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Assuming the mass of the moon is 7.4 ×10²² kg and it's radius is 1 .7 × 10⁶ m. Calculate the gravitational energy of a 1kg mass at the moon's surface

User Diona
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Final answer:

To find the gravitational potential energy of a 1kg mass on the moon's surface, use the formula U = -G * M * m / r. With values G = 6.67 × 10^-11 N·m^2/kg^2, M = 7.4 × 10^22 kg, m = 1 kg, and r = 1.7 × 10^6 m, we get U = -2.72 × 10^7 J.

Step-by-step explanation:

To calculate the gravitational potential energy (U) of a 1 kg mass at the moon's surface, one uses the formula U = -G * M * m / r,

where G is the gravitational constant (6.67 × 10^-11 N·m^2/kg^2),

M is the mass of the moon (7.4 × 10^22 kg),

m is the mass of the object (1 kg),

and r is the radius of the moon (1.7 × 10^6 m).

Substituting these values into the formula, we get:

U = -(6.67 × 10^-11 N·m^2/kg^2) * (7.4 × 10^22 kg) * (1 kg) / (1.7 × 10^6 m)

After calculations, the gravitational potential energy at the moon's surface for a 1 kg mass is approximately:

U = -2.72 × 10^7 J

The negative sign indicates that gravitational potential energy is considered to be a binding energy -- it's the energy required to move the mass away from the moon to an infinitely distant point.

User Moabi
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