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Acceleration due to gravity?

  1. Oct 21, 2015 #1

    faiziqb12

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    using Newtons equation for gravitational force
    one can fling that the acceleration due to gravity, g' above the surface of earth as

    g' = g (d/(d+h))

    but I find that there is a different equation for the same as

    g' = g ( 1- 2h/r )

    I know the first formula is right
    but I can't doubt the first formula.....
    however the unit of h and r in the second formula is km as compared to the m of the first formula
    please help me derive the second formula
     
  2. jcsd
  3. Oct 21, 2015 #2
    The first formula is wrong, and the second formula is an approximation to the corrected version of the first formula for small values of h/r.

    Chet
     
  4. Oct 21, 2015 #3

    faiziqb12

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    so as you have said the first formula is wrong
    then please show how its wrong

    and yes please show the derivation method of the second equation

    thanks
     
  5. Oct 21, 2015 #4
    Gravity varies inversely with distance (a) to the first power or (b) to the second power?
     
  6. Oct 21, 2015 #5

    faiziqb12

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    obviously to the 2nd power
     
  7. Oct 21, 2015 #6

    faiziqb12

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    I'm sorry but I missed the square in my second formula

    the correct one is
    g' = g (d / ( d+h )) ^ 2
     
  8. Oct 21, 2015 #7
    Good. Now let x = h/d. Please re-express your equation in terms of x.
     
  9. Oct 21, 2015 #8

    faiziqb12

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    the new formula is then
    g' = g ( 1 / (1+x) ) ^ 2
     
  10. Oct 21, 2015 #9

    faiziqb12

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    what am I supposed to do further
    please suggest
     
  11. Oct 21, 2015 #10
    Good, this is correct even with all those parentheses. But, here's a piece of advice: if you don't simplify your mathematical expressions when you are at your present stage, you are going to encounter real problems (manipulating the mathematics) when you get to more complicated analyses. So, I'm going to simplify it for you:
    $$g'=\frac{g}{(1+x)^2}$$
    Have you gotten far enough in calculus to be able to expand this in a Taylor series about x = 0?

    Chet
     
  12. Oct 21, 2015 #11

    faiziqb12

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    I'm sorry
    but I can't. I'm just studying in class 9th
    isn't there an alternative method
     
  13. Oct 21, 2015 #12
    Yes. From what you learned about geometric progressions, what is the infinite sum 1-x+x2-x3.... equal to?
     
  14. Oct 21, 2015 #13

    jtbell

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    Or look up the "binomial approximation." It's a very useful thing to know for situations like this.
     
  15. Oct 21, 2015 #14

    faiziqb12

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    thanks chestmiller
    looks like I can do it now

    it would 've your goodness if you show me the whole method involving this progression
     
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