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Error Propogation - E of Gravity due to r

  1. Sep 16, 2007 #1
    1. The problem statement, all variables and given/known data
    The acceleration due to gravity is given by Newton's universal law of gravitation as:

    Derive an algebraic expression for the error in gravity (Eg) due to the uncertainty in r. You may assume that the errors in G & M = 0; (EG & EM = 0)

    Let E=error in for internet purposes
    2. Relevant equations


    3. The attempt at a solution


    This is calculus, i can't see a classical algebraic way of doing this..

    any help plz?
  2. jcsd
  3. Sep 16, 2007 #2
    Suppose f is a function of r. Then:

    [tex]f + \delta f \approx f(r) + \delta r f^{\prime}(r)[/tex]

    so [tex]\delta f \approx \delta r f^{\prime}(r)[/tex]

    Can you see why this is the case?
  4. Sep 16, 2007 #3
    in the second half of that you are taking the derivative of the function, as far as i am convinced this course is an algebra based course and i'm trying to figure out an algebraic response to this question, without taking the derivative at any point.... would it be
  5. Sep 16, 2007 #4
    Okay, then:

    [tex]g + \delta g = \frac{GM}{(r + \delta r)^2}[/tex]

    Knowing that [tex]g = \frac{GM}{r^2}[/tex]

    Apply binomial expansions as necessary.
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