Volume 4 Issue 2
Authors: D. Delikaraoglou; G. Manoussakis
Abstract: This work aimed to study isocurvature surfaces of Earth’s normal gravity field and their relation to partial derivatives of a plumb line curvature. An isocurvature surface of a gravity field is a surface along which the value of the plumb line curvature is constant. The normal gravity field is a symmetrical gravity field; therefore, isocurvature surfaces are surfaces of revolution. To study an isocurvature surface, special assumptions are made to form a vector equation, which will hold only for a small coordinate patch of the isocurvature surface. The gradient of a normal plumb line curvature is vertical to the isocurvature surface pointing to the direction along which the curvature of the plumb line decreases or increases the most. In order to show the significance of isocurvature surfaces, it was shown that it is possible to determine the value of the surface derivative of a plumb line’s curvature without differentiating the original complicated function of a plumb line curvature.
Keywords: Plumb Lines; Curvature; Normal Gravity Field; Plumbline Curvature; Isocurvature Surface