paper discusses the escape velocity for a limited material distribution in a gravity field. This requeres examining the Newton’s law of gravitation , the gravitational field vector of a limited material distribution in a specific point and potential function togother with the potential energy. In paper, have proved that potential energy vanished in infinity . This requires also examining Hamilton’s function then we have found the escape velocity of a material point from a sphere’s surface ,when the motion of the material point is vertical , horizontal or oblique . We found the escape velocity for a material point from a disk in the vertical and oblique cases. In paper, we also find out the escape velocity from a ring in both vertical and oblique cases . It is appeared that the escape velocity from the ring identifies with that we get from the sphere case.
References used
M.L.Boas,Mathematical methods in Physical Sciences,3rd edition, Wiley ,2006
Michael Fowler, University of Virginia, Physics 152 Notes, May, 2007
K. Abdullah, Propriétés du système séculaire, , thèse de doctorat de l'Observatoire de Paris, Paris 2001
rate research
Read More
In this search, we study the gravitational field engendered by a
material segment around itself. In the beginning, we discuss the
concept of the gravitational field generated by arbitrary curve. It turns out
that this field depends on the concept
of linear mass, and is directly relate to the distance of the position, to which we calculate the field from the tangents of curve, and not from the curve itself.
Material segment is a special case of material curves, and characterized by the confusability of all its tangents, that allow simplify the calculations, and find a simplified formula of the field. We end our research by comparing the field of material segment, with a field of appropriate circular arc.
Contrary to what it is expected, it appear in the end that the field of material segment is inversely proportional to the distance from that segment, and not to the square of distance
In this paper, we study the gravitational field generated by a
straight material segment around itself. At first we discuss the
calculation of the field, outside the support of the segment, and on
this support, then we discuss the self field. We a
lso study values of
this field in special points.
We also study the field generated by a set of segments,, where we
interest in the value of this field in the common special points, and show
the cases where this field is finite, or infinite. We provide a set of
properties concerning the components of this field.
We also discussed the concept of falling on the material segment, where
we define the particular type of motion which we call successive motion,
and we show its conditions. This motion really present a falling on the
material segment.
Singularities in general are considered to be one of the important issues in
algebraic geometry and applied mathematics, among them the ADE or simple
singularities which drew attention since they have appeared separately in
various areas of scient
ific applications. The name comes from three graphs
characterized by letters A, D and E denoting types of Lie groups. Arnold
stated them in a direct manner. Many people gave studies about the subject
like Roczen.M who presented the canonical resolution in dimension 3 and
Char ≠ 2. giving an equivalent non-singular variety is what meant by
resolution, Canonical resolution adds a description of the exceptional loci.
Within the last thirty years, the recent development in GPS, satellite tracking techniques and processing strategies has revolutionized development of Earth gravity field models. In addition, the increase of gravity data coverage led to an increase i
n the resolution and accuracy of these models. This in turn led to a noticeable improvement in determination of geoid surfaces which are essential in transformation of the geodetic height to the orthometric height. This study utilizes the normal gravity field for estimating offsets the Syrian leveling network from the EGM2008 geoid defined by its geopotential value W0=62636856.0 m2s-2. This approach uses the average of the gravity potential values at the GPS/levelling points in some areas in Syria. The gravity potential value in the study regionis estimated using the Earth gravity field model EGM2008. The residuals between the actual gravity potentials and the values at the Syrian height reference surface are estimated in the range between [-4.51 m2s-2 ~ 10.62m2s-2] and a mean value of -6.72±0.70 m2s-2 with 95% confidence level. This corresponds to [-46.0 cm ~ 108.4 cm] and a mean value of -63.7±7.1 cm which means that the Syrian height datum is located underneath the global geoid.
In the paper, we study gravitational field generated by a special type of homogeneous material curves that are denoted circumscribed curves.
Characteristic state of these curves is the linking of each one of them to a circle, and the circumscribing
of him around the circle, or an arc of
him, according to a precise meaning.
The circumscribed curve consists of arcs of a circle, and straight segments, their right supports are tangents to the circle. In special case, where this curve is a polygon, the sides are tangents to a circle. In this case, we call the polygon, circumscribed polygon.
The study shows that the center of the circle, around it, a homogeneous material curve circumscribed, is an equilibrium center.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
