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11-1 Lines that Intersect Circles

8. The International Space Station orbits Earth at an altitude of 240 miles. What is the distance from the space station to Earth's horizon to the nearest mile?

  • Geometry -

    radius of earth: 6378
    radius of orbit: 6618

    draw a right triangle with legs 6378 and d, and hypotenuse 6618

    6378^2 + d^2 = 6618^2
    d^2 = 3119040
    d = 1766 mi

  • Geometry -

    Sorry Steve, you made a major error with your units... the radius of the Earth is around 6378 km not 6378 miles.

    You are trying to find the distance from the Space Station to the horizon, which would be the point of tangency. The tangent line from the Space Station will form a right angle with the center of the Earth. The radius of the Earth is 4000 miles, and the distance from the center of the earth to the Space Station is 4240 miles from the center of the Earth (radius + altitude).

    Use Pythagorean Theorem:
    radius of Earth squared + distance to horizon squared = distance from center of earth to Space Station squared.
    4000^2 + x^2 = 4240^2
    x^2 = 1977600
    x = 1406.27

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