Week 5 Wed. Orbits and Gravity OpenStax Astronomy Ch. 3

Johannes Kepler and the Laws of Planetary Motion

Kepler used decades of Tycho’s observations in his mathematical calculations, to determine the shape of the planetary orbits, and the speed of the planets as they went around the Sun. This massive effort resulted in three major statements about the characteristics of planetary orbits: Kepler’s three laws of planetary motion.

Kepler’s three laws of planetary motion Orbital paths of the planets are ellipses. An imaginary line connecting the planet with the Sun sweeps out equal areas of the ellipse in equal intervals of time. The square of a planet’s orbital period is proportional to the cube of its semi-major axis. Kepler published this in 1609, the same year that Galileo built his first telescope.

Kepler’s laws of planetary motion Kepler’s first law: The orbital paths of the planets are elliptical, with the Sun at one focus. Kepler’s second law: An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time. Kepler’s third law: The square of the planet’s orbital period is proportional to the cube of its semimajor axis.

An Ellipse can be drawn with string and TWO foci

For an ellipse, r1 + r2 = 2a The eccentricity is defined as: e = c/a A circle results when e = 0 Ellipse demonstration: https://www.intmath.com/plane-analytic-geometry/ellipse-interactive.php UNL demonstration: http://astro.unl.edu/naap/pos/animations/kepler.html Interactive Graph https://www.intmath.com/plane-analytic-geometry/ellipse-interactive.php

Some Properties of Planetary Orbits

Key terms for orbits Perihelion – the point in the orbit that is closest (peri-) to the Sun (helios). Aphelion – the point in the orbit that is furthest from the Sun. Then for the orbits of the Moon and spacecraft: Perigee – the point in an orbit around the Earth that is closest to Earth. Apogee – the point in an orbit around the Earth that is furthest from Earth. Semimajor axis – half (semi) of the longest (major) line (axis) across the ellipse

Kepler’s laws of planetary motion Kepler’s first law: The orbital paths of the planets are elliptical, with the Sun at one focus. Kepler’s second law: An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time. Kepler’s third law: The square of the planet’s orbital period is proportional to the cube of its semimajor axis.

Kepler’s Second Law: equal areas in equal time This also means higher speed at closer distances.

Another graphic on Kepler’s Second Law: See: http://astro.unl.edu/naap/pos/animations/kepler.html

The Astronomical Unit is about 150,000,000 km

Kepler’s laws of planetary motion Kepler’s first law: The orbital paths of the planets are elliptical, with the Sun at one focus. Kepler’s second law: An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time. Kepler’s third law: The square of the planet’s orbital period is proportional to the cube of its semimajor axis.

Kepler’s Third Law: P2 (in years) = a3 (in a. u Kepler’s Third Law: P2 (in years) = a3 (in a.u.) Basically, it means that large orbits have long periods. The data are easier to understand if we use years and A.U.