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Homework Help: Meaning of gradient and intercept

  1. May 10, 2013 #1
    1. The problem statement, all variables and given/known data

    The velocity of a body travelling in a circular orbit around another body situated at the centre of
    the circle, is given by
    v = √(GM/r)
    where G is the Universal Gravitational constant, M is the mass
    of the central body and r is the radius of the orbit. By taking natural logs (ln) of both sides
    rearrange the equation in the form of a straight line equation, with r as the independent variable
    and identify the meaning of the gradient and the meaning of the intercept

    2. Relevant equations

    v = √(GM/r)

    3. The attempt at a solution

    ln v = (1/2)ln(GM) - (1/2)lnr

    y = ln v
    x = lnr
    c = (1/2)ln(GM)
    m = -1/2

    I solved the first part but was unsure as to how to answer this part of the question 'identify the meaning of the gradient and the meaning of the intercept'
  2. jcsd
  3. May 10, 2013 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    For the line, y = mx + b, m is the gradient and of course, b is the intercept.

    Rewrite the original equation with rational exponents rather than radicals.
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