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.