Great Circle vs Direct Tunnel

Introduction

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The shortest distance (path) between cities (A and B) on the surface of the earth is a great-circle distance. Instead, what if we drilled a tunnel directly between city A and city B?

Create an interactive program to:

  1. let the user select city A and city B from a list of cities
  2. convert the latitude and longitude values from degrees to radians
  3. calculate distances and angles
  4. display distances and angles
  5. loop

Great-Circle

Note: The great-circle route is the shortest course between two points on the surface of a sphere. This is why when you fly from Los Angles to London, You leave LA flying north east and fly over Greenland instead flying directly east.

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Great-circle distance (Wikipedia)

List of City Latitude/Longitude

Note: Add your own cities to the list.

CityLatitude/Longitude
DDD° MM′ SS.S″
Athens, Greece37°58'N, 23°43'E
Beijing, China39°55'N, 116°25'E
Royal Observatory
Greenwich, England
51.4769°N, 0.0005°E
London, England51°32'N, 0°5'W
Los Angeles, California34°3'N, 118°15'W
Moose Jaw, Saskatchewan, Canada50°7'W, 105°31'N
Moscow, Russia55°45'N, 37°36'E
New York City, New York40.7128°N, 74.0060°W
Nome, Alaska64°25'N, 165°30'W
Paris, France48°48'N, 2°20'E
Tokyo, Japan35°40'N, 139°45'E
San Francisco, California37°47'N, 122°26'W
Washington, D.C.38°53'N, 77°02'W
Wellington, New Zealand41°17'S, 174°47'E

Definition: The great-circle distance is the distance along a great circle. It is the shortest distance between two points on the surface of a sphere.

Code

Calculate Great-Circle Distance
Calculate Great-Circle Angle
Calculate Center of the Earth to the Center of the Tunnel Distance

For the following projects assume the Earth is a perfect sphere. It is not.

Project #0

What is its actual shape of the Earth?

Hint: The Earth is an oblate ...

Project #1

What is the great-circle distance on earth for:

To be consistent, use the values in the "Useful Information" table below.

Note: Project #1 does not require any fancy math. Just division.

Project #2

How much shorter would the tunnel be compared to the great-circle distance?

Project #3

What is the deepest distance between the tunnel and the surface of the earth?

Useful Information

  1. The distance from the center of the earth to point A and point B are the same distance. They are two side of an isosceles triangle.

    Definition: An isosceles triangle is a triangle that has two sides of equal length.

  2. 3.14159pi
    24875.11circumference of Earth in miles
    based on global average radius
    40030.14circumference of Earth in kilometers
    based on global average radius
    3959radius of Earth in miles
    global average (wikipedia)
    6,371radius of Earth in kilometers
    global average (wikipedia)
    5280feet per mile
    3.28084feet per meter
    1.60934kilometers per mile
    1000meters per kilometer
    360degrees in a circle
    60minutes per degree
    60seconds per minute

  3. Sine of acute anglethe length of the side opposite the angle divided by the length of the longest side (the hypotenuse)
    Cosine of acute angle the length of the side adjacent to the angle divided by the length of the longest side (the hypotenuse)

    Note: Acute angles measure less than 90 degrees. Right angles measure 90 degrees. Obtuse angles measure more than 90 degrees.