Challenge 3 – X Marks the Spot
One interesting feature of the August 21, 2017 total solar eclipse is that its path of totality across the continental US crosses over the paths of earlier and later eclipses.
Each of the crossing points can be determined by fitting a linear equation to pairs of points along each track, and then solving the two equations to find the common, intersection, point. The table below gives the coordinates for the pair of points along the track of the indicated eclipse in columns 2 and 3, and the pair of points along the 2017 eclipse track in the vicinity of the crossing point. Note, west longitudes are represented by negative values.
Date | Points on Track (x,y) | Points on 2017 track (x,y) | ||
March 27, 1503 | -120.3909, 44.5979 | -120.0146, 44.6565 | -120.5228, 44.665 | -119.9789, 44.6298 |
July 20, 1506 | -84.4358, 35.4652 | -84.3177, 35.4960 | -84.4311, 35.502 | -84.3577, 35.4673 |
February 3, 1562 | -120.363, 44.5793 | -120.142, 44.6907 | -120.315, 44.6525 | -120.0273, 44.6335 |
July 21, 1618 | -116.299, 44.3373 | -116.069, 44.2655 | -116.288, 44.3133 | -116.082, 44.2931 |
October 23, 1623 | -82.3516, 34.4652 | -82.2205, 34.4889 | -82.3533, 34.4969 | - 82.2517, 34.4465 |
April 10, 1679 | -105.056, 42.4475 | -104.882, 42.5335 | -105,032, 42.5534 | -104.854, 42.5149 |
May 22, 1724 | -106.646, 42.863 | -106.486, 42.9746 | -106.982, 42.9498 | -106.378, 42.8331 |
June 24, 1778 | -82.0044, 34.1958 | -81.8732, 34.2543 | -81.9336, 34.2883 | -81.7688, 34.2054 |
June 16, 1806 | -94.1216, 39.3396 | -93.8339, 39.4166 | -94.0507, 39.4681 | -93.9546, 39.4345 |
November 30, 1834 | -104.432, 42.5221 | -104.314, 42.4365 | -104.478, 42.4328 | -104.241, 42.3801 |
July 29, 1878 | -109.885, 43.5263 | -109.734, 43.3992 | -109.861, 43.4666 | -109.761, 43.4376 |
January 1, 1889 | -111.763, 43.7302 | -111.56, 43.8244 | -111.8, 43.7647 | -111.671, 43.744 |
May 28, 1900 | -81.7427, 34.1474 | -81.6363, 34.1974 | -81.7556, 34.1986 | -81.6626, 34.1523 |
June 8, 1918 | -116.657, 44.3977 | -116.465, 44.3285 | -116.685, 44.3534 | -116.474, 44.333 |
March 7, 1970 | -80.1134, 33.3385 | -80.087, 33.3617 | -80.1454, 33.3792 | -80.0596, 33.3354 |
April 8, 2024 | -89.3028, 37.6203 | -89.2653, 37.6434 | -89.31, 37.6617 | -89.2417, 37.6335 |
May 11, 2078 | -81.6753, 34.1319 | -81.5688, 34.1711 | -81.6763, 34.1591 | -81.5716, 34.1065 |
Problem 1: Use the Two-Point Formula to create a linear equation in Standard Form for each track
y2 – y1
y-y1 = -------------- (x – x1)
x2 – x1
using the pair of points (x1,y1) and (x2,y2) along each track.
Problem 2: From the two linear equations in the form y = mx + b, solve them for the common intersection point where x is the longitude of the point and y is the latitude of the point.