Astronomy

Homework

# Scholars Online Astronomy - Chapter 4: 5-8: Kepler's Elipses and Newton's Gravity

## Homework

Reading: Astronomy, Chapter 4: Gravitation and the Motions of the Planets, sections 5-8

• Section 5: Galileo's observations of the phases of Venus, the craters of the moon, sunspots, and the moons of Jupiter effectively contradicted Aristotelian assumptions of perfect, unchanging matter moving with uniform circular motion around the earth.
• Section 6: Newton provided a physical explanation for Kepler's observations in three laws of motion describing inertia, the relationship between force and acceleration (F = ma) and the interaction of forces (the equal and opposite force rule).
• Section 7: Newton's universal law of gravitation describes a fundamental property of matter: all matter attracts all other matter, with a force dependent on the mass of each object and the distance between them: F = GMm/r2.
• Section 8: Gravitational forces will distort objects that are not rigid solids by acting with different amounts of force on the near and far sections of the object. This is how the moon causes tides in earth's oceans, and how galaxies distort one another.
• 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

Kepler's Third Law

• Simple form for planets orbiting the sun, period in Earth years and distances in astronomical units (AU):
• Newtonian form, all situations, period in seconds, distances in meters, masses in kg (to match units of G);

Newton's law of gravity:

Escape velocity:

### Web Lecture

Read the following weblecture before chat: Aristotle, Ptolemy, Copernicus, Brahe, Kepler, Galileo, Newton: steps to planetary theory

### Study Activity

Your Planetarium Program: Center the planetarium on Jupiter and set it to display the locations of the four Galilean moons at 9pm for any night in October 2018. "Observe" their motions by advancing the planetarium one day at a time for at least five days. Draw a diagram of the position of each moon each day relative to Jupiter. Can you determine the periods of the moons from your observations? Can you see all four moons for each observation?

Optional websites: Planetary Motion by Heather Welch.

Follow the directions to place your planet anywhere on the screen and then give it an intial velocity (speed and direction).

• Try to put the planet in a stable orbit (one where the ellipse or circl repeats itself).
• Try to put your planet in a parabolic orbit (extreme ellipse), and note the behavior when the planet is at perhelion and aphelion.
• Try to put your planet in a hyperbolic orbit. What happens to the planet?

### 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

• Required: Complete the Mastery exercise with a passing score of 85% or better.
• Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

### 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.