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Geodesy Fundamentals
Published in Julio Sanchez, Maria P. Canton, William Perrizo, Space Image Processing, 2018
Julio Sanchez, Maria P. Canton
The adoption of the ellipsoid as a model for the earth’s shape brings about several associated complications. In the first place, the shape of the ellipsoid requires at least two parameters. In geodesic calculations, these are usually the semi-major axis and the flattening, as mentioned in Section 6.3. Another consideration relates to the shortest distance between two points. We have seen that on the sphere this shortest distance is the arc of a great circle. Furthermore, the great circles from point A to point Β on the surface of a sphere coincide with the great circle from point Β to point A, since the normals to points A and Β intersect at a common point, the center of the sphere. On the other hand, the flattening of the ellipsoid determines that the normals of two points at different latitudes do not intersect.
Mapping Applications
Published in Pearson Frederick, Map Projections:, 2018
We consider two points on the spherical model of the Earth. The shortest distance between these points on the surface of the sphere is along the great circle. However, as one moves along the great circle, the angle formed by the tangent to the great circle and the tangent to the local meridian is constantly changing. This angle is the instantaneous bearing. The loxodrome is a line which has the characteristic that the angle between the tangent to the loxodrome and the tangent to the local meridian is constant. Thus, the bearing is constant. Since in navigation it is relatively easy to maintain a constant bearing, the loxodrome is the curve of choice. However, a loxodrome is of greater length than the great circle distance, unless along the equator or a meridian.
Introduction to Dynamics: Implications on the Design of Precision Machines
Published in Richard Leach, Stuart T. Smith, Basics of Precision Engineering, 2017
Patrick Baird, Stuart T. Smith
The analysis of dynamics makes use of scalars, vectors and coordinate systems, which were introduced in Chapter 3. For objects in motion, it is important to initially distinguish between distance and speed (both scalar quantities), and displacement and velocity (both vector quantities which take the direction of the path into account). Distance is the overall length of a path travelled by an object in any direction; displacement is the change in position in a particular direction. Speed is the distance travelled in unit time; velocity is the displacement per unit time. Vectors are typically displayed in bold type: for example if ν is speed, v is velocity; however, for simplicity when describing derivatives of displacements, the parameter x˙ may be used without bold type. In other cases, where convenient, normal type will be used rather than bold type to represent the magnitude of a vector, in which the actual direction is not contextually important or defined along a coordinate axis.
A data analytic-based logistics modelling framework for E-commerce enterprise
Published in Enterprise Information Systems, 2023
Abhishek Verma, Yong-Hong Kuo, M Manoj Kumar, Saurabh Pratap, Velvet Chen
The merged dataset contained the latitudes and longitudes of sellers and customers along with the values of customer ID, seller ID, order ID, freight value, price and weight. We considered the great-circle distance to conduct the analysis, calculated using geo-locations and haversine formula (Equation 5). The haversine formula calculates the shortest distance between two points on a sphere when their latitude and longitude are provided. The calculated distance is known as the great-circle distance between the points on the map. However, considering the total of the US, driving distances through road are approximately 18% more than the straight-line distances (Shih 2015). The distance between customer and seller of an order ranged from 0.12 miles to an upper limit value of 5434.99 miles.
Journey to the moon and to the sun on the Koch Curve
Published in International Journal of Mathematical Education in Science and Technology, 2021
Let's go to the Moon first. The average distance from the Earth to the Moon is about 400 thousand km, or about 400 million meters. Using the formula (3) we calculate that to reach the Moon, you need to do about n = 69 iterative steps. It seems not much. It is enough to do only 69 simple iterations and we will be on the moon. Let's check if it is physically feasible. With this number of iterations, the Koch Curve will have line segments. That's a lot. Each of these line segments will have a length of approximately meter. The diameter of the hydrogen atom is about meter. Thus, the length of a single line segment in such a Koch Curve would be as much as 23 orders smaller than the diameter of the hydrogen atom. The smallest length in nature, the so-called Planck length, is about meter. This means that the length of a single line segment of our Koch Curve would be only 2 ranks longer than the Planck length. This makes traveling to the Moon practically impossible in this way.
Performance analysis on improved efficiency in a hybrid solar still and solar heater
Published in International Journal of Ambient Energy, 2020
S. Mohamed Iqbal, K. Karthik, Jee Joe Michael
The sun is a ‘more or less average’ star with a mass equal to nearly one-third of a million earths. Spectral measurements have confirmed the presence of nearly all the known elements in the sun. As is typical of many stars, about 94% of the atoms and nuclei in the outer parts are hydrogen; about 5.9% are helium, and a mixture of all the other elements makes up the remaining one-tenth of 1%. A gaseous globe with a radius of 7 × 105 km has a mass about 2 × 1030 kg. This is greater than the earth's mass by a factor of about 330,000. The total rate of energy output from the sun 3.8 × 1033 ergs/s (3.8 × 1023 kW). At a mean distance of 1.496×108 km from the sun, the earth intercepts about 1 part in 2 billion of this energy.