Results 1 to 3 of 3

Math Help - Finding the radius of the earth

  1. #1
    Member Chokfull's Avatar
    Joined
    May 2009
    From
    Neverland
    Posts
    108
    Thanks
    1

    Finding the radius of the earth

    OK---i have a problem.

    you lie on a beach and watch a sunset. then you stand and watch it set again--you are higher and can see that supposedly.

    my book says that you then use these values:
    h=1.70 m (your height)

    t=11.1 s (the time between sunsets)

    then using the picture and the Pythagorean theorem, with d as the distance between your eyes and the tangent to the earth from the second sunset, you get
    d^2 + r^2 = (r + h)^2 = r^2 + 2rh + h^2
    or
    d^2 = 2rh + h^2

    but you remove h^2 because your height is insignificant compared to the radius of the earth and the term 2rh

    then you use the number of hours in a day, the rotation of the earth in a day, and t to find \theta:

    \frac \theta {360^o}

    which solves to 0.04625^o

    then you can get d = r\tan \theta from the picture and, substituting for d in the first equation, r^2\tan^2\theta = 2rh

    which when you plug in the values (like \theta = 0.04625) makes 5.22 * 10^6 m

    The problem is in the fact that we replaced the value for the \theta from the angle between the sunsets with the \theta from the angle from the center of the earth. i cant figure out how that works.


    Here is the picture:
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    see:

    Attachment 12590

    Angle \text{uvA}=\theta so \text{vuA} is 90-\theta and so \text{uOB}=\theta

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Chokfull's Avatar
    Joined
    May 2009
    From
    Neverland
    Posts
    108
    Thanks
    1
    Quote Originally Posted by CaptainBlack View Post
    see:

    Attachment 12590

    Angle \text{uvA}=\theta so \text{vuA} is 90-\theta and so \text{uOB}=\theta

    CB
    wow ok thanks. i dont know why the book didnt explain that.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] finding the radius problem
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: May 5th 2011, 01:11 PM
  2. Radius of Earth
    Posted in the Pre-Calculus Forum
    Replies: 17
    Last Post: March 1st 2010, 05:16 PM
  3. ...finding the radius
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 20th 2009, 06:12 AM
  4. Finding the radius, solving, and finding theta?
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: June 13th 2009, 03:37 PM
  5. Finding a convergence radius
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 27th 2009, 07:34 AM

Search Tags


/mathhelpforum @mathhelpforum