Final answer:
The gravitational potential energy of the asteroid at its position is 5.53 × 10^8 joules.
Step-by-step explanation:
The gravitational potential energy of an object can be calculated using the formula Potential Energy = mass × gravity × height. In this case, the mass of the asteroid is 250 kg, the height is 1350 km above the surface of the moon (which is 1.35 × 10^6 meters), and the gravity can be calculated using the formula gravity = G × (mass of the moon) / (radius of the moon)^2, where G is the gravitational constant (6.674 × 10^-11 N(m/kg)^2), the mass of the moon is 7.35 × 10^22 kg, and the radius of the moon is 1.737 × 10^6 meters. Plugging in the values, we get:
gravity = (6.674 × 10^-11 N(m/kg)^2) × (7.35 × 10^22 kg) / (1.737 × 10^6 meters)^2 = 1.63 m/s^2
Potential Energy = (250 kg) × (1.63 m/s^2) × (1.35 × 10^6 meters) = 5.53 × 10^8 joules.