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Homework Help: Astronomy Que

  1. Mar 16, 2008 #1
    Astronomy Que!!!!!

    1. The problem statement, all variables and given/known data
    Three stars lie on a line (1,2,3). The distance from star 1 to star 3 is labelled as D. If star 1 is four times that of star 3, and seven times of star 2, what is the distance between star 1 and 2 if the net force of star 2 is zero?

    2. Relevant equations

    3. The attempt at a solution
    Since the net force for star 2 is zero, I know that the force between star 1 and 2 is the same as the force between start 2 and 3


    I tried to sub in values to find the force between star 1 and 3


    but i'm not sure where to go from here...

    Thank you
  2. jcsd
  3. Mar 16, 2008 #2

    So then, the distance between star 1 and star 2 is x, and the distance between star 2 and star 3 is D-x. Can you go on from here?
  4. Mar 16, 2008 #3
    errr..I think so.
    Here's what I've 'tried' so far


    Cross multiply:
    G's cancel, so do m2


    if 4m3=7m2
    then m3=(7/4)m2


    now to find for x?



    not sure if it's the right way, or if i'm just messing around with variables, or if the force between 1 and 3 has any use (yikes!)
    Anyone willing to verify?

    but yeeeah...times like these when I wonder why I took physics as an option when I'm planning to do arts *sighs*
    thanks for your help!
    Last edited by a moderator: Mar 16, 2008
  5. Mar 16, 2008 #4
    1. Where did that G/4 come from?
    2. [tex]F \propto \frac{1}{r^2}[/tex]
  6. Mar 16, 2008 #5
    whoops, the G's cancel out too

    I got the 1/4 from dividing G7m2 by G(7/4)m2

    to get x=D/5
  7. Mar 16, 2008 #6
    Does [tex]\frac{7m_2}{m_3}=\frac{1}{4}[/tex] when [tex]m_3=\frac{7m_2}{4}[/tex]?

    You also haven't addressed my 2nd point.
  8. Mar 16, 2008 #7
    no, it is not 1/4...but 4 instead

    as for your second point: the inverse proportionality of distance to Force...
    the larger the distance, the smaller the force....
  9. Mar 16, 2008 #8
    But it's not distance, it's distance squared.
  10. Mar 16, 2008 #9
    so what you're saying is that I have to square my x and D-x values right?
  11. Mar 16, 2008 #10
    Well, if the formula is given by [tex]F=\frac{Gm_1m_2}{r^2}[/tex], should you?
  12. Mar 16, 2008 #11
    merde. i feel like I am going around in circles...

    ok, so if i squared it

    square rooting it, i get

    cross multiplying and expanding...
  13. Mar 16, 2008 #12
    Looks good to me.
  14. Mar 16, 2008 #13
    yay! thanks for your help and patience Snazzy!
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