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Rearranging of formulas

  1. May 27, 2009 #1
    1. The problem statement, all variables and given/known data

    (i)
    Combine Equations A and B to give a single equation for v and substitute this in place of v in Equation C.
    (ii)
    Rearrange your answer to part (i) to make r the subject of the equation.


    2. Relevant equations

    Equation A
    z = Δλ/λ0

    Equation B
    v = zc

    For a planet such as the one orbiting Gliese, the speed v is linked to the mass of the star M and the planet’s orbital radius, by Equation C:

    Equation C
    v2 = GM/r

    G is Newton’s universal constant of gravitation.

    3. The attempt at a solution

    (i) v = (Δλ/λ0)c -> (Δλ/λ0)c2 = GM/r
    (ii) this is where I'm not sure, is the above correct? I always get roots confused.
     
    Last edited: May 27, 2009
  2. jcsd
  3. May 27, 2009 #2

    Ouabache

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    Are you sure about your result for [itex]v^2[/itex] in equ. (i)?
    It looks like you only squared part of your expression for [itex]v[/itex].
     
  4. May 27, 2009 #3
    ((Δλ/λ0)c)2 = GM/r
     
  5. May 27, 2009 #4

    Ouabache

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    That looks good to me, now they ask you to rearrange your expression
    to make r the subject of the equation. Shall we interpret this to mean solving for r ?
     
    Last edited: May 27, 2009
  6. May 27, 2009 #5
    ((Δλ/λ0)c)2 = GM/r

    So do I multiply the r to both sides now or remove the root?

    (Δλ/λ0)c = √(GM/r) or ((Δλ/λ0)c)2/r = GM
     
    Last edited: May 27, 2009
  7. May 27, 2009 #6

    Ouabache

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    what are you solving for? that will help you decide which direction to take.
     
  8. May 27, 2009 #7
    I'm trying to make r the subject.

    ((Δλ/λ0)c)2/r = GM

    r = ((Δλ/λ0)c)2xGM
     
  9. May 27, 2009 #8

    Ouabache

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    Your algebra doesn't look quite right.
    To this expression: ((Δλ/λ0)c)2 = GM/r

    are you sure you multiplied both sides by r ??
     
  10. May 27, 2009 #9
    ((Δλ/λ0)c)2 = GM/r

    ((Δλ/λ0)c)2 x r = GM

    totally not sure
     
  11. May 27, 2009 #10

    Ouabache

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    Looks good, you're almost there now.
     
  12. May 27, 2009 #11
    so then:

    r = GM/((Δλ/λ0)c)2
     
  13. May 27, 2009 #12

    Ouabache

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    well done :approve:
     
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