- #1

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^{2}/kg

^{2}. How would you determine the distance, x, between the centers of the two spheres at time t?

I have been trying to solve this problem using many methods, but have been unsuccessful.

I have been using the gravitational acceleration equation: g = G*m/r

^{2}

as well as the derivatives of acceleration: a = g, v = gt + v

_{0}, x = 1/2*gt

^{2}+ v

_{0}t + x

_{0}

I tried approximating on intervals of 1 second, i.e. x(0) = 10, x(1) = 9.95, x(2)= 9.8, x(3) = 9.547, etc.

However, I was unable to reconcile this pattern to an integral using an infinitely short time.

How do I solve this problem?

(It's not for homework, just curiosity.)