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The value of g above and below the earth

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  1. Mar 6, 2016 #1
    1. The problem statement, all variables and given/known data

    The value of g at a point P inside the earth and at another point Q outside the earth is g/2. Maximum possible distance in terms of radius of earth between P and Q is? (g being the acceleration due to gravity on the surface).

    2. Relevant equations
    gh = (1+h/r)-2g
    gd = (1-d/r)g

    3. The attempt at a solution
    I don't understand what maximum distance is. The value of g reduces whether we go above or below the earths surface and there is only one point above and below that correspond to g/2 and so there is only one distance between those two points. How does maximum distance come into this?
    Just using the formulas I get:
    d= R/2
    h = R(√2-1) or -R(√2+1) // what does that negative sign actually mean in the second one?
    Distance between the two points =
    -(2√2+1)R/2 or (2√2-1)R/2 // again a negative sign.
    And I suppose maximum means I should choose the first and the answer is right. But I just don't get what the answer means. How can there be more than one distance between P and Q? What do those negative signs mean?
    Please point out where my understanding is flawed.
     
  2. jcsd
  3. Mar 7, 2016 #2

    RUber

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    Homework Helper

    The positive R can be thought of as toward the North pole, and the -R can be though of as toward the South pole.
    Maximum distance would not be where both points were in the +R position, right?
     
  4. Mar 7, 2016 #3

    ehild

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    Gold Member

    P can be anywhere on the green sphere.

    upload_2016-3-7_7-25-42.png
     
  5. Mar 7, 2016 #4
    ohhh.That never struck me at all.
    Thank you ehild and RUber.
     
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