The James Webb Space Telescope (JWST) is a now space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly 1.5 million fm from the earth, in a position with the Earth between the telescope and the Sun. The primary mirror of the JWST will consist of 18 hexagonally shaped segments that when fitted together will be 6.5 m in diameter (over 2.5 times the diameter of the Hubble). With a larger mirror, the JWST will be able to collect more light to “see” deeper into space. The primary mirror when pieced together will function as a parabolic mirror with a focal length of 131.4 m. Suppose that a coordinate system is chosen with ( 0 , 0 ) at the center of a cross section of the primary mirror. Write an equation of the parabolic cross section of the mirror for − 3.25 ≤ x ≤ 3.25 . Assume that x and y are measured in meters.
The James Webb Space Telescope (JWST) is a now space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly 1.5 million fm from the earth, in a position with the Earth between the telescope and the Sun. The primary mirror of the JWST will consist of 18 hexagonally shaped segments that when fitted together will be 6.5 m in diameter (over 2.5 times the diameter of the Hubble). With a larger mirror, the JWST will be able to collect more light to “see” deeper into space. The primary mirror when pieced together will function as a parabolic mirror with a focal length of 131.4 m. Suppose that a coordinate system is chosen with ( 0 , 0 ) at the center of a cross section of the primary mirror. Write an equation of the parabolic cross section of the mirror for − 3.25 ≤ x ≤ 3.25 . Assume that x and y are measured in meters.
Solution Summary: The author calculates the parabolic cross section of the mirror with focal length of 131.4m.
The James Webb Space Telescope (JWST) is a now space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly 1.5 million fm from the earth, in a position with the Earth between the telescope and the Sun. The primary mirror of the JWST will consist of 18 hexagonally shaped segments that when fitted together will be 6.5 m in diameter (over 2.5 times the diameter of the Hubble). With a larger mirror, the JWST will be able to collect more light to “see” deeper into space.
The primary mirror when pieced together will function as a parabolic mirror with a focal length of 131.4 m. Suppose that a coordinate system is chosen with
(
0
,
0
)
at the center of a cross section of the primary mirror. Write an equation of the parabolic cross section of the mirror for
−
3.25
≤
x
≤
3.25
. Assume that x and y are measured in meters.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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Solve the linear system of equations attached using Gaussian elimination (not Gauss-Jordan) and back subsitution.
Remember that:
A matrix is in row echelon form if
Any row that consists only of zeros is at the bottom of the matrix.
The first non-zero entry in each other row is 1. This entry is called aleading 1.
The leading 1 of each row, after the first row, lies to the right of the leading 1 of the previous row.
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