Math Application

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 d and h.

(b) If d is to be 3500 miles, how high must the camera orbit above Earth?

(c) If the camera orbits at a height of 400 miles, what distance d on the surface can be seen?

  1. 👍
  2. 👎
  3. 👁
  1. surely you could have looked up the radius of the earth for us, which is needed to do the question.

    1. 👍
    2. 👎
  2. 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 d and h.
    (b) If d is to be 3500 miles, how high must the camera orbit above Earth?
    (c) If the camera orbits at a height of 400 miles, what distance d on the surface can be seen?

    Draw a circle with center O. Locate a point C outside the circle.
    Draw lines from point C to the tangency points on both sides of the circle.
    The arc length between these two tangency points is the distance "d" visible to the camera.
    With the earth's radius of 3963 miles. the central angle between the two tangency points is defined by µ = (2)arccos(3963/h + 3963))º.
    Therefore, the visible distance "d" = Rµ, where µ is in radians.

    This should enable you to find the other two answers you seek.

    1. 👍
    2. 👎
  3. Here is the raidus of Earth as given in the book:

    3960 miles.

    1. 👍
    2. 👎
  4. Here is the raidus of Earth as given in the book:

    3960 miles.

    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. 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.

  3. 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

  4. Physics

    What is the Earth's gravitational force on you when you are standing on the Earth and when you are riding in the Space Shuttle 380 km above the Earth's surface? Answer as a fraction of the surface gravity of Earth. (The Earth's

  1. 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?

  2. Physical Science

    Many people mistakenly believe that the astronauts who orbit Earth are "above gravity." Earth's mass is 6×1024kg, and its radius is 6.38×106m (6380 km). Use the inverse-square law to find a height above Earth's surface at that

  3. AP physics

    suppose that the surface (radius=r) of the space station is rotating at 35.8 m/s. what must be the value of r for the astronauts to weigh one-half their earth weight?

  4. 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

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