# Two objects have masses of #4 MG# and #7 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #36 m# to #45 m#?

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The change in gravitational potential energy between the two objects can be calculated using the formula:

ΔPE = G * (m1 * m2) * (1/r1 - 1/r2)

Where: ΔPE is the change in gravitational potential energy, G is the gravitational constant (6.674 × 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two objects (in this case, 4 MG and 7 MG), r1 and r2 are the initial and final distances between the objects (36 m and 45 m).

Substituting the given values into the formula:

ΔPE = (6.674 × 10^-11) * (4 * 10^6) * (7 * 10^6) * (1/36 - 1/45)

Calculating the values:

ΔPE = (6.674 × 10^-11) * (4 * 10^6) * (7 * 10^6) * (0.02778 - 0.02222)

ΔPE = (6.674 × 10^-11) * (4 * 10^6) * (7 * 10^6) * 0.00556

ΔPE ≈ 0.09395 J

Therefore, the change in gravitational potential energy between the objects is approximately 0.09395 joules.

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