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Kepler's law question

  1. Nov 19, 2013 #1
    1. The problem statement, all variables and given/known

    A star at the edge of the Andromeda galaxy appears to be orbiting the center of that galaxy at the speed of about 200km/s. The star is about g*10^9AU from the center of the galaxy. Calculate a rough estimate of the mass of the Andromeda galaxy. Earth orbital radius is 1.40*10^8

    2. Relevant equations

    Fg=gm1m2/r^2

    3. The attempt at a solution

    1 a.u. = 1.40*10^8 km = 1.40*10^11 m

    For the mass of the entire galaxy, M, you will have to assume a spherical distribution of mass, with the star in question at the outside, at distance R. ( what does that mean by assume spherical)

    In that case, the centripetal acceleration of the star is
    V^2/R = G M/R2

    Solve for M.

    M = R V^2/G

    I got this solution from a web page however I'm trying to understand how it works.

    Isn't fg=Gm1m2/r^2

    And then that will be equal to centripetal force
    Why in the above solution did they omit the one of the mass??
     
  2. jcsd
  3. Nov 19, 2013 #2

    rude man

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    That formula derives from equating centripetal and gravitational forces on m:
    GmM/R^2 = mv^2/R.
    m is divided out.

    Don't write V for velocity. Use v.
    V is for Volts.
     
  4. Nov 19, 2013 #3
    So I did M=2000m/s^2* 7.45*10^20m/ 6.67*10^-11

    And I still didn't get the right ans which is 4*10^41kg

    Note: the 7.45*10^20 was obtained by taking the 5*10^9 AU multiplying it by 1.49*10^8km and then by 1000 to convert it to m
     
  5. Nov 19, 2013 #4

    rude man

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    200 km/s is not 2000 m/s!

    I don't know what "g x 10^9 AU" is. What is the "g" in that expression for R?
     
  6. Nov 19, 2013 #5
    I know my mistake now. I converted it wrong . The g is supposed to be a 5
     
  7. Oct 18, 2016 #6
    This person wrote the question wrong. There is no g, it's "The star is about 5 x 10^9 AU from the centre..." The answer is 4.47 x 10^41 kg :)

    - convert the velocity to m/s
    -use the formula m=(v^2*r)/G
    -multiply the star's radius with the Earth's orbital radius then convert to m

    then plug everything in and you're good to goooo!
     
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