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Homework Help: Mass of Io

  1. Jan 30, 2010 #1
    Io, a satellite of Jupiter, has an orbital period of 1.43 days and an orbital radius of 4.35X10^5 km. From this data, determine the mass of Jupiter.

    So step one: I cried.
    then I tried to use the equation:
    T^2=4(pi)^2/(GXMj) X R^3
    thus
    (123552)^2= (39.478)/(6.672X10^-11)(Mj) X (4.34X10^5)^3

    35161.29=(39.478)/(6.672X10^-11)(Mj) X (8.17465X10^16)

    Mj=1.3756X10^24

    Apparently I was wrong...
    Anyone have any ideas what I did to mess this up?
     
  2. jcsd
  3. Jan 30, 2010 #2

    tiny-tim

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    Hi BoldKnight399! :smile:

    (please don't use X for "times" … either use * or nothing … oh and have a pi: π and try using the X2 tag just above the Reply box :wink:)
    I'm not sure what your fomula is :redface:, but anyway where did 35161.29 come from (did you take a square-root instead)?
     
  4. Jan 30, 2010 #3
    I just used the formula:
    T^2=(4(Pi)^2/G*M)*R^3

    and i have no idea what I did to get 35161.29 in addition, what do you mean about having pi=n?
     
  5. Jan 30, 2010 #4
    ok so I tried it then having the time correctly squared:
    (1.526X10^10)=(39.478/(6.673*10^-11)(M)) * (8.321*10^16)
    and i got that the Mass of Jupiter was 3.19*10^18

    that was wrong. I don't understand what I am doing wrong
     
  6. Jan 30, 2010 #5

    tiny-tim

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    (please use the X2 tag just above the Reply box)

    Try using m instead of km ! :wink:

    (oh, and it wasn't n, it was π :biggrin:)
     
  7. Jan 30, 2010 #6
    alright, so it became:
    (1.526X10^10)=(39.478/(6.673*10^-11)(M)) * (8.321*10^19)
    M=3.2259*10^21

    still wrong. I thought I had everything right.
     
  8. Jan 30, 2010 #7

    tiny-tim

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    erm :redface:

    cubed? :smile:
     
  9. Jan 30, 2010 #8
    wow...I am not having a good physics day I guess. Thank you so much. I got:
    3.16*10^27 and that was right.
     
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