Newton's Law of Gravitation: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Newton's Law of Gravitation. Understanding the underlying formula is key to arriving at the correct answer below:

If the universal constant of gravitation \( G \) were decreasing uniformly with time, the gravitational force between the satellite and the Earth would weaken. However, the satellite's angular momentum would remain conserved because angular momentum depends on the mass, velocity, and radius of orbit, and not directly on \( G \).

According to the law of conservation of angular momentum:

\[
L = m v r
\]

where \( L \) is angular momentum, \( m \) is the satellite's mass, \( v \) is its velocity, and \( r \) is the orbital radius. Since no external torque acts on the system, angular momentum is conserved even if \( G \) changes.

However, the satellite’s orbital parameters like its velocity and orbital radius might change over time due to the weakening gravitational force, but the total angular momentum will remain constant.