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Homework Help: Venus and gravity

  1. Jun 12, 2005 #1
    1. The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth.

    Compute the acceleration due to gravity on the surface of Venus from these data.
    What is the weight of a 5.00-kg rock on the surface of Venus?

    2. Venus orbits the sun in a nearly circular orbit. The radius of the orbit of Venus is 1.08x10^11 m, the period of Venus is 224.7 days(1.94 x 10^7 s)

    Calculate the mass of the sun.

    -------------------------------------------------------------------------
    ** I know F_grav = m * g and F_grav = GM_Earth*m/d^2

    M_Earth = 5.98 x 10^24 kg and R_Earth = 6.38 x 10^6 m

    I conclude: M_Venus = 4.88x10^24 kg and R_Venus = 6.06 x 10^6 m

    Please help. I'm stuck
     
  2. jcsd
  3. Jun 12, 2005 #2

    HallsofIvy

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    It's not necessary and probably not a good idea to calculate the mass and radius of Venus! Instead use ratios.

    Basic gravity formula: [tex]F= \frac{GmM}{r^2}[/tex] where G is the "universal" gravitational constant, M the mass of the planet, m the mass of the falling object, and r is the radius of the planet. Since mg= F, [tex]g= \frac{GM}{r^2}[/tex].
    In particular, for the earth [tex]g_e= 9.81 m/s^2= \frac{GM_e}{r_e^2}[/tex] and for Venus [tex]g_v= \frac{GM_v}{r_v^2}[/tex].

    Divide the second equation by the first and the "G" terms cancel:
    [tex]\frac{g_v}{9.81}= \frac{M_v}{M_e}\left(\frac{r_e}{r_v}\right)^2[/tex]. You are given those ratios.
     
    Last edited by a moderator: Jun 12, 2005
  4. Jun 12, 2005 #3
    but I did: g_v = [(M_v*r_v^2)/(M_e*r_e)]*9.81 = 4.60 x 10^7 m/s^2

    what did I do wrong?
     
  5. Jun 12, 2005 #4
    oh, I see now
     
  6. Jun 12, 2005 #5
    but I did [(M_v*M_e)/(r_v*r_e)^2]*9.81 = 7.22 m/s^2 what did I do wrong?
     
  7. Jun 12, 2005 #6

    dextercioby

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    Check the units in that [].They don't match.

    Daniel.
     
  8. Jun 12, 2005 #7
    [(M_v/M_e)*(r_v*r_e)^2]*9.81 = 7.22 m/s^2

    [(4.88x10^24 kg/5.98x10^24 kg)*(6.06x10^6 m*6.38x10^6 m)^2]*9.81 = 7.22 m/s^2
     
  9. Jun 12, 2005 #8
    sorry it was [(4.88x10^24 kg/5.98x10^24 kg)*(6.06x10^6 m/6.38x10^6 m)^2]*9.81 = 7.22 m/s^2
     
  10. Jun 12, 2005 #9
    that got me 0.816 * 0.902 * 9.81 = 7.22
     
  11. Jun 12, 2005 #10

    Janus

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    The problem is in the bold part:
    [(4.88x10^24 kg/5.98x10^24 kg)*(6.06x10^6 m/6.38x10^6 m)^2]*9.81 = 7.22 m/s^2

    You are dividing Venus' radius by the Earth's radius, and you should be dividing the Earth's radius by Venus' radius.
     
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