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Learning Goal

Part of: Newton's Law of Gravitation — 1 of 2 chapter items

Kepler's Laws of Planetary Motion

7.1

"Based on the motion of the planets about the sun, Kepler devised a set of three classical laws, called Kepler's laws of planetary motion, that describe the orbits of all bodies satisfying these two conditions: 1. The orbit of each planet around the sun is an ellipse with the sun at one focus. 2. Each planet moves so that an imaginary line drawn from the sun to the planet sweeps out equal areas in equal times. 3. The ratio of the squares of the periods of any two planets about the sun is equal to the ratio of the cubes of their average distances from the sun." "The planet's closest approach to the sun is called perihelion and its farthest distance from the sun is called aphelion." "where T is the period (time for one orbit) and r is the average distance (also called orbital radius). This equation is valid only for comparing two small masses orbiting a single large mass. Most importantly, this is only a descriptive equation; it gives no information about the cause of the equality."

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"Based on the motion of the planets about the sun, Kepler devised a set of three classical laws, called Kepler's laws of planetary motion, that describe the orbits of all bodies satisfying these two conditions:

  1. The orbit of each planet around the sun is an ellipse with the sun at one focus.
  2. Each planet moves so that an imaginary line drawn from the sun to the planet sweeps out equal areas in equal times.
  3. The ratio of the squares of the periods of any two planets about the sun is equal to the ratio of the cubes of their average distances from the sun."
    "The planet's closest approach to the sun is called perihelion and its farthest distance from the sun is called aphelion."
    "where T is the period (time for one orbit) and r is the average distance (also called orbital radius). This equation is valid only for comparing two small masses orbiting a single large mass. Most importantly, this is only a descriptive equation; it gives no information about the cause of the equality."

What you'll learn

  1. State and explain Kepler's three laws of planetary motion
  2. Identify the two conditions an orbiting system must satisfy for Kepler's laws to apply
  3. Describe the anatomy of an elliptical orbit — foci, perihelion, aphelion, semi-major and semi-minor axes, eccentricity
  4. Apply Kepler's first law (constant focal-distance sum) to find unknown distances in an orbit
  5. Apply Kepler's second law and the ellipse-area formula A = πab to relate area swept to elapsed time, and explain why orbital speed varies
  6. Apply Kepler's third law (T₁²/T₂² = r₁³/r₂³) to relate the periods and orbital radii of two satellites of the same parent body

Slides

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