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 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 2

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 3

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 4

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 5

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 6

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 7

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.

Question 8

1. It increases, because centripetal force depends on $v^2$ (correct answer)
2. It decreases, because a faster satellite needs less inward force
3. It becomes tangential, in the direction of motion
4. It becomes zero, because the satellite is moving faster

Explanation: This question tests understanding of the motion of orbiting satellites. The centripetal force required for circular motion is Fc = mv²/r, which increases with the square of the speed. If a satellite's speed increases while maintaining the same radius, the required centripetal force must increase proportionally to v². Since gravity at a fixed radius r remains constant (GMm/r²), the satellite would need additional inward force to maintain circular motion at the higher speed. Choice B incorrectly suggests that faster motion requires less force, contradicting the physics of circular motion. The strategy is to remember that centripetal force depends on v²—doubling speed quadruples the required force.

Question 9

1. An outward centrifugal force away from the planet
2. A tangential gravitational force in the direction of motion
3. The planet's gravitational force directed toward the planet's center (correct answer)
4. A forward thrust force to keep the speed constant

Explanation: This question tests understanding of the motion of orbiting satellites. For any object in circular motion, a centripetal force directed toward the center is required to continuously change the velocity's direction. In the case of a satellite orbiting a planet, the gravitational force provides this centripetal force, pulling the satellite toward the planet's center. This inward force causes the satellite to continuously accelerate toward the center, changing its velocity direction to maintain circular motion. Choice A is incorrect because centrifugal force is a fictitious force that only appears in rotating reference frames, not an actual force acting on the satellite. The key strategy is to remember that for orbital motion, gravity IS the centripetal force—no additional forces are needed.

Question 10

1. The satellite must have a larger orbital speed (correct answer)
2. The satellite must have a smaller orbital speed
3. The satellite must fire thrusters continuously to prevent falling inward
4. No change is needed because the centrifugal force increases automatically

Explanation: This question tests understanding of the motion of orbiting satellites. For circular orbits, gravitational force equals centripetal force: GMm/r² = mv²/r, giving orbital speed v = √(GM/r). If the planet's mass M increases while radius r stays constant, the orbital speed must increase proportionally to √M. A more massive planet exerts stronger gravity at the same distance, requiring the satellite to move faster to generate sufficient centripetal acceleration. Choice C incorrectly suggests continuous thrust is needed, but once at the correct speed, gravity alone maintains the orbit. The key principle is that orbital speed increases with planet mass: v ∝ √M at fixed radius.

Question 11

1. It would continue in a straight line tangent to the orbit at P (correct answer)
2. It would spiral outward due to centrifugal force
3. It would move radially outward away from Earth
4. It would remain in the same circular orbit due to inertia

Explanation: This question tests understanding of the motion of orbiting satellites. Newton's first law states that an object in motion continues with constant velocity unless acted upon by a net force. If Earth's gravity suddenly vanished, the satellite would no longer experience the centripetal force keeping it in circular motion. Without this inward force, the satellite would continue moving in the direction it was traveling at point P—tangent to the orbit, in a straight line northward. Choice B incorrectly invokes centrifugal force, which is fictitious, and choice D violates Newton's first law by suggesting circular motion without force. The key principle is that removing the centripetal force causes motion to continue tangentially in a straight line.

Question 12

1. North, because gravity acts along the motion
2. Toward Earth's center, because gravity provides centripetal acceleration (correct answer)
3. Away from Earth's center, due to centrifugal force
4. Zero, because the speed is constant in a circular orbit

Explanation: This question tests understanding of the motion of orbiting satellites. In circular motion, acceleration always points toward the center of the circle, regardless of the velocity's direction. For a satellite orbiting Earth, the gravitational force provides the centripetal acceleration, which must point toward Earth's center. Even though the satellite's speed remains constant in a circular orbit, its velocity direction continuously changes, requiring a centripetal acceleration. Choice D incorrectly assumes that constant speed means zero acceleration, but acceleration includes changes in direction, not just speed. The strategy is to remember that in circular motion, acceleration always points toward the center, perpendicular to the velocity.

Question 13

1. The satellite's inertia pushes it outward, balancing gravity
2. Gravity provides an inward (centripetal) net force toward Earth's center (correct answer)
3. A tangential gravitational force continuously speeds it up along the path
4. The satellite must use thrust forward to avoid falling inward

Explanation: This question assesses the concept of the motion of orbiting satellites in AP Physics 1, focusing on the force responsible for maintaining circular orbits. The gravitational force between the satellite and Earth acts as the centripetal force, directed inward toward Earth's center. This force provides the necessary acceleration to change the direction of the satellite's velocity, keeping it in a circular path without changing its speed. For a circular orbit, the centripetal force requirement is met exactly by gravity, ensuring stable motion. A common distractor is choice A, which incorrectly invokes inertia as an outward force, but inertia is not a force and does not balance gravity. A transferable strategy is to always identify the source of the centripetal force in circular motion problems and equate it to mv²/r.

Question 14

1. A smaller orbital speed, because stronger gravity pulls it around more easily
2. The same orbital speed, because radius alone determines circular motion
3. A larger orbital speed, because stronger gravity requires greater centripetal acceleration (correct answer)
4. Continuous thrust outward to balance the increased inward gravity

Explanation: This question examines the motion of orbiting satellites in AP Physics 1, considering effects of planet mass on circular orbits. Gravitational force GMm/r² provides centripetal force mv²/r, so v = √(GM/r). Larger M increases v for the same r, as stronger gravity requires greater centripetal acceleration via higher speed. The orbit remains circular with adjusted speed. Choice A wrongly suggests smaller speed, but stronger gravity demands faster motion to prevent falling inward. Derive the orbital speed equation from force balance to predict changes in parameters like mass or radius.

Question 15

1. Displacement is radial; gravity is tangential
2. Displacement is tangent; gravity is radial inward (correct answer)
3. Both displacement and gravity are tangent
4. Both displacement and gravity are radial outward

Explanation: This question examines the geometric relationship between displacement and force in orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. Over a short time, the satellite's displacement is tangent to the orbit (in the direction of velocity), while gravitational force points radially inward toward the planet's center. These directions are perpendicular, which explains why gravity does no work on the satellite. Choice A incorrectly reverses the directions. When analyzing orbital motion geometry, recognize that displacement is tangential while gravitational force is radial.

Question 16

1. It would double
2. It would quadruple (correct answer)
3. It would halve
4. It would become zero

Explanation: This question examines how speed changes affect centripetal acceleration requirements. In circular orbit, gravitational force provides the centripetal force required for circular motion. The required centripetal acceleration equals v²/r, so doubling the speed at the same radius increases the acceleration requirement by a factor of (2v)²/r = 4v²/r, which is four times the original value. This demonstrates the quadratic relationship between speed and acceleration in circular motion. Choice A incorrectly suggests a linear relationship. When speed changes in circular motion, apply the v²/r relationship to find that acceleration changes as the square of the speed change.

Question 17

1. $\Delta \vec{v}$ points tangent to the orbit
2. $\Delta \vec{v}$ points radially inward (correct answer)
3. $\Delta \vec{v}$ points radially outward
4. $\Delta \vec{v}$ is zero because speed is constant

Explanation: This question examines the direction of velocity change in circular orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. Over a short time, the change in velocity Δv points in the same direction as the acceleration, which is radially inward toward the center. Although the velocity vector is tangent to the orbit, the change in velocity vector points toward the center because the velocity is turning inward. Choice A incorrectly suggests Δv is tangent to the orbit. When finding velocity change direction, recognize that Δv points in the acceleration direction, which is centripetal (inward).

Question 18

1. Its speed increases, changing the required centripetal force (correct answer)
2. Gravity becomes tangential and stops pointing inward
3. A centrifugal force appears and cancels gravity
4. Its acceleration becomes zero because thrust replaces gravity

Explanation: This question examines the immediate effects of tangential thrust in orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. When the satellite's engines provide thrust in the direction of motion, the satellite's speed increases immediately. This increased speed changes the required centripetal force from mv²/r to m(v+Δv)²/r, creating a mismatch with the available gravitational force. Choice B incorrectly suggests gravity changes direction, but gravitational direction depends only on position. When tangential thrust is applied, the immediate effect is increased speed, which changes the force balance needed for circular motion.

Question 19

1. A tangential gravitational force in the direction of motion
2. An outward centrifugal force that balances gravity
3. A net inward gravitational force directed toward the planet's center (correct answer)
4. A forward thrust force that keeps the satellite from falling

Explanation: This question tests understanding of motion of orbiting satellites. For any object in circular motion, a net inward force is required to continuously change the direction of velocity, and for satellites, this force is gravity. The gravitational force from the planet acts radially inward toward the planet's center, providing the centripetal force needed to maintain circular motion. Choice A is incorrect because gravitational force always points toward the planet's center, never tangentially. The key strategy is to remember that gravity provides the centripetal force for orbital motion, always pointing toward the center of the orbit.

Question 20

1. It must increase in magnitude and still point toward the planet's center (correct answer)
2. It must decrease because faster motion reduces the need for inward force
3. It must become tangential to keep the moon moving faster
4. It must point outward to prevent the moon from spiraling inward

Explanation: This question probes the motion of orbiting satellites in AP Physics 1, examining net force changes with speed in circular orbits. Gravitational force acts as centripetal force, but if speed increases at fixed r, required centripetal force mv²/r increases. Therefore, net force must increase in magnitude while remaining directed toward the center to maintain the orbit. Gravity would need to adjust, but in practice, speed and radius are linked for stable orbits. Choice B is incorrect, as faster speed actually increases the centripetal force requirement, not decreases it. Always use the centripetal force formula mv²/r to analyze how changes in v or r affect the needed force.