Answer :
Final answer:
The potential energy of the body at the given distance is 4.5 * 10^13 J and the gravitational potential at that distance is 5.7 * 10^7 J/kg.
Explanation:
The potential energy of a body at a distance from the center of the Earth can be calculated using the formula:
Potential Energy = mass * gravitational acceleration * distance
In this case, the mass of the body is 67 kg, the distance from the center of the Earth is 6.6 * 1010 m, and the gravitational acceleration is approximately 9.8 m/s2.
Substituting the values into the formula, we get:
Potential Energy = 67 kg * 9.8 m/s2 * 6.6 * 1010 m
= 4.5 * 1013 J
The gravitational potential at a distance from the center of the Earth can be calculated using the formula:
Gravitational Potential = gravitational constant * mass / distance
In this case, the mass of the Earth is approximately 5.97 * 1024 kg, the distance from the center of the Earth is 6.6 * 1010 m, and the gravitational constant is approximately 6.6743 * 10-11 N m2/kg2.
Substituting the values into the formula, we get:
Gravitational Potential = (6.6743 * 10-11 N m2/kg2) * (5.97 * 1024 kg) / (6.6 * 1010 m)
= 5.7 * 107 J/kg
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