Homework

# Scholars Online Astronomy - Chapter 4: 1-4: Planetary Orbits

## Homework

Reading: Astronomy, Chapter 4: Gravitation and the Motions of the Planets

• Section 1: Geocentric models dominated the Greek and Roman accounts of stellar motion, especially the theories of Eudoxus, Aristotle, and Ptolemy, who had to account for prograde and retrograde motion, differences in the apparent speed of the planets even in prograde motion, and changes in the brightness of the planets.
• Section 2: Copernicus' heliocentric model addressed the above issues by changing the relative positions of the sun and earth.
• Section 3: Brahe's observations of the supernova of 1572 and the comet of 1577 proved that stars changed and there were no physical spheres separating the planetary orbits.
• Section 4: Kepler effectively destroyed the last premise of classical and medieval astronomy by showing that planets move in ellipses with the sun at one of the foci, that their velocity varies so that a line from the sun to the planet sweeps out equal areas in equal times, and that the period of the planet's orbit around the sun and radial distance of a planet from the sun are related as p2 = a3.
• Box 2: Kepler's third law: p2 = a3 works providing we use consistent units (years and AU); otherwise we need a constant.This is where we get into the nitty gritty about observations.

### Key Formulae to Know

Synodic (phase to phase as seen from Earth S) and Sidereal periods (complete revolution on orbit P)

• Inferior planets: add synodic and Earth inverses to get period inverse
• Superior planets: subtract synodic inverse from Earth's inverse to get period inverse
• Kepler's Third Law:

Simple form for planets orbiting the sun, period in Earth years and distances in astronomical units (AU):

### Web Lecture

Read the following weblecture before chat: Aristotle, Ptolemy, Copernicus, Brahe: First steps to planetary theory, sections 1-4

### Study Activity

Planetarium program: Set up Stellarium so that you are looking south and use the controls at the bottom of the window to turn off atmosphere and horizon. Then wind the clock back to July 15, 2020, at midnight and pause the clock advance. Leave the date-and-time window visible (you may want to move it to the top of the page). Find and select Mars (just on or below the East horizon) and center it in your screen. Then hit "Shift-T". This turns planet tracking on. Now start moving through time by holding down the arrow above the day in the date-and-time display. Advance until at least Jan 1, 2021. What happens?

UNL Tools Exercises

• Interactives:
• Use the Gravity Interactive tasks to explore the the concept of gravity.
• Use the Kepler's Law tasks to explore how Kepler's Three Laws work.
• ClassAction:
• Use Renaissance Astronomy to explore how Copernicus, Kepler, and Newton changed our view of the solar system and the forces holding planets in place. Save the Gravity questions for next time. There are a lot of questions here, so try to discover what you don't know or have a hard time visualizing, and bring questions to class!
• NAAP Labs:
• Select the Solar System Models. Read Basic Observations, Elongation, and Early Modeling, then select the Ptolemaic System Simulator.
• The simulation defaults ot Mars. Start the animation. What pattern does the planet describe over time? Where is the sun as Mars moves around Earth?
• Select one of the outer planets (Mars, Jupiter, Saturn), and rerun the animation. What happens to the pattern? Where is the sun as this outer planet moves around earth?
• Can this model account for change in brightness (planet moves nearer/farther from earth)?
• Can this model account for stationary and retrograde motion?
• Can this model account for variation in the rate of progress of the planet relative to the background sky as seen from earth?
• Now under the Heliocentric Model, read about Heliocentricism, Elongations and Configurations. Then start the Planetary Configurations simulator.
• Allow the simulation to run for Mars. Where is it at maximum east and west elongation? At conjunction and opposition?
• Can this model account for change in brightness (planet moves nearer/farther from earth)?
• Can this model account for stationary and retrograde motion?
• Can this model account for variation in the rate of progress of the planet relative to the background sky as seen from earth?

### Chat Preparation Activities

• Essay question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
• Go over the list of Key Words and Key Ideas at the end of the chapter. If you don't remember the definition of the key word, review its use (the page number on which it is explained is given).
• Read through the Review Questions and be prepared to discuss them in class. If any of them confuses you, ask about it!
• Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

### Chapter Quiz

• There is no chapter quiz yet -- we haven't finished the chapter.

### Lab Work

Read through the lab for this week; bring questions to chat on any aspect of the lab, whether you intend not perform it or not. If you decide to perform the lab, be sure to submit your report by the posted due date.