The gravitational force between the 5 kg rock and the moon is approximately 2.04 × 10^4 N.
To determine the force of gravitation between the rock and the moon, you can use Newton's law of gravitation, which is given by the formula:
F = G × m1 × m2 / r^2
where:
F is the force of gravitation,
G is the gravitational constant (6.67430 × 10^-11 Nm^2/kg^2),
m1 and m2 are the masses of the two objects,
r is the separation between the centers of the two masses.
In this case:
m1 is the mass of the rock (5 kg),
m2 is the mass of the moon (2.2 × 10^23 kg),
r is the distance between the center of the rock and the center of the moon (30,000 m + radius of the moon).
Let's calculate it:
r = 30,000 m + 30,000 m = 60,000 m
F = (6.67430 × 10^-11 Nm^2/kg^2 × 5 kg × 2.2 × 10^23 kg) / (60,000 m)^2
Now, plug in the values and calculate:
F ≈ (6.67430 × 10^-11 × 5 × 2.2 × 10^23) / (60,000)^2
F ≈ (7.34175 × 10^13) / (3.6 × 10^9)
F ≈ 2.03882 × 10^4 N
Therefore, the force of gravitation between the rock and the moon is approximately 2.04 × 10^4 N (rounded to the nearest hundredths).