AP Physics 1 Quiz: Motion Of Orbiting Satellites

What this quiz covers

This quiz focuses on Motion Of Orbiting Satellites, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics 1.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. The $2r$ orbit, because it has a larger path length
2. The $r$ orbit, because it is closer to the planet (correct answer)
3. They require the same inward acceleration because both are circular
4. Neither requires inward acceleration if no thrust is used

Explanation: 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.

Question 2

1. It is tangent east
2. It is tangent west
3. It is radially inward (correct answer)
4. It is radially outward

Explanation: 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.

Question 3

1. The faster satellite (correct answer)
2. The slower satellite
3. Either; speed does not depend on radius in orbit
4. Neither; thrust sets orbital speed, not radius

Explanation: 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.

Question 4

1. It points toward Earth’s center (correct answer)
2. It points tangent to the orbit in the direction of velocity
3. It points outward to balance the inward acceleration
4. It is zero because the satellite is in free fall

Explanation: 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.

Question 5

1. It is larger at $2r$ because the satellite has more time to fall
2. It is the same at $r$ and $2r$ because gravity is always $mg$
3. It is larger at $r$ because gravity is stronger closer to the planet (correct answer)
4. It is larger at $2r$ because centrifugal force adds to gravity

Explanation: 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.

Question 6

1. It doubles because a larger mass needs more speed to stay in orbit
2. It halves because the planet pulls harder on a larger mass
3. It remains the same because orbital speed at a given radius depends on the planet and $r$, not the satellite’s mass (correct answer)
4. It becomes zero unless the satellite provides thrust

Explanation: 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.

Question 7

1. Satellite Y, because it has a longer path and must move faster
2. They have the same speed, because both are in circular motion
3. Satellite X, because a smaller orbital radius requires a larger speed to remain in orbit (correct answer)
4. Satellite Y, because gravity is weaker so less speed is needed

Explanation: 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.

Question 8

1. Gravity provides an inward force that continually turns the velocity (correct answer)
2. Gravity provides a tangential force that keeps the satellite moving
3. Gravity is balanced by centrifugal force so no net force acts
4. Gravity is unnecessary; inertia alone keeps the satellite in orbit

Explanation: 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.

Question 9

1. It increases because gravity does positive work each quarter orbit
2. It decreases because gravity opposes the motion
3. It remains constant because gravity is perpendicular to displacement (correct answer)
4. It is zero because the satellite is in free fall

Explanation: 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.

Question 10

1. A force tangent to the orbit in the direction of motion
2. A force directed radially inward toward the planet (correct answer)
3. An outward centrifugal force equal to the inward force
4. A continuous thrust provided by the spacecraft engines

Explanation: 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.

Question 11

1. Because inertia keeps it moving; gravity mainly changes direction (correct answer)
2. Because gravity provides a forward push along the orbit
3. Because centrifugal force provides the necessary forward motion
4. Because engines constantly supply the centripetal force

Explanation: This question explains why satellites don't need continuous propulsion in orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. According to Newton's first law, objects in motion tend to stay in motion unless acted upon by a net force. The satellite's inertia keeps it moving tangentially, while gravity continuously changes its direction without changing its speed. No forward push is needed because there's no resistance in space. Choice B incorrectly suggests gravity provides forward motion rather than directional change. When explaining orbital motion, emphasize that inertia maintains motion while gravity changes direction.

Question 12

1. Increase the satellite’s speed
2. Decrease the satellite’s speed (correct answer)
3. Increase the satellite’s mass while keeping speed the same
4. Add an outward centrifugal force generator

Explanation: This question examines how to reduce the required centripetal force. In circular orbit, gravitational force provides the centripetal force required for circular motion. The required centripetal force equals mv²/r, so decreasing the satellite's speed at fixed radius r decreases the force requirement. This would create a mismatch where gravitational force exceeds the centripetal force needed, causing the satellite to move to a smaller orbit. Choice A incorrectly suggests increasing speed, which would increase the force requirement. When reducing required centripetal force at fixed radius, decrease the orbital speed according to F = mv²/r.

Question 13

1. It doubles
2. It halves
3. It stays the same (correct answer)
4. It becomes zero because heavier objects resist turning

Explanation: This question examines how mass affects acceleration in circular orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. The gravitational acceleration equals GM/r², which depends only on the planet's mass and orbital radius, not the satellite's mass. When the satellite's mass doubles, both the gravitational force and the required centripetal force double proportionally, so the acceleration GM/r² remains unchanged. Choice A incorrectly suggests acceleration depends on the satellite's mass. When analyzing orbital acceleration, remember that gravitational acceleration is independent of the orbiting object's mass.

Question 14

1. The satellite at $4r$
2. The satellite at $r$ (correct answer)
3. They are equal because both are in free fall
4. Neither; centripetal acceleration requires a tangential force

Explanation: This question compares centripetal accelerations at different orbital radii. In circular orbit, gravitational force provides the centripetal force required for circular motion. Centripetal acceleration equals GM/r² for orbital motion, decreasing with the square of the distance. The satellite at radius r experiences acceleration GM/r², while the satellite at radius 4r experiences acceleration GM/(4r)² = GM/16r². Therefore, the satellite at radius r has 16 times greater centripetal acceleration. Choice A incorrectly suggests the outer satellite has greater acceleration. When comparing orbital accelerations, apply the inverse square relationship with radius.

Question 15

1. The heavier object must move faster to keep from falling inward
2. The lighter object must move faster because it experiences less gravity
3. They have the same orbital speed at the same radius (correct answer)
4. Neither can maintain orbit without thrust, so speed depends on engine power

Explanation: This question explores satellite motion in AP Physics 1, comparing speeds for different masses in circular orbits. Gravity supplies centripetal force: GMm/r² = mv²/r, where m cancels, yielding v = √(GM/r). Thus, orbital speed depends only on M and r, not satellite mass. Both objects at same r have identical speeds. Choice A incorrectly assumes heavier objects need faster speeds, but mass independence is key in gravitational orbits. Use the mass-canceling property in the orbital speed formula to compare scenarios involving different objects.

Question 16

1. A constant-magnitude force directed toward the planet’s center (correct answer)
2. A force that is always tangent to the orbit, keeping the speed constant
3. No net force, since the satellite is not speeding up
4. Two forces: gravity inward and an equal centrifugal force outward

Explanation: This question tests concepts in AP Physics 1 satellite motion, describing the net force in circular orbits. Gravitational force toward the planet's center provides the constant-magnitude centripetal force for uniform circular motion. This force is always radial inward, matching the centripetal requirement mv²/r. No tangential force is needed since speed is constant. Distractor D introduces centrifugal force, which is not a real force but a perceived effect in rotating frames. When analyzing orbits, equate gravitational force to centripetal force and check if the net force is purely radial for circular paths.

Question 17

1. Left, because acceleration is in the direction of velocity
2. Upward, away from the planet due to centrifugal force
3. Downward, toward the planet’s center (correct answer)
4. Zero, because the speed is constant

Explanation: This question tests the motion of orbiting satellites in AP Physics 1, particularly the direction of acceleration in circular orbits. Gravitational force from the planet pulls the probe inward, serving as the centripetal force toward the center. This centripetal force causes centripetal acceleration, which is always directed toward the center of the circle, regardless of the velocity direction. Even though speed is constant, acceleration is nonzero due to the changing velocity direction. Choice B is a distractor that mentions centrifugal force, which is a fictitious force and not present in the inertial frame analysis. Remember, for any circular motion, apply the strategy of determining acceleration direction as radially inward and using a = v²/r.

Question 18

1. Satellite B, because a larger radius requires a larger speed to stay in orbit
2. Satellite A, because the closer satellite must move faster in circular orbit (correct answer)
3. They have the same speed because both are in circular motion
4. Neither can orbit without continuous thrust, so speed cannot be compared

Explanation: This question evaluates understanding of satellite motion in AP Physics 1, comparing speeds in different circular orbits. Gravity provides the centripetal force, so GMm/r² = mv²/r, simplifying to v = √(GM/r). Thus, for the same planet, smaller radius r means larger orbital speed v. Satellite A, with smaller r, requires greater speed to balance the stronger gravity at closer distance. Distractor C assumes speeds are equal due to circular motion, but speed depends on radius as shown in the equation. A useful strategy is to derive orbital speed from equating gravitational and centripetal forces, then compare variables directly.

Question 19

1. A tangential force continuously speeds it up
2. An inward net force produces centripetal acceleration (correct answer)
3. An outward centrifugal force bends the path inward
4. The satellite’s inertia causes it to curve without forces

Explanation: This question explains the cause of curved motion in orbital dynamics. In circular orbit, gravitational force provides the centripetal force required for circular motion. The velocity direction changes because a net inward force (gravitational force) produces centripetal acceleration toward the center. This acceleration continuously turns the velocity vector, causing the satellite to follow a curved path rather than moving straight. Choice A incorrectly suggests tangential force speeds up the satellite, but tangential force would change speed, not direction. To explain curved motion, identify that perpendicular net force causes acceleration that changes velocity direction.

Question 20

1. Increase its speed at F (briefly) in the tangential direction (correct answer)
2. Apply a brief inward radial thrust at F
3. Apply a brief outward radial thrust at F only
4. Turn off gravity by moving far enough away instantly

Explanation: This question addresses orbital mechanics and energy changes. In circular orbit, gravitational force provides the centripetal force required for circular motion. To move to a larger radius orbit, the spacecraft needs more energy. Briefly increasing speed in the tangential direction adds kinetic energy, which transforms the circular orbit into an elliptical transfer orbit that reaches a higher altitude. Choice B incorrectly suggests radial thrust, which would change the orbit shape rather than the energy. When changing orbital radius, apply tangential thrust to change orbital energy rather than radial thrust.