Models of Motions in Our Sky (Power Point 02) Image Credit: Astropix.com

Student Learning Objectives Examine the contributions of ancient and modern astronomy to the understanding of gravity and planetary motion. Identify the significance of early contributions Compare and contrast models for the solar system Apply Kepler’s Laws to our Solar System

How did Greek philosophers describe motions in the sky? Basic Greek theories for the sky were based on an Earth based perspective. Heavenly bodies are spheres - move in circles Heavens are unchangeable Earth is stationary Earth at center Geocentric model

Early Science Aristotle (300 BC) used logic to determine Earth must be at the center. Eratosthenes (200 BC) calculated circumference of Earth using observation and geometry. Image Credit: sciencebuddies.org

Discussion Use your experience to explain why Aristotle would have assumed Earth was stationary and at the center of the system.

Hipparchus & Magnitudes Hipparchus (150 BC) began mapping the sky, and characterized stars according to their comparative brightness. Brightest 2nd Brightest 3rd Brightest Etc. We now call the comparative brightness apparent magnitude. Sun −26.7 Full Moon −12.6 Venus −4.4 Vega Naked Eye Limit +6 Binoculars Limit +10

Practice 1 Which would appear fainter to us when viewed from Earth with our eyes?   −4 magnitude star +4 magnitude star 0 magnitude star If two stars have the same energy output, what would make one star appear fainter than the other, when viewed from Earth?

The Epicylce Model Ptolemy (150 AD) developed an epicycle model to explain the “backwards” motion of Mars. Retrograde Motion http://www.lasalle.edu/~smithsc/Astronomy/retrograd.html

Ptolemy’s Epicycle Model https://www.youtube.com/watch?v=EpSy0Lkm3zM

Image Credit: slideshare.net Heliocentric Model Copernicus (1500’s) used mathematics/geometry to determine the Sun was much larger than Earth. Logically, the larger object must be at the center Sun centered system Image Credit: slideshare.net

Key Players & Their Models Stationary Earth Center Orbits Circles Orbital Speeds Same Method Aristotle   observation Ptolemy Copernicus mathematics Discussion Compare and contrast 2 of these models. What did all of these model have wrong?

One More Geocentric Tycho Brahe (1500’s) designed and utilized new instruments for measuring precise angles in the sky. Although Tycho Brahe believed in the geocentric system, his measurements were later used to provide proof for the heliocentric system https://www.youtube.com/channel/UCgdxVfxpAXcxtka1o3TD2Cg

1st Telescope Observations Galileo (1600’s) used a telescope to make observations that provided proof of the Sun centered system. Venus was seen to go through phases like the moon which provided proof for the location of the Sun relative to Venus.

Image Credit: wordpress.com

Galilean Moons Image Credit: commons.wikimedia.org

What are Kepler’s Laws? Kepler’s laws result in accurate predictions of future motion. Kepler (1600’s) used Tycho Brahe’s observations and measurements of planetary positions to develop three laws of planetary motion based on ellipses.

Planets move in elliptical orbits with the Sun at one focus Ellipses Kepler’s 1st Law Planets move in elliptical orbits with the Sun at one focus Image Credit: study.com

Equal Areas Kepler’s 2nd Law Planets sweep out equal areas of space in equal time intervals. Credit: www.wonderwhizkids.com

Orbital Period Kepler’s 3rd Law The orbital period of a planet is related to the semi-major axis of it’s orbit. (P2 = a3) Image Credit: Wikimedia commons

How do we measure birthdays? Practice 2 Apply Kepler’s Laws to our Moon. Which planet has the longer orbital period? Saturn: a = 9.54 AU Jupiter: a = 5.2 AU How do we measure birthdays? http://www.exploratorium.edu/ronh/age/index.html

The planets in our solar system follow orbits that are nearly circular. Image Credit: NASA

Circles vs Ellipses The elongation of the elliptical orbit is calculated as the eccentricity of the ellipse. (e = 0 to 1) Image Credit: NASA Earth Observatory

Credit: Windows to the Universe