Geometry

posted by .

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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics: Astronauts and space

    When out in space in International Space Station (ISS), Astronauts experience weightlessness. The ISS’s orbit is 354 km (that is 3.54 x 105 m) above the surface of the earth.The distance separating the center of the earth from the …
  2. Physics

    I have a question about the International Space Station-Its been orbiting earth at 350km-If the radius of the earth is 6,370 km, what is the period of orbit for the Space Station?
  3. Physics-Please help

    I have a question about the International Space Station-Its been orbiting earth at 350km-If the radius of the earth is 6,370 km, what is the period of orbit for the Space Station?
  4. physics

    The International Space Station, launched in November 1998, makes 15.65 revolutions around the earth each day in a circular orbit. Apply Newton's second law to the space station and find its height (in kilometers) above the earth's …
  5. Physics

    When out in space in International Space Station (ISS), Astronauts experience weightlessness. The ISS’s orbit is 354 km (that is 3.54 x 105 m) above the surface of the earth. The distance separating the center of the earth from the …
  6. math

    the international space station orbits 350 km above earth's surface. earth's radius is about 6370 km.use the pythagorean theorem to find the distance from the space station to earth's horizon.
  7. math

    The space station is going 17500 mph as it orbits the earth. How long will it take to orbit 1 time if the earths diameter is 7926 miles and the space station orbits at 240 miles above the earth.
  8. physics

    A 2130-kg space station orbits Earth at an altitude of 455 km. Find the magnitude of the force with which the space station attracts Earth. The mass and mean radius of Earth are 5.98 × 1024 kg and 6370 km, respectively
  9. Physics, Please Help

    A 2130-kg space station orbits Earth at an altitude of 455 km. Find the magnitude of the force with which the space station attracts Earth. The mass and mean radius of Earth are 5.98 × 1024 kg and 6370 km, respectively.
  10. geometry

    The radius of the earth is approximately 6371 km.If the international space station (ISS) is orbiting 353 km above the earth, find the distance from the ISS to the horizon(x)

More Similar Questions