AP Physics 1: Algebra-Based Practice Quiz: Motion of Orbiting Satellites

Correct Answer: B

The first point in the content explicitly states that the description of motion applies to a system of two objects 'interacting only via gravitational forces.'

Correct Answer: B

The content states that 'the motion of the central object itself is negligible' in a system where the satellite's mass is 'negligible in comparison to the central object’s mass.' This implies the mass difference is the reason for the simplification.

Correct Answer: C

The third point of the provided content directly states that 'The motion of satellites in orbits is constrained by conservation laws.'

Correct Answer: C

The content states that for circular orbits, total mechanical energy, gravitational potential energy, angular momentum, and kinetic energy are constant. Velocity is a vector quantity; while its magnitude (speed) is constant in a circular orbit, its direction is continuously changing, so the velocity itself is not constant.

Correct Answer: C

The provided text defines escape velocity directly: 'The escape velocity of a satellite is the satellite’s velocity such that the mechanical energy of the satellite–central-object system is equal to zero.'

Correct Answer: C

According to the text, for circular orbits, 'the system’s total mechanical energy, the system’s gravitational potential energy, and the satellite’s angular momentum and kinetic energy are constant.' Option C lists three of these constant quantities. Gravitational force and acceleration are vectors that change direction, and velocity is also a vector that changes direction.

Correct Answer: B

The text defines escape velocity as the point where the total mechanical energy is zero. Total mechanical energy is the sum of kinetic energy (always positive) and potential energy (negative in a gravity well). To have a velocity greater than escape velocity, the satellite must have more kinetic energy. This additional kinetic energy makes the total mechanical energy (KE + PE) greater than zero, hence positive.

Correct Answer: C

The text directly addresses this simplification by stating that in a system with a massive central object and a satellite of negligible mass, 'the motion of the central object itself is negligible.' The key condition is the mass of the satellite being 'negligible in comparison to the central object’s mass.'

Correct Answer: C

Gravitational potential energy depends on the mass of the objects and the distance between their centers. The text states that for a circular orbit, potential energy is constant. A circular orbit is defined by a constant radius, or distance from the central object. Therefore, the constant potential energy is a result of the constant distance.

Correct Answer: D

The text states that for a circular orbit, the system's total mechanical energy and gravitational potential energy are constant. Since total mechanical energy is the sum of kinetic and potential energy (E = K + U), if both E and U are constant, K must also be constant. This relationship is a direct application of the conservation of energy, which is one of the 'conservation laws' mentioned as constraining satellite motion.

Correct Answer: D

The very first point of the content defines the scope: 'Describe the motions of a system consisting of two objects interacting only via gravitational forces.' While point 2 discusses a specific case of this system, point 1 provides the general description of the system being discussed.