Historical Models of our Solar System and Kepler’s Laws of Planetary Motion

Geocentric Model Earth is center of our Solar System Aristotle- Over 2000 years ago, Unexplained on how planets appear to move backwards Ptolemy- Planets move in small circles or epicycles

Heliocentric Model Sun is center of our Solar System Copernicus- Over 450 years ago (1543 ad) First to suggest heliocentric theory and vaguely mapped out the planets orbiting the sun in a circular orbit. Theory published on his deathbed. Initially not supported and took over 50 years for it to be accepted. Now backwards motion of planets (retrograde) was explained.

Galileo Supporter of Copernicus’s Heliocentric theory House arrest Observed moons orbiting Jupiter and theorized objects can revolve around other planets not just Earth placed under house arrest and was forced to denounce theory or be executed

Solar System precisely measured Tycho Brahe- studied Solar System and made very accurate recordings of his observations Tycho’s assistant, Kepler, used information for the details of orbits Tycho’s published recording of the solar system not used by Kepler until after Tycho’s death

Kepler’s Laws of Planetary Motion 1st Law - Law of Ellipses Each planet orbits the sun in a path called an ellipse or elongated circle Ellipse is a closed curve whose path is determined by 2 points or foci within the ellipse Focus 1 is the Sun and Focus 2 is an imaginary point Semi-major axis = average distance from sun (AU); ½ major axis 1st Law) Law of Ellipses Each planet orbits the sun in a path called an ellipse or elongated circle Ellipse is a closed curve whose path is determined by 2 points or foci within the ellipse (circle use 1 point or focus ) One focus or point is located within the sun The other focus or point is not within an object The major axis runs through both foci points and the semimajor axis is the planet’s average distance from the sun

Eccentricity Degree of elongation or shape of planet’s orbit Ratio between the foci and length of major axis Circular =0 Very elongated =1 Elliptical orbits can vary in shape and can be described in terms of Eccentricity (e) Eccentricity is the degree of elongation or shape of a planet’s elliptical orbit. It is the ratio of the distance between the foci and the length of the major axis. circular =0 and extremely elongated e=1

2nd Law – Law of Equal Areas An imaginary line between the Sun and a planet sweeps out equal areas in equal times as the planet travels around the ellipse. Perihelion planet is closest to the sun, Aphelion planet is furthest away from sun

3rd Law – Law of Periods Mathematical relationship P2 = a3 a= semi-major axis (planets average distance from Sun measured in AU’s) p= planet’s orbital period (time) We can predict the period of rotation if we know the length of the semimajor axis Or we can predict the length of the semimajor axis if we know the period of rotation

Newton Used Kepler’s Laws of planetary motion and published Principia for short. In this publication, considered to be the greatest piece of scientific literature ever written. Contains Newton’s laws of motion including universal gravitation.

Einstein (1879-1955) Changed Newton’s gravitational theory based on findings of Mercury’s orbit. Developed Theory of Relativity. It completely changed the way we study gravity and even changed our understanding of the universe. Theory of relativity- gravitational mass is identical to inertial mass. Einstein’s theory of general relativity is based on the idea that we live in a four dimensional universe called space-time. It tells us that all matter shapes space-time by curving it, so to speak, and that these curves determine how matter moves through space-time. In other words, the orbits of the planets are not caused by a direct attraction to the Sun, they simply follow straight lines in curved space.

Kepler’s Laws Simulations Click http://www.physics.sjsu.edu/tomley/kepler.html Bibliography http://www.astro.umass.edu/~myun/teaching/a100/images/geocentric.jpg http://www.physics.hku.hk/~nature/CD/regular_e/lectures/images/chap04/heliocentric.jpg http://www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/galileo5.jpg http://galileo.rice.edu/sci/brahe.html http://www.asu.cas.cz/~had/tycho.jpg http://cseligman.com/text/history/ellipse2.jpg http://www.windows.ucar.edu/the_universe/uts/kepler3_small.gif http://library.thinkquest.org/27585/frameset_intro.html http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/imgrel/merc.gif http://zebu.uoregon.edu/~soper/Orbits/eccentricity.gif http://www.physics.hku.hk/~nature/CD/regular_e/lectures/images/chap04/geocentric.jpg http://outreach.atnf.csiro.au/education/senior/cosmicengine/images/cosmoimg/keplerellipse.gif