A space camera circles the Earth at a height of h miles above the surface. Suppose that d distance, IN MILES, on the surface of the Earth can be seen from the camera.

(a) Find an equation that relates the central angle theta to the height h.

(b) Find an equation that relates the observable distance d and theta.

  1. 👍
  2. 👎
  3. 👁
  1. Draw a circle with the camera a distance h above it. Draw lines tangent from the camera location (P) to the two sides of the Earth (with radius R). Also draw lines from the points of tangency to the center of the Earth. You should have two congruent right triangles, each with a hypotenuse h + R. Let theta be the angle subtended by observed portion of the Earth as seen from the center of the Earth. I don't know if that is what they call the "central angle" or not. It will be bisected by the line from the camera to the center of the Earth

    (a) cos (theta/2) = R/(R +h)

    (b) d = theta * R
    where theta is in radians

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Science

    1.)Why is Earth’s temperature just right for life? (1 point) A.)Earth’s core is hot enough to heat Earth’s surface. B.)Earth’s magnetic field creates suitable temperatures on Earth’s surface. C.)Earth’s crust is warmed

  2. Science

    Can someone please please help me? I don't have a text book, i have a online book and it isn't working. Can someone please be nice and help me? Science isn't my subject! 1. Why is Earth’s temperature just right for life? (1

  3. 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.

  4. calculus

    the weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. if a person weighs 180 pounds on the surface of the earth and the radius of the

  1. physics

    radius R of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface.) You may use the following constants: The universal gravitational constant G is

  2. physics

    If the average speed of an orbiting space shuttle is 19600 mi/h, determine the time required for it to circle the Earth. Make sure you consider the fact that the shuttle is orbiting about 200 mi above the Earth's surface, and

  3. Geometry One Question

    Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 151 ft from camera 2, which was 122 ft from camera 3. Cameras 1 and 3 were 139 ft apart. Which camera had to cover the greatest angle?

  4. trig

    A space shuttle 200 miles above the earth is orbiting the. Earth once every 6 hours. how far does the shuttle travel in one hour? Note the radius of earth about 4000 miles.

  1. Calculus

    When estimating distances from a table of velocity data, it is not necessary that the time intervals are equally spaced. After a space ship is launched, the following velocity data is obtained. Use these data to estimate the

  2. Geometry

    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?

  3. physic

    A satellite used in a cellular telephone network has a mass of 2010kg and is in a circular orbit at a height of 770km above the surface of the earthTake the gravitational constant to be G = 6.67×10−11N⋅m2/kg2 , the mass of

  4. math 15

    find the minimum height above the surface of the earth so that the pilot at point a can see an object on the horizon at c 125 miles away. assume the diameter of the earth to be 8000 miles.

You can view more similar questions or ask a new question.