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Gravity and Planets

  1. Nov 16, 2006 #1
    Im not sure if this is done right...

    Im guessing use Net force = ma
    The net force is the Gravitational force, Gm1m2 / r^2 is = m2 4 (pie)^2 r/ T^2

    for the 4 (pie)^2 r/ T^2 r is the distance form the planet's center, to the moon, for T, find how many second 40 days is.

    and the other r is the planet's radius

    m2 cancels

    solve for m1, and yo uhave the mass of the planet.

    I guess plug in numbers after that, into the equaltion Fg = Gm1 m2 / r^2

    m2 would be the 70 kg







    Can someone help me out and tell me if what i am doing looks right?
     
  2. jcsd
  3. Nov 17, 2006 #2

    OlderDan

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    All the r in your first equation are the same. r is the distance from the center of Krypton to the center of its moon. The r in the second equation is the radius of the planet. I assume that Fg is the force of gravity, or weight at the planet's surface. If that is what you mean, then you should have the correct result.
     
  4. Nov 17, 2006 #3
    Yes thats what i meant. The other r (the one in the 2nd equation) is the radius. So i know how to set it up, the problem is im not good at plugging it in. What am i doing wrong?


    m1/3.6x10^17=39.47 r/t^2
    m1/3.6x10^17=39.47 (6x10^8)/1.194x10^13
    when i solve for m1 i get 6.84x10^14...that doesnt seem right?

    and if its right, how do u multiply that times 70 kg...which is m2?
     
  5. Nov 17, 2006 #4
    So am i wrong? And if so, where am i plugging them in wrong?
     
  6. Nov 17, 2006 #5

    OlderDan

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    It doesn't look right, but you have not included enough steps to find out what you are doing. I suggest you solve the equation algebraically for m1 before entering any numbers,
     
  7. Nov 17, 2006 #6
    m1/r^2=4pi^2 r/t^2
    thats basically as far as i can solve it...
    plug in 345600 for t, and 6x10^8 for r, then its just basic calculator plug ins from there getting m1/r^2=.0019...so what am i doing wrong?
     
  8. Nov 17, 2006 #7

    OlderDan

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    What became of G? Why not multiply both sides by r² ?
     
  9. Nov 17, 2006 #8
    Oops forgot G.


    Gm1=4pi^2 r^3/t^2

    That would be simplified then...so why does my answer look so wrong when i plug in 345600 for t, and 6x10^8?
     
  10. Nov 17, 2006 #9
    Then...
    Gm1=39.478 r^3/3456000^2
    Gm1=39.478 r^3/1.194x10^13
    then you devide each side by G...so what am i doing wrong? Maybe im taking r^3 wrong? How do you do that just to make sure im doing it right.
     
  11. Nov 17, 2006 #10

    OlderDan

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    Gm1=4pi²*r³/t²
    m1=4*pi²*r³/(t²*G) = 1.07 x 10^25 kg on my calculator

    Edit: The original value posted was incorrect because it used the OP's value for t that was off by a factor of 10. The value in the quote has been corrected, and the correction for m1 made here
     
    Last edited: Nov 17, 2006
  12. Nov 17, 2006 #11
    1.07 x 10^27 kg now needs to be multiplied by m12 which is 70kg. so can i just multiply 1.07x10^27 by 70, then divide it by r^2 and thats it?

    Quick question, if im doing R^2, would that mean if r is 6.4x10^6 that r^2 is 6.4x10^12?
     
  13. Nov 17, 2006 #12
    can u show me the steps because i still cant get that answer, after that i know how to do it...thanks.
     
  14. Nov 17, 2006 #13

    OlderDan

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    NO

    (6.4x10^6)^2 = 6.4x10^6x6.4x10^6 = (6.4)^2x10^12 = 40.96x10^12 = 4.096x10^13

    Maybe this is your problem??
     
  15. Nov 17, 2006 #14
    can u show me the steps because i still cant get that answer...i get like 7.139x10^13, then i multiply it by 70 and 9.8 and divide it by (6.4x10^6)^2 and get 1195. Howd u get 1.07x10^27? What do you do after you get it? if u plug it in to the 2nd equation you get a crazy number.
     
  16. Nov 17, 2006 #15

    OlderDan

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    t = 40days*(24hr/day)*(60min/hr)*(60sec/min) = 3.456x10^6 s <== You had this as 3.456x10^5 and I used your number, so my exponent was a bit off

    t² = (3.456x10^6 s)(3.456x10^6 s) = 3.456²x10^12 s² = 1.194x10^13 s²

    t²*G = (1.194x10^13 s²)*(6.673x10^-11 N m²/kg²) = 7.97x10² N m² s²/kg² = 7.97x10² m³/kg


    m1 = 4*pi²*r³/(t²*G) = 4*3.14²*(6x10^8 m)³/(7.97x10² m³/kg)

    m1 = 4*9.870*6³x10^24 m³/(7.97x10² m³/kg)

    m1 = 8.527 x10^27 kg/(7.97x10²)

    m1 = 1.07 x10^25 kg
     
    Last edited: Nov 17, 2006
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