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6.6Energy and Momentum of Rotating Systems

Motion of Orbiting Satellites — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 13 of 13 1 quiz

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Lesson summary

6.6 Motion of Orbiting Satellites — AP PHYSICS 1 notes: Describe the motion of two objects interacting only through gravity, using force, energy and angular momentum.Model — the satellite's mass is negligible compared with the central object, whose motion is taken as negligible (…

  • Centripetal force
  • Ug = −Gm1m2/r
  • Always negative
  • Circular orbit total energy
  • Definition
  • Orbital speed

Section 1 of 9Satellite–central object systems

Satellite–central object systems
Model
  • Model the satellite's mass is negligible compared with the central object, whose motion is taken as negligible.
    • (both really orbit a common centre of mass)
Types
  • Types natural satellites and artificial satellites.
    • (moons, planets, comets)
Free fall
  • Free fall astronauts feel weightless because they are in free fall.

Section 2 of 9Circular orbits

Centripetal force
  • Centripetal force gravity: GMm/r2 = mv2/r, so v = √(GM/r), independent of the satellite's mass.
Period
  • T = 2πr/v, giving T2 = (4π2/GM)r3 .
    • (Kepler's third law)
Constants
  • Constants total energy, gravitational potential energy, kinetic energy and angular momentum are all constant.
Work
  • Work gravity is perpendicular to the velocity and does no work.
Larger r
  • Larger r smaller speed, longer period, smaller gravitational force.

Section 3 of 9Gravitational potential energy and total energy

Gravitational potential energy and total energy
Ug
−Gm1m2/r
  • defined as the work to assemble the system from infinite separation; zero at infinity.
Always negative
  • Always negative for a bound system.
Circular orbit total energy
  • E = −GMm/(2r), whose magnitude equals the kinetic energy.

Section 4 of 9Elliptical orbits

Energy
  • Energy total mechanical energy is constant but Ug and K each change.
Speed
  • Speed greatest at closest approach and least at the farthest point.
Angular momentum
  • Angular momentum conserved because gravity acts along the line to the centre (zero torque): mv1r1 = mv2r2.
Work
  • Work gravity does work, transferring energy between K and U.

Section 5 of 9Escape velocity

Definition
  • Definition the speed for which the system's mechanical energy is zero.
Result
  • ½mvesc2 − GMm/R = 0, so vesc = √(2GM/R).
Behaviour
  • Behaviour a satellite at escape speed moves away until its speed reaches zero at infinite distance.

Section 6 of 9Analysing an elliptical orbit

1
Identify the system (satellite + central body) and note gravity exerts no torque about the central body.
2
Write conservation of angular momentum at two points: mv1r1 = mv2r2.
3
Write conservation of energy: ½mv12 − GMm/r1 = ½mv22 − GMm/r2.
4
Solve for the unknown speed or distance.
5
Check that the speed is larger at the smaller distance.

Section 7 of 9More from the specification

1Centripetal gravitational acceleration near Earth
  • Centripetal gravitational acceleration near Earth satellites in low circular orbits experience gravitational attractive forces directed toward Earth's centre of mass.
2Acceleration
  • Rate of change of velocity.
3Static friction
  • Friction between surfaces at rest relative to each other; fs ≤ μsFN.
4Gravitational field
  • Region where mass experiences gravitational force.
5Rotational inertia
  • Resistance to angular acceleration, I = Σmr2.
6Translational motion
  • Motion in which all points move with the same velocity.
7Slipping
  • Start of relative sliding between surfaces.
8Radius
  • Distance from the centre to the circular path.
9Friction
  • Force parallel to the surface opposing relative motion or its tendency.
10Linear
  • A graph that is a straight line through the origin, so resistance is constant.

Section 8 of 9Key terms

TermMeaning
Orbital speedv = √(GM/r) for a circular orbit.
Orbital periodT2 proportional to r3 (Kepler's third law).
Gravitational potential energyU = −GMm/r with zero at infinity.
Escape speedMinimum launch speed to reach infinity, √(2GM/R).
Elliptical orbitOrbit with constant E and L but varying speed.

Section 9 of 9Exam technique

1
Using the satellite's height instead of the distance from the centre for r.
2
Including the satellite's mass in the orbital speed.
3
Forgetting that Ug is negative for a bound system.
4
Assuming a satellite speeds up when it moves to a higher circular orbit.

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