* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Orbital Geometry Notes
International Ultraviolet Explorer wikipedia , lookup
Circumstellar habitable zone wikipedia , lookup
Astrobiology wikipedia , lookup
Copernican heliocentrism wikipedia , lookup
History of astronomy wikipedia , lookup
Aquarius (constellation) wikipedia , lookup
Rare Earth hypothesis wikipedia , lookup
Equation of time wikipedia , lookup
Dialogue Concerning the Two Chief World Systems wikipedia , lookup
Planets beyond Neptune wikipedia , lookup
Directed panspermia wikipedia , lookup
Geocentric model wikipedia , lookup
Late Heavy Bombardment wikipedia , lookup
Extraterrestrial life wikipedia , lookup
Planets in astrology wikipedia , lookup
Kepler (spacecraft) wikipedia , lookup
Tropical year wikipedia , lookup
Satellite system (astronomy) wikipedia , lookup
Definition of planet wikipedia , lookup
Planetary system wikipedia , lookup
Exoplanetology wikipedia , lookup
IAU definition of planet wikipedia , lookup
Astronomical unit wikipedia , lookup
History of Solar System formation and evolution hypotheses wikipedia , lookup
Solar System wikipedia , lookup
Formation and evolution of the Solar System wikipedia , lookup
Orbital Geometry Johann Kepler • In 1600, Johann Kepler developed his “Laws of Planetary Motion.” He observed that the planets traveled in closed curves (ellipses), rather than circular paths. Ellipses • The center of an ellipse differs from a circle in that there are two fixed points (foci) rather than one. • Kepler's first law: the orbits of the planets around the sun are ellipses, with the Sun at one of the foci. • The eccentricity of an ellipse can be thought of as the degree of nonroundness, or ovalness, of the orbit. Eccentricity = distance between foci/length of major axis • e = d/L • The smaller the eccentricity, the more circular the orbit. The Solar System • Looking at the Solar System Data table, most of the planets have fairly circular orbits (low eccentricities) with the exception of Mercury. The Earth’s Orbit • The earth actually receives 7% less radiation in the summer of the northern hemisphere than the winter! Why is it warmer here in the summer? Other Solar Systems Comet Eccentricities Kepler’s Second Law • An imaginary line joining a planet to the Sun will sweep over equal areas in equal periods of time. • The consequence of this: planets travel faster when they are closest to the sun, and slower when they are farther away. • Closest point: perihelion (Jan 3) Farthest point: aphelion (July 4) • At the perihelion, kinetic energy is at a maximum, potential energy a minimum. At the aphelion, the opposite is true. Kepler's Third Law • The square of any planets period of revolution (orbital period) T2 is proportional to the cube of the mean radius (R3) • In other words, farther the planet is from the sun, the larger the orbit and the longer its period. • The mean radius is expressed in astronomical units (AU) • 1 AU equals 150,000,000 km, or 1 earth-sun radius • This is a function of Newton’s Law of gravitation. Find the eccentricity of each of the following ellipses: Lab 4 Ellipses