In the context of Newton's law of gravity, what force is primarily responsible for the mutual attraction that drives the motion of massive objects such as planets and moons?

• A. The electrostatic force described by Coulomb's law $F=k\frac{q1q2}{r^2}$
• B. The frictional force proportional to the normal force $F=\mu N$
• C. The gravitational force described by $F=G\frac{m1m2}{r^2}$
• D. The buoyant force from a surrounding fluid as given by Archimedes' principle $F={\rho }_{f}gV$

Answer: (C)

Verified step by step guidance

1. Identify the fundamental force responsible for the mutual attraction between massive objects such as planets and moons. This force is the gravitational force.
2. Recall Newton's law of universal gravitation, which states that every two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
3. Express this mathematically as \(F = G \frac{m_1 m_2}{r^2}\), where \(F\) is the gravitational force, \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between their centers.
4. Understand that this gravitational force is distinct from other forces such as the electrostatic force \(F = k \frac{q_1 q_2}{r^2}\), frictional force \(F = \mu N\), or buoyant force \(F = \rho_f g V\), which do not govern the large-scale motion of planets and moons.
5. Conclude that the gravitational force described by Newton's law of gravitation is the primary force driving the motion of massive celestial bodies.