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:

- let the user select city A and city B from a list of cities
- convert the latitude and longitude values from degrees to radians
- calculate distances and angles
- display distances and angles
- loop

*
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.
*

Great-circle distance (Wikipedia)

*Note: Add your own cities to the list.*

City | Latitude/Longitude DDD° MM′ SS.S″ |
---|---|

Athens, Greece | 37°58'N, 23°43'E |

Beijing, China | 39°55'N, 116°25'E |

Royal Observatory Greenwich, England | 51.4769°N, 0.0005°E |

London, England | 51°32'N, 0°5'W |

Los Angeles, California | 34°3'N, 118°15'W |

Moose Jaw, Saskatchewan, Canada | 50°7'W, 105°31'N |

Moscow, Russia | 55°45'N, 37°36'E |

New York City, New York | 40.7128°N, 74.0060°W |

Nome, Alaska | 64°25'N, 165°30'W |

Paris, France | 48°48'N, 2°20'E |

Tokyo, Japan | 35°40'N, 139°45'E |

San Francisco, California | 37°47'N, 122°26'W |

Washington, D.C. | 38°53'N, 77°02'W |

Wellington, New Zealand | 41°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.*

Calculate Great-Circle Distance

Calculate Great-Circle Angle

Calculate Center of the Earth to the Center of the Tunnel Distance

What is its actual shape of the Earth?

*Hint: The Earth is an oblate ...*

What is the great-circle distance on earth for:

- one degree
- one minute
- one second

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

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

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

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

- 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.* -
3.14159 pi 24875.11 circumference of Earth in miles

based on global average radius40030.14 circumference of Earth in kilometers

based on global average radius3959 radius of Earth in miles

global average (wikipedia)6,371 radius of Earth in kilometers

global average (wikipedia)5280 feet per mile 3.28084 feet per meter 1.60934 kilometers per mile 1000 meters per kilometer 360 degrees in a circle 60 minutes per degree 60 seconds per minute -
Sine of acute angle the 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.*