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March 17th, 2010, 07:17 PM   #1
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Finding the acceleration of two masses with gravity relati..

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Finding the acceleration of two masses with gravity relative to a fixed grid/or-point.

Funny, as soon as I go to post this, I see a post by dedanoe stating errors about newton's G. If he is right, I may already be at fault. But here is what I did to find the force between to masses, A (m_1) 8kg, B (m_2) 4kg, at a distance of 2m:
Code:
    6.67 x 10^-11 m^3
G = -----------------
        kg * s^2

         m_1 *  m_2
F = G * -------------
             r^2

m_1 = 8kg
m_2 = 4kg
r = 2m

Thus:
    [6.67 x 10^-11m^3]   [8kg * 4kg]
F = [----------------] * [---------]
    [    kg * s^2    ]   [ (2m)^2  ]
=
    [6.67 x 10^-11m^3]   [ 32kg^2 ]
F = [----------------] * [--------]
    [    kg * s^2    ]   [  4m^2  ]
=
    [2.13 x 10^-9m^3 * kg^2]
F = [----------------------]
    [    4m^2 * kg * s^2   ]
=
    [2.13 x 10^-9m^3 * kg^2]
F = [----------------------]
    [    4m^2 * kg * s^2   ]
=
    [5.33 x 10^-10m^3 * kg^2]
F = [-----------------------]
    [     m^2 * kg * s^2    ]
=
    [5.33 x 10^-10m * kg] |           [kg * m]                                     [kg * m]
F = [-------------------] | 1 N = 1 * [------]  5.33 x 10^-10 N = 0.000000000533 * [------]
    [        s^2        ] |           [ s^2  ],                                    [ s^2  ]
If I have made no errors the force should be 5.33 x 10^-10 N. What I want to find now is the acceleration on each object unique to another fixed point at which defines their state. If a = f/m then it should be correct to say for mass A, that a = (5.33 x 10^-10 N)/8kg. But isn't this is the acceleration of mass A, (to the fixed point I just defined), as if B was fixed? How would I find out the acceleration of both objects? It would be correct to say that mass B will have greater acceleration than mass A. right?

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March 18th, 2010, 05:41 PM   #2
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Re: Finding the acceleration of two masses with gravity relati..

Never mind. I was doing it wrong. Just found this: http://www-istp.gsfc.nasa.gov/stargaze/Sgravity.htm
Helped me out a bit. I was doing it separately. Being that F = ma, and G(m m2)/r^2 = F; m G(m2)/r^2 = ma = G(m2)/r^2 = a, ("a" usually as "g".) Which allowed me to find the earths acceleration to be ~9.81[...]m/s^2.

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