Kepler’s Laws

Kepler’s Laws of Planetary Motion Kepler started as an assistant to Danish astronomer Tycho Brahe. Using instruments called quadrants, Brahe measured the positions of planets so accurately that his measurements are still valid today. Brahe headed the world’s first great observatory in Denmark, prior to the telescope. After Brahe’s death, Kepler devoted many years of his life to the analysis of Brahe’s measurements.

Kepler’s Laws of Planetary Motion Tycho Video Brahe headed the world’s first great observatory in Denmark, prior to the telescope.

Johannes Kepler (1571-1630) Kepler’s Laws of Planetary Motion Recall that: Kepler expected circular orbits a small discrepancy led him to ellipses… Johannes Kepler (1571-1630) After Brahe’s death, Kepler devoted many years of his life to the analysis of Brahe’s measurements. 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

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

Kepler’s Laws of Planetary Motion Kepler also found that the planets don’t go around the sun at a uniform speed but move faster when they are nearer the sun and more slowly when they are farther from the sun.

Kepler’s Second Law: A line that connects a planet to the sun sweeps out equal areas in equal times.

Kepler’s Laws of Planetary Motion Kepler’s Third Law After ten years of searching for a connection between the time it takes a planet to orbit the sun and its distance from the sun, Kepler discovered a third law.

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 orbit at faster speeds.

Kepler’s Laws of Planetary Motion The ratio is the same for all planets. If a planet’s period is known, its average orbital radial distance is easily calculated. Kepler’s laws apply not only to planets but also to moons or any satellite in orbit around any body.

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).

Kepler’s Laws of Planetary Motion Kepler was the first to coin the word satellite. He had no clear idea why the planets moved as he discovered. He lacked a conceptual model.

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