Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Radius of a planet

  1. Sep 25, 2012 #1
    A person stands on a cliff overlooking the sea. He is 100m above the sea level and he observes the horizon to be 5mrad below the local horizontal.

    How do you calculate the radius from this information without using a calculator? Trigonometry I am guessing, but I need a better hint.
  2. jcsd
  3. Sep 25, 2012 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    Always draw the picture.

    Place an origin O and draw a circle radius R about it. That's your planet.

    The observer is at point A, a distance R+h from O - draw the line OA.
    The point B, on the circle, is where the tangent to the circle also goes through point A.
    The angle between BA and the tangent to OA (through A) is ##\alpha##.

    In your case, h=100m and ##\alpha##=5mrad.
    This will give you two right-angle triangles to work your trig on.
    You may be able to make an approximation based on h<<R.
  4. Sep 25, 2012 #3
    I tried it with:

    AB^2 + R^2 = (R+100)^2

    AB = (R+100)sinA

    But i can't solve the equation without the calculator.
  5. Sep 25, 2012 #4


    User Avatar
    Science Advisor

    Why do you need to solve it without a calculator?
  6. Sep 25, 2012 #5

    Alas, I just remembered small angle approximation.

    cosA = 1-(A^2/2)

    cosA = R/R+100

    R ≈ 8000000

    I did not enjoy this problem.
  7. Sep 25, 2012 #6

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    hehehe well done.
    They get easier.

    @hallsofivy: I suspect that it's part of the instructions in the homework - however: does not mean that a calculator cannot be used to figure out how to do it without a calculator.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook