This question tests understanding of the motion of orbiting satellites within the context of energy and momentum in rotating systems (AP Physics C: Mechanics). Kepler's second law states that a satellite sweeps out equal areas in equal times, which is a consequence of angular momentum conservation. As a satellite in elliptical orbit approaches perigee (closest point to Earth), its distance r from Earth decreases while angular momentum L = mrv remains constant. Choice B is correct because it accurately applies angular momentum conservation: as r decreases at perigee, v must increase to maintain constant L = mrv. Choice D is incorrect because it misstates the energy relationship - gravitational potential energy actually becomes more negative (decreases) at smaller r. To help students: Emphasize the connection between Kepler's second law and angular momentum conservation, use area-sweeping diagrams to visualize the law, and practice calculating speeds at apogee and perigee using L conservation. Show energy conservation as a separate constraint.

This question tests understanding of the motion of orbiting satellites within the context of energy and momentum in rotating systems (AP Physics C: Mechanics). In circular orbital motion, gravitational force serves as the centripetal force, always pointing toward the center of the circular path and providing the acceleration needed to continuously change the velocity's direction. The gravitational force F = GMm/r² must equal the required centripetal force mv²/r for circular motion, leading to the orbital velocity relationship v = √(GM/r). Choice C is correct because it accurately describes gravity pointing toward Earth's center and providing the centripetal acceleration ac = v²/r necessary for curved motion. Choice D is incorrect as it suggests magnetic forces replace gravity in orbit, a fundamental misconception - gravity is the only significant force acting on satellites. To help students: Use free body diagrams showing only gravitational force on the satellite, emphasize that this single force causes the acceleration that curves the path, and demonstrate how setting Fgrav = Fcentripetal yields orbital relationships. Address the misconception that satellites are beyond gravity's reach.

This question tests understanding of the motion of orbiting satellites within the context of energy and momentum in rotating systems (AP Physics C: Mechanics). For circular orbits, gravitational force provides the centripetal force needed to maintain the satellite's circular path around Earth. The gravitational force on a satellite of mass m at distance r from Earth's center is GMm/r², where G is the gravitational constant and M is Earth's mass. Choice B is correct because it accurately states that gravitational force equals GMm/r² and this must equal the required centripetal force mv²/r directed toward Earth's center. Choice A is incorrect because magnetic forces play no role in satellite orbits - gravity alone provides the centripetal force. To help students: Emphasize that for any circular orbit, the gravitational force IS the centripetal force, practice setting GMm/r² = mv²/r to derive orbital velocity, and use free-body diagrams showing only gravity acting radially inward. Have students verify dimensional consistency and practice with numerical examples.

This question tests understanding of the motion of orbiting satellites within the context of energy and momentum in rotating systems (AP Physics C: Mechanics). Angular momentum L = mrv is conserved for a satellite when no external torques act, which is true for central forces like gravity. When orbital radius r decreases due to an inward impulse, conservation of angular momentum requires that velocity v must increase to keep L constant. Choice B is correct because it accurately applies conservation of angular momentum: as r decreases, v must increase proportionally so that the product mrv remains constant. Choice A is incorrect because it states speed decreases, which would violate angular momentum conservation when radius decreases. To help students: Emphasize that gravity exerts no torque about the central body, practice applying L = mrv for different orbital scenarios, and use the ice skater analogy where pulling arms inward increases rotation speed. Have students calculate specific velocity changes for given radius changes.

This question tests understanding of the motion of orbiting satellites within the context of energy and momentum in rotating systems (AP Physics C: Mechanics). Kepler's third law states that the square of the orbital period is proportional to the cube of the orbital radius, or T² ∝ r³. This relationship can be derived from Newton's laws by equating gravitational and centripetal forces and using the relationship between period and velocity. Choice B is correct because it accurately states that T ∝ r^(3/2), which follows from taking the square root of both sides of T² ∝ r³. Choice C is incorrect because it suggests T ∝ r², which would imply T² ∝ r⁴, violating Kepler's third law. To help students: Derive Kepler's third law from first principles using F = ma, practice applying the T² ∝ r³ relationship to compare orbital periods, and use log-log plots to verify the 3/2 power relationship. Emphasize that this law applies to all satellites orbiting the same central body.

This question tests understanding of the motion of orbiting satellites within the context of energy and momentum in rotating systems (AP Physics C: Mechanics). Kepler's second law (equal areas in equal times) is a direct consequence of angular momentum conservation, as gravitational force exerts zero torque about the central body. In an elliptical orbit, the perpendicular component of velocity v⊥ varies inversely with distance r to maintain constant angular momentum L = mrv⊥. Choice B is correct because conservation of angular momentum requires the satellite to move faster when closer to Earth (perigee) and slower when farther away (apogee), as rv⊥ must remain constant. Choice C is incorrect as it claims constant speed throughout the ellipse, which would violate both energy conservation and angular momentum conservation in a varying gravitational field. To help students: Use visual demonstrations of equal area sweeping, derive Kepler's second law from L = constant, and have students calculate velocities at different points in elliptical orbits. Emphasize the distinction between constant angular momentum and varying linear speed.

This question tests understanding of the motion of orbiting satellites within the context of energy and momentum in rotating systems (AP Physics C: Mechanics). When a satellite moves to a higher orbit, both its kinetic and potential energies change, but total mechanical energy increases due to work done by the boosting force. In a higher orbit, the satellite moves more slowly (v = √(GM/r) decreases with increasing r), so kinetic energy K = ½mv² decreases. Choice B is correct because it accurately states that kinetic energy decreases while gravitational potential energy U = -GMm/r becomes less negative (increases) as r increases. Choice A is incorrect because it reverses the energy changes - kinetic energy actually decreases in higher orbits. To help students: Emphasize that orbital speed decreases with altitude, practice calculating both K and U for different orbits, and show that total energy E = -GMm/2r becomes less negative (increases) for higher orbits. Use energy bar charts to visualize the trade-off between kinetic and potential energy.

This question tests understanding of the motion of orbiting satellites within the context of energy and momentum in rotating systems (AP Physics C: Mechanics). Angular momentum conservation is a fundamental principle in orbital mechanics, stating that L = mrv⊥ remains constant when no external torques act on the system. Since gravitational force points radially toward Earth's center, it exerts zero torque about that center, making angular momentum conserved throughout the orbit. Choice A is correct because as r decreases, v⊥ must increase proportionally to maintain constant L = mrv⊥, explaining why satellites move faster at perihelion (closest approach) in elliptical orbits. Choice B is incorrect as it contradicts the conservation principle - if r decreases and v⊥ also decreased, angular momentum would not be conserved. To help students: Use the ice skater analogy (pulling arms in while spinning), derive why central forces produce zero torque, and practice applying L = mrv⊥ = constant to various orbital scenarios. Emphasize that this principle leads directly to Kepler's second law of equal areas.

This question tests understanding of the motion of orbiting satellites within the context of energy and momentum in rotating systems (AP Physics C: Mechanics). When raising a satellite from a lower to higher circular orbit, both kinetic and potential energies change in specific ways determined by the orbital mechanics relationships. Since v = √(μ/r), as r increases, velocity decreases, causing kinetic energy K = ½mv² to decrease. Choice B is correct because K decreases while U = -GMm/r becomes less negative (increases toward zero), and the total energy E = -GMm/(2r) also becomes less negative, representing an overall energy increase. Choice C is incorrect as it claims kinetic energy increases when moving to a higher orbit, contradicting the v ∝ 1/√r relationship - a common misconception among students. To help students: Use energy bar charts showing K, U, and E at different orbital radii, emphasize that work must be done against gravity to raise the orbit, and practice numerical examples. Reinforce that satellites in higher orbits move more slowly but have greater total mechanical energy.

This question tests understanding of the motion of orbiting satellites within the context of energy and momentum in rotating systems (AP Physics C: Mechanics). For circular orbits, the period T and radius r are related by T = 2π√(r³/GM), which can be rearranged to solve for r when T is known. Squaring both sides gives T² = 4π²r³/GM, and solving for r yields r = (GMT²/4π²)^(1/3). Choice B is correct because it properly rearranges the period formula to isolate r, giving r = (GMT²/4π²)^(1/3) for a geostationary satellite with T = 24 hours. Choice A is incorrect because it omits the factor of 2 in the denominator, using 2π instead of 4π². To help students: Practice algebraic manipulation of the period formula, emphasize keeping track of all factors including 2π vs 4π², and work through the calculation with actual values for Earth to find r ≈ 42,000 km. Show how this places geostationary satellites about 36,000 km above Earth's surface.