RURAL ECONOMIC DEVELOPMENT FOR COMMUNITY SELF-RELIANCE

Community/Rural/Urban Development,

Space-based tests of gravity with laser ranging

Existing capabilities in laser ranging, optical interferometry and metrology, in combination with precision frequency standards, atom-based quantum sensors, and drag-free technologies, are critical for the space-based tests of fundamental physics; as a result, of the recent progress in these disciplines, the entire area is poised for major advances. Thus, accurate ranging to the Moon and Mars will provide significant improvements in several gravity tests, namely the equivalence principle, geodetic precession, PPN parameters $\beta$ and $\gamma$, and possible variation of the gravitational constant $G$. Other tests will become possible with development of an optical architecture that would allow proceeding from meter to centimeter to millimeter range accuracies on interplanetary distances. Motivated by anticipated accuracy gains, we discuss the recent renaissance in lunar laser ranging and consider future relativistic gravity experiments with precision laser ranging over interplanetary distances.Comment: 14 pages, 2 figures, 1 table. To appear in the proceedings of the International Workshop "From Quantum to Cosmos: Fundamental Physics Research in Space", 21-24 May 2006, Warrenton, Virginia, USA http://physics.jpl.nasa.gov/quantum-to-cosmos

An Alternative Approach To High School Geometry

Introduction and Terminology The fundamental ideas of analytic geometry are usually attributed to the French mathematician and philosopher Descartes (1596-1650). The key to the expression of geometric facts in algebraic form lies in the representation of a point in the plane by means of a pair of real numbers called the coordinates of the point. This paper is devoted to some detailed proofs of fundamental theorems in High School Geometry based on an alternative approach. The analytic geometry approach seems to be a more powerful attack upon many of the problems of High School Geometry than the methods which we have thus far employed. Analytic geometry not only simplifies the proofs of many of the propositions with which we are familiar, but enables us to attack successfully problems which we could handle in elementary geometry only with great difficulty, or not at all. With the tools already developed- the formulas for distance, point of division (midpoint), and slope- will aid in solving many problems of High School Geometry. In analytic geometry, the methods of algebra are combined with those of Euclidean geometry in the solution of geometry problems. The properties of a geometric figure depend upon the relations of the parts and not upon the particular position which the figure is drawn. Therefore, the properties of any geometric figure are independent of the way in which the axes are chosen. In the pr~of of geometric properties of figures it will, in general, be possible to choose the axes in more than one way The axes will be chosen in the way which gives the simplest algebra. The writer would like to point out that analytic geometry is not a different geometry but is a different approach to geometry. This approach was used to prove theorems previously developed by the synthetic approach. In all such cases the analytic proof is not the only proof, but in many cases, it is a far simpler proof

Revolution From Within: Changing Military Perspectives in Peru

In October 1968 the world read the news of the latest version of a very old phenomenon-another revolution in Latin America. This time it was Peru; the democratically elected government of President Fernando Belaunde Terry had been overthrown by a junta com• posed of the chiefs of the armed forces. The leader of the coup, Gen. Juan Velasco Alvarado, described the new government as revolutionary in nature and proclaimed as its goal the radical transformation of Peru\u27s economy and social institutions into instruments for the benefit of all Peruvians