Motion of Orbiting Satellites - AP Physics 1

1. A probe travels in a circular orbit around a planet. At the top of the orbit, its velocity points left. Which direction is the probe's acceleration at that instant?
   Answer: Downward, toward the planet's center 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.
2. A moon moves in a circular orbit around a planet. At point Z, its velocity is tangent east. Which statement about the moon's instantaneous acceleration vector is correct?
   Answer: It points toward the planet's center This question identifies the acceleration direction in circular orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. The moon's instantaneous acceleration vector points in the same direction as the net force, which is the gravitational force toward the planet's center. This centripetal acceleration continuously changes the velocity direction while maintaining constant speed. Choice A incorrectly suggests the acceleration is tangent to the orbit. When finding acceleration direction, identify the direction of the net force using Newton's second law.
3. A satellite of mass $m$ is in a circular orbit of radius $r$ around a planet. At point P, its velocity is tangent and points west. If the satellite's mass doubles (same orbit), what happens to its orbital speed?
   Answer: It remains the same because orbital speed at a given radius depends on the planet and $r$, not the satellite's mass 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.
4. A satellite moves in a circular orbit. At point R, its velocity is tangent east. Which is the best description of gravity's role in this motion?
   Answer: Gravity provides an inward force that continually turns the velocity 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.
5. A satellite of mass $m$ moves in a circular orbit of radius $r$ around a planet. At a point where its velocity is east, which is true about the satellite's acceleration at that instant?
   Answer: It is toward the planet's center because gravity provides centripetal acceleration This question tests understanding of motion of orbiting satellites. For any satellite in circular orbit, acceleration always points toward the center of the orbit, which is the planet's center. This centripetal acceleration is provided by the gravitational force, which also points radially inward, and its magnitude is GM/r² where G is the gravitational constant, M is the planet's mass, and r is the orbital radius. Choice A incorrectly states that acceleration follows velocity direction, but in circular motion, acceleration is perpendicular to velocity. The strategy is to remember that orbital acceleration always points toward the central body, providing the continuous direction change needed for circular motion.
6. A satellite moves in a circular orbit around Earth. At point P, its velocity is tangent and points north. If Earth's gravitational force on the satellite suddenly vanished, what path would the satellite follow immediately after P?
   Answer: It would continue in a straight line tangent to the orbit at P 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.
7. A satellite is in a circular orbit around a planet. At point V, its velocity is tangent east. Which statement about the net force is correct?
   Answer: It is radially inward and approximately constant in magnitude This question describes the characteristics of the net force in circular orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. The net force points radially inward toward the planet's center and has approximately constant magnitude for circular orbits (exactly constant for perfectly circular orbits around a point mass). This inward force provides the centripetal acceleration needed to maintain circular motion. Choice A incorrectly suggests the force is tangential, which would change the satellite's speed. To characterize forces in circular orbits, identify that the net force is radial, inward, and approximately constant in magnitude.
8. Two satellites travel in circular orbits around the same planet. Satellite 1 orbits at radius $r$, Satellite 2 at radius $2r$. At a point where both velocities are tangent, which satellite has greater centripetal acceleration?
   Answer: Satellite 1, because gravity is stronger at smaller radius This question tests understanding of motion of orbiting satellites. Centripetal acceleration in orbit equals GM/r², where G is the gravitational constant, M is the planet's mass, and r is the orbital radius. Since gravitational force (and thus centripetal acceleration) decreases with the square of distance, Satellite 1 at radius r experiences stronger gravity than Satellite 2 at radius 2r. Choice A incorrectly assumes that being farther means greater acceleration, when actually gravity weakens with distance. The key strategy is to remember that centripetal acceleration in orbit decreases as orbital radius increases.
9. A satellite is in circular orbit around Earth. At point U, its velocity is tangent north. Which statement about the gravitational force on the satellite at U is correct?
   Answer: It points toward Earth's center 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.
10. A satellite moves in a circular orbit of radius $r$ around a planet. At point V, its velocity is tangent west. If the satellite's speed increases while staying at radius $r$, what must happen to the net force magnitude?
    Answer: It must increase This question relates centripetal force to orbital speed changes. In circular orbit, gravitational force provides the centripetal force required for circular motion. The required centripetal force equals mv²/r, so if speed increases while radius stays constant, the required force increases proportionally to the square of the speed. Since gravitational force at radius r is fixed, the satellite cannot maintain circular orbit at the same radius with higher speed. Choice B would decrease the required force, contradicting the physics. When speed increases at fixed radius, the required centripetal force must increase according to F = mv²/r.
11. A satellite is in circular orbit. At point K1, its velocity is tangent west. Which force is responsible for the satellite's centripetal acceleration?
    Answer: Gravity toward the planet This question identifies the source of centripetal acceleration in orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. The satellite's centripetal acceleration is caused by gravitational force from the planet, which acts inward toward the planet's center. This gravitational force provides all the centripetal acceleration needed to maintain circular motion. Choice B incorrectly invokes centrifugal force, which is not a real force acting on the satellite. When identifying the cause of centripetal acceleration, recognize that gravitational attraction provides the necessary inward force.
12. A satellite moves in a circular orbit around a planet. At point A, its velocity is tangent south. Which vector best represents the net force on the satellite at A?
    Answer: A vector directed radially inward This question identifies the net force vector in circular orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. The net force must point toward the center of the circular path to provide the centripetal acceleration needed for circular motion. Since the satellite orbits the planet, the net force points radially inward toward the planet's center. Choice A incorrectly suggests the force is tangential, which would change the satellite's speed rather than its direction. To determine net force direction in circular motion, identify the center of the circular path and draw the force vector pointing inward.
13. A moon is in a circular orbit around a planet. At point W, its velocity is tangent east. Which description of the moon's motion is consistent with Newton's first law?
    Answer: It would move straight tangent if the inward force were removed This question applies Newton's first law to circular orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. According to Newton's first law, objects naturally move in straight lines at constant velocity unless a net force acts. The moon curves into circular motion only because gravitational force continuously pulls it toward the planet's center. Without this inward force, the moon would move straight tangent to its orbital path. Choice A incorrectly suggests no net force acts, but circular motion requires centripetal force. Apply Newton's first law by recognizing that curved motion requires a net force to change the natural straight-line motion.
14. A moon is in a circular orbit around a planet. At point R1, its velocity is tangent east. Which statement about the moon's motion is correct at that instant?
    Answer: It is accelerating toward the planet's center This question examines the nature of acceleration in circular orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. Even though the moon's speed is constant, it is accelerating because acceleration includes changes in velocity direction. The moon's velocity vector continuously changes direction as it moves around the orbit, requiring centripetal acceleration toward the planet's center. Choice B incorrectly equates constant speed with zero acceleration. When analyzing circular motion, remember that constant speed doesn't mean zero acceleration if the direction is changing.
15. A satellite is in a circular orbit of fixed radius around a planet. At point D, its velocity is tangent west. If the satellite's mass doubles (same orbit), what happens to its acceleration?
    Answer: It stays the same 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.
16. A satellite travels in a circular orbit of radius $r$. At point K, its velocity is tangent north. If the radius were reduced (same central body), which must be true for a new circular orbit?
    Answer: The satellite must move faster This question relates orbital radius to orbital speed requirements. In circular orbit, gravitational force provides the centripetal force required for circular motion. For circular orbits, the relationship v = √(GM/r) shows that smaller radius requires higher orbital speed. When the radius decreases, the gravitational field strength increases, requiring higher speed to maintain the balance between gravitational force and centripetal force needs. Choice A incorrectly suggests slower motion at smaller radius. When orbital radius changes, use the relationship that speed must increase as radius decreases for stable circular orbits.
17. A satellite moves in a circular orbit around Earth. At point E, its velocity is tangent east. Which statement about forces is correct at E?
    Answer: Gravity acts radially inward and is the net force This question clarifies the role of gravitational force in orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. Gravity acts radially inward toward Earth's center and is the only real force acting on the satellite (neglecting drag). This gravitational force provides all the centripetal force needed to maintain circular motion. Choice C incorrectly invokes centrifugal force, which is not a real force but an apparent force in rotating reference frames. To analyze forces in orbital motion, recognize that gravity alone provides the centripetal force with no need for additional real forces.
18. A satellite moves in a circular orbit. At point W, its velocity is tangent north. Which statement best addresses the misconception of "centrifugal force" for this satellite?
    Answer: No outward force is needed; the net real force is inward This question addresses the misconception of centrifugal force in orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. From an inertial reference frame, only real forces act on the satellite. The gravitational force provides the inward centripetal force, and no outward force is needed or exists. Centrifugal force is only apparent in the satellite's rotating reference frame and is not a real force. Choice A incorrectly treats centrifugal force as real and equal to gravity. To avoid centrifugal force misconceptions, analyze orbital motion from inertial reference frames where only real forces appear.
19. A satellite orbits a planet in a circular path. At point G, the velocity is tangent north. Which statement best explains why the velocity direction changes?
    Answer: An inward net force produces centripetal acceleration 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.
20. A satellite is in circular orbit. At point Y, its velocity is tangent south. If the satellite's speed is constant, what can be said about the work done by gravity over a small arc near Y?
    Answer: Gravity does approximately zero work because it is perpendicular to motion This question examines work done by gravity in circular orbital motion. In circular orbit, gravitational force provides the centripetal force required for circular motion. When the satellite moves along a small arc with constant speed, gravity is perpendicular to the displacement. Since work equals F·d·cos(θ) and θ = 90°, the work done by gravity is zero over any small arc. Choice A incorrectly suggests gravity does positive work by pulling forward, but gravity points radially inward, not tangentially. When calculating work in circular motion, recognize that centripetal forces are perpendicular to displacement and do zero work.

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