Question

What is the acceleration of the moon toward earth due to their mutual attraction the massive earth is 5. 98×10 to the 24th power kilograms the distance between them is 3. 8×10 to the eighth power meters and G equals 6. 673×10 to the -11th power newton meter squared per kilograms squared?

Answer 1

2.76×10^-3 m/s²

Explanation:

You want to know the acceleration of the moon toward the Earth, given its distance is 3.8×10^8 meters, Earth's mass is 5.98×10^24 kg, and the gravitational constant is 6.673×10^-11 N·m²/kg².

Acceleration

The acceleration of one body by another is ...

a = GM/r²

where G is the gravitational constant, M is the body creating the gravitational field, and r is the distance between the masses.

Application

a = (6.673×10^-11)(5.98×10^24)/(3.8×10^8)² N/kg

a = (6.673·5.98/3.8²)×10^(-11+24-16) m/s² ≈ 2.76×10^-3 m/s²