RANDY L. PHELPS
This is the Celestial
Mechanics Module
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Procedure
1. For this module, please look through the
"lecture" notes for "Celestial Mechanics". These notes contain the
material, in condensed form, that I will expect you to become familiar with. I am
sure you will have questions about the material, especially since it is presented in the
form of lecture notes. To help you fill in the blanks, I have added web links that
you can follow, in order to gain further insight into the material.
2. Additionally, you should complete the
following Web exercise to help you understand the material, and reinforce the concepts:
Web-Exercise 1: Newton's Cannon
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Upon completing
this assignment, you should be comfortable with the following material:
- Definitions and Concepts: Properties of conic
sections, specifically circles and ellipses
- Kepler’s Laws: What are Kepler’s Laws?
Various ways to use Kepler’s 3rd Law
- Newton’s Laws: What are Newton’s Laws of
Motion? What is Newton’s Law of Gravity? How can it be shown that the laws are
Universal?
- Energy: Kinetic, Potential and Total Energy.
- Orbits: Circular Orbits, Circular Velocity, Escape
Velocity, Interplanetary Trajectories.
Upon completing
this assignment, you should be able to answer these, and similar questions
General
Concepts
- What are the characteristics of ellipses, parabolae and hyperbolae?
- What are the unique characteristics of an ellipse with zero eccentricity?
- What do each of "Kepler's Laws of Planetary Motion" say?
- Which planet did Kepler use to determine his "Laws of Planetary
Motion", and why was his choice fortuitous?
- What do each of "Newton’s Laws of Motion" say?
- Which orbits the Sun with a longer period, an inner planet or an outer
planet?
- What is an acceleration?
- Does the acceleration of an object at the Earth's surface depend on how
massive it is?
- Does an object moving in a circular orbit, with constant speed,
accelerate?
- What will happen to a satellite given the so-called "circular
velocity"?
- If a satellite receives just less than the circular velocity, what will
happen to it?
- Where, in a planet's orbit around the Sun, is it located when it is at
perihelion?
- What quantities must be known in order to calculate a satellite's orbit?
- What is the mathematical form of "Newton's Law of Gravity"?
- What is the mathematical form of the equation describing gravitational
potential energy?
- What is the mathematical form of the equation describing kinetic energy?
Applications
- If two objects, with equal masses are moved twice as far from each other,
how does the force of gravity between them change?
- If two objects, with equal masses are moved three times as far from each
other, how does the force of gravity between them change?
- If two objects have equal masses, and one is replaced with a mass twice
as great, how does the force of gravity between them change?
- If two objects have equal masses, and one is replaced with a mass four
times as great, how does the force of gravity between them change?
- Explain in detail how the falling of an apple and the orbit of the Moon
demonstrate that the force of gravity is universal?
These questions, and similar ones, will form the basis of the exam
material for this section of the course. If you have problems with the material,
please see me. If you are unable to answer some of the questions, I will help
you before the date specified on the syllabus, provided you show me the results of your
inquiry into the material.
That is, you must provide me the answers you
we able to obtain for all questions, including your attempts at problem questions, before
I will help you with any of them!
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