Calculating Gravity: Determine G from Acceleration

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The discussion focuses on calculating gravitational acceleration and the gravitational constant G using two spheres with specified masses and distance. The initial calculation for acceleration yields 0.3 m/s², but the user questions its correctness and considers using Newton's second law for an alternative approach. They derive a different acceleration value of 2.9 x 10^-7 m/s² using the gravitational force formula, leading to confusion over the discrepancies between the two results. The user seeks clarification on the correct method for determining acceleration in this context. The thread highlights the complexities involved in gravitational calculations and the importance of consistent methodologies.
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Sorry.. I think I posted this post already but I can't find the original thread..

Problem:
Two spheres of masses m = 1.00 g and m' = 1.00 * 10^2
kg are isolated from all other bodies and are initially at
rest, with their centers a distance r = 15.0 cm apart. One
minute later, the smaller sphere has moved 0.534 mm
toward the larger sphere. Compute the acceleration and
the value of G.

Solution:
Acceleration: x = xi + Vxi(t) + (a)(t^2)/2

0.149m = a(1s)^2/2
a = (0.149m)(2) = 0.3 m/s/s

Is this correct for acceleration?

Could I have also used Newtons second law some how to solve for acceleration?
such as...
F = (m1)(m2)(G)/.149^2 = 2.98*10^-11
F = F1... 2.98*10^-11 = (m1)(a)
a = 2.98*10^-11/m1 = 2.9*10^-7

But obviously these answers are not the same...
 

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