Where you are going wrong is with your equation for Gravitational Potential Energy:
 Quote by bobbles22
Gravitational Potential Energy = Eg = (GMm)/r
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You left out the all-important minus sign in front:
GPE = -(GMm)/r
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However, as it gets closer, the force from the Earth increased, as the separation 'r' off the objects decreases, the gravitational potential energy increases.
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Using the correct expression, you'll see that the GPE
decreases (becomes more negative) as objects approach and r decreases.
See:
Gravitational Potential Energy