1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Mass of Planet

  1. Nov 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Io, a satellite of jupiter has an orbital period of 1.77 days and an orbital
    radius of 4.22 x 10^5 km. From this Data determine the mass of Jupiter

    2. Relevant equations
    Kepler's Third Law

    3. The attempt at a solution
    I keep getting turned around. I know the answer but I
    keep finding different ways to start
    I also used T^2 = Ka^3
    But that seems independ of Mass?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Nov 9, 2008 #2
    A generic equation for orbitting bodies that you may want to commit to memory or have handy for some quick calculations is:

    [tex]T=2\pi a\sqrt{a/GM}[/tex].
  4. Nov 9, 2008 #3
    That was nowhere to be found in my book. Thanks...
    Should I next find acceleration by taking 1.77 days
    and making it 152928s and then find the circumference
    to be 2.65 x 10^9 and then velocity is 17338 m/s?
    Is this the right direction to go.
  5. Nov 9, 2008 #4
    The a given in that equation is the radius. I remember it from long ago, but, if it's not found in your book, don't bother with it. We can derive it from scratch, can't we? ;)

    You want to find the mass of the planet, given by the equation [tex]\vec{F}=\vec{G}Mm/\vec{R}^2[/tex]. You know that this system follows uniform circular motion, too: [tex]\vec{a}=\vec{v}^2/\vec{r}[/tex]. And, that period is time, which can be related with displacement and velocity: [tex]\vec{x}/\vec{v}=T[/tex]. Do you agree?
  6. Nov 9, 2008 #5
    I agree
  7. Nov 9, 2008 #6
    Then you can solve for M. :) Let me know what you try.
  8. Nov 9, 2008 #7
    Except how can I use your first equation when I don't know the mass of Io?
  9. Nov 9, 2008 #8
    Because [tex]\vec{f}=m\vec{a}[/tex] so the small masses cancel. ;)
  10. Nov 9, 2008 #9
    So a = G(M/r^2)
  11. Nov 9, 2008 #10
    Yup, which is also equal to the quotient between the square of velocity and radius. Just relate the equations, you'll end up with M.
  12. Nov 9, 2008 #11
    So I get v^2 = G(M/r)
    I'm not sure how to get M =
  13. Nov 9, 2008 #12
  14. Nov 9, 2008 #13
    I'm just not seeing it sorry
  15. Nov 9, 2008 #14
    [tex]\frac{4\pi^2\vec{r}^2}{T^2}=\frac{\vec{G}M}{\vec{r}}\rightarrow M=\frac{4\pi^2\vec{r}^3}{\vec{G}}[/tex].
  16. Nov 10, 2008 #15
    Thanks alot for the help but using that equation I don't get the right answer for some reason.
  17. Nov 10, 2008 #16
    You forgot the T^2 in the formula.
    And never mind the vectors. G is not a vector and r^3 is the magnitude cubed and not the vector cubed.

    M=4Pi^2 r^3/(G T^2)

    I've got about 1.9 x 10^27 and it's very close to the accepted mass of Jupiter.
    The period should be in seconds, right?
  18. Nov 10, 2008 #17
    asleight's posts are so full of errors, you're better off ignoring them.
  19. Nov 10, 2008 #18
    I figured that out. Thanks again. You were a great help.
    Talk to you soon.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook