This question compares centripetal acceleration at different orbital radii. In circular orbit, gravitational force provides the centripetal force required for circular motion. The centripetal acceleration equals v²/r, but for orbits, the relationship is more directly given by GM/r², where acceleration decreases with the square of the distance. Since the satellite at radius r is closer to the planet, it experiences stronger gravitational field and thus larger inward acceleration. Choice A incorrectly focuses on path length rather than gravitational field strength. When comparing orbital accelerations, remember that closer orbits require greater centripetal acceleration due to stronger gravitational fields.

This question identifies the direction of gravitational acceleration in orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. Gravitational acceleration always points toward the center of the gravitating body, regardless of the spacecraft's position or velocity direction. At point H1, even though the velocity is tangent east, the gravitational acceleration points radially inward toward the planet's center. Choice A incorrectly suggests the acceleration follows the velocity direction. When finding gravitational acceleration direction, remember it always points toward the center of the attracting mass.

This question relates orbital speed to orbital radius. In circular orbit, gravitational force provides the centripetal force required for circular motion. For circular orbits around the same planet, the relationship v = √(GM/r) shows that higher orbital speed corresponds to smaller orbital radius. The faster satellite must be at the smaller radius to maintain the balance between gravitational force and centripetal force requirements. Choice B incorrectly suggests the slower satellite is closer. When relating orbital speed to radius, use the inverse relationship: higher speed corresponds to smaller radius for circular orbits.

This question examines the gravitational force in orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. The gravitational force on the satellite always points toward Earth's center, regardless of the satellite's position in the orbit. This inward gravitational force acts as the centripetal force that keeps the satellite in circular motion. Choice D incorrectly suggests the force points outward, which would cause the satellite to spiral away from Earth. To identify gravitational force direction, remember that it always points toward the center of the gravitating body.

This question tests understanding of the motion of orbiting satellites. The gravitational force follows Newton's law: F = GMm/r², which decreases with the square of the distance. At radius r, the force is GMm/r², while at radius 2r, it becomes GMm/(2r)² = GMm/4r², which is one-fourth as strong. This means gravity is stronger on satellites closer to the planet, providing the greater centripetal force needed for their faster orbital motion. Choice B incorrectly treats gravity as a constant mg, which only applies near Earth's surface, not for orbital distances. The strategy is to remember that gravitational force follows an inverse square law: doubling distance reduces force to one-fourth.

This question tests understanding of the motion of orbiting satellites. From the orbital equation GMm/r² = mv²/r, we can solve for speed: v = √(GM/r). Notice that the satellite's mass m cancels out, meaning orbital speed depends only on the planet's mass M and orbital radius r. This is because while a more massive satellite experiences stronger gravity (F ∝ m), it also requires more force to accelerate (F = ma), and these effects exactly cancel. Choice A incorrectly assumes mass affects speed, ignoring this cancellation. The strategy is to remember that orbital speed is independent of satellite mass—all objects orbit at the same speed at a given radius.

This question tests understanding of the motion of orbiting satellites. For circular orbits, the gravitational force provides the centripetal force: GMm/r² = mv²/r, which simplifies to v = √(GM/r). This shows that orbital speed decreases as radius increases—satellites closer to the planet must move faster to maintain circular motion. At radius r, satellite X needs speed v = √(GM/r), while at radius 2r, satellite Y needs speed v = √(GM/2r) = √(GM/r)/√2, which is smaller. Choice A incorrectly assumes that a longer path requires faster speed, but this ignores that gravity weakens with distance. The key insight is that orbital speed follows v ∝ 1/√r—closer satellites orbit faster.

This question explains gravity's role in maintaining orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. Gravity acts as an inward force that continuously turns the satellite's velocity vector, changing its direction while maintaining constant speed. This turning action prevents the satellite from moving in a straight line and keeps it in circular orbit. Choice B incorrectly suggests gravity acts tangentially, which would change speed rather than direction. To understand orbital mechanics, recognize that gravity's inward pull continuously curves the satellite's path into a circle.

This question examines energy conservation in circular orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. The satellite's kinetic energy remains constant because its speed is constant throughout the circular orbit. Gravity is always perpendicular to the satellite's instantaneous displacement, so the work done by gravity over any small arc is zero (W = F·d = 0 when F ⊥ d). Choice A incorrectly suggests gravity does positive work by pulling forward. When analyzing work in circular orbits, recognize that perpendicular forces do no work, conserving kinetic energy.

This question identifies the force responsible for changing velocity direction in orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. The spacecraft maintains constant speed but continuously changes direction, which requires a net force perpendicular to the velocity. Gravitational force acts radially inward toward the planet, providing exactly this perpendicular force needed to curve the spacecraft's path. Choice C incorrectly invokes centrifugal force, which is not a real force acting on the spacecraft. When analyzing forces that change only direction, identify the force perpendicular to the velocity vector.