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Other Objects Pull Both Ways.

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Posted by Duane Eddy on April 24, 2003 17:30:41 UTC

The other objects in the universe will be pulling in random directions and will not consistently change the results in one direction.
The introduction of other mass objects may confuse the issue but it does not change the result.

The equation I stated defines the total acceleration of two mass objects toward each other, not the force toward each other.

I determined the equation as followes:

M1 = mass 1
M2 = mass 2
F1 = Force on mass 1 toward mass 2
F2 = Force on mass 2 toward mass 1
A1 = Aacceleration of mass 1 towards mass 2
A2 =Aacceleration of mass 2 towards mass 1
G = Gravitational constant
R = Distance beteen objects
AT = Total combined acceleration of objects.

(1) F1 = F2 = G (M1 x M2) / (R^2)

(2) F1 = M1 x A1

(3) F2 = M2 x A2

(4) AT(total acceleration) = A1 + A2

F1 = F2 Equation (1)

M1 x A1 = M2 x A2 By substitution (2) and (3)

(5) A1 = ( M2 x A2 ) / M1 Solve for A1

AT = A1 + A2 Equation (4)

AT = ( M2 x A2 ) / M1 + A2 By substitution (5)

(6) AT = ( M2 / M1 + 1 ) x A2 Factor A2

F2 = M2 x A2 = G x (M1 x M2) / (R^2) Equation (1) and (3)

(7) A2 = (G x M1) / (R^2) Solve for A2

AT = ( M2 / M1 + 1 ) x A2 Equation (6)

AT = ( M2 / M1 + 1 ) x (G x M1 ) / ( R^2) Substitute A2 equation (7)

(8) AT = (G / R(^2) ) x ( M2 + M1) Simplify

Total ACCELERATION due to gravity is proportional to the sum of the masses.
If the masses are equal then the acceleration is affected equally by a change in either mass.

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