Kepler’s Laws

Recall that Hired Kepler, to analyze the data. Tycho Brahe kept accurate records of planetary positions. Hired Kepler, to analyze the data. Remind students that one arcminute is equivalent to the width of a fingernail at arm’s length…

Also recall Johannes Kepler (1571-1630) He expected circular orbits a small discrepancy led him to ellipses… Johannes Kepler (1571-1630) Kepler quote offers a good opportunity to talk about the nature of science, and how failure to match observations should force a change in hour hypotheses…

Dr. Carl Sagan

An ellipse looks like an elongated circle What is an ellipse? Use this slide to review ellipses and the definition of eccentricity. An ellipse looks like an elongated circle

Kepler's Laws Kepler’s First Law: All planets move in elliptical orbits, with the sun at one focus.

Kepler’s Second Law: A line that connects a planet to the sun sweeps out equal areas in equal times. means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.

p = orbital period in years a = avg. distance from Sun in AU Kepler’s Third Law: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. p2 = a3 p = orbital period in years a = avg. distance from Sun in AU This means more distant planets orbit the Sun at slower average speeds, planets closer to the Sun obit at faster speeds obeying the relationship

Graphical version of Kepler’s Third Law Use these graphs to show the meaning of the equation for Kepler’s third law. Note: if your students are not too afraid of the math, show them why a planet’s average speed is 2πa/p (circumference of orbit divided by orbital period), then substitute from Kepler’s third law to show that speed is proportional to 1/√a so that they can understand the shape of the curve in (b).

Thought Question: An asteroid orbits the Sun at an average distance a = 4 AU. How long does it take to orbit the Sun? 4 years 8 years 16 years 64 years Hint: Remember that p2 = a3

An asteroid orbits the Sun at an average distance a = 4 AU An asteroid orbits the Sun at an average distance a = 4 AU. How long does it take to orbit the Sun? 4 years 8 years 16 years 64 years We need to find p so that p2 = a3 Since a = 4, a3 = 43 = 64 Therefore p = 8, p2 = 82 = 64