Table of Contents
What is spherical coordinates in physics?
Spherical coordinates determine the position of a point in three-dimensional space based on the distance ρ from the origin and two angles θ and ϕ. If one is familiar with polar coordinates, then the angle θ isn’t too difficult to understand as it is essentially the same as the angle θ from polar coordinates.
Why do we use spherical coordinates?
Spherical coordinates are useful in analyzing systems that have some degree of symmetry about a point, such as the volume of the space inside a domed stadium or wind speeds in a planet’s atmosphere. A sphere that has Cartesian equation x2+y2+z2=c2 has the simple equation ρ=c in spherical coordinates.
Who invented spherical coordinates?
Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-17th century, though the actual term polar coordinates has been attributed to Gregorio Fontana in the 18th century.
What is a spherical path called?
A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere. A great circle is the largest circle that can be drawn on any given sphere.
Are spherical and polar coordinates the same?
Spherical Coordinates Theta is the same as the angle used in polar coordinates. Phi is the angle between the z-axis and the line connecting the origin and the point.
Why are lines of longitude called great circles?
Each line of longitude, or meridian, is the same length and represents half of a great circle. This is because each meridian has a corresponding line on the opposite side of the Earth. When combined, they cut the globe into equal halves, representing a great circle.
Why equator is called great circle?
A great circle has the same boundary and same centre point as its sphere. Great circles are seen on all meridians on Earth. All the lines of longitude meet at the poles, intersecting the Earth in half. Thus a great circle always splits the Earth into two halves, so that the Equator is a great circle.
Are spherical coordinates the same as polar coordinates?