Physics 502, Capstone Project I

This material can be found online at URL

http://spiff.rit.edu/classes/phys502/phys502.html

Progress

• Week 1: A simple check of theory vs. simulation.
  Place two masses in space, M1 and M2. Fix M2 in place so it cannot move. Place M1 at a starting distance D, at rest. At time t=0, release M1. Use numerical integration to simulate its motion at least as far as the close approach to M2; if possible, follow the motion to a second close approach to M2.

  Print out time, position, velocity, KE, GPE of M1 at each timestep. Compare the values at the first 10 timesteps to the (exact) values you derive from theory. How well do they agree?

• Week 2:
• Earth, Sun, real gravity. Start Earth motionless, release. Use timesteps of 1 hour, 1 minute. Graph pos vs. time, total energy vs. time, total energy vs. correct (from theory) energy.
• Earth, Sun, softened gravity: G M m / ( (abs(R)+alpha)^2 ) Start Earth motionless, release. Use timesteps of 1 hour, 1 minute. Graph pos vs. time, total energy vs. time, total energy vs. correct (from theory) energy. Investigate values of alpha: what is too SMALL a value? what is too BIG a value?
• Enhanced goal: write a 2-D version in which the Earth can move in both x-dir and y-dir.
• Week 3:
• Write a short report which describes the effect of softening parameter "alpha" on a 1-D simulation. Start Earth motionless, release. Use timesteps of 1 hour, 1 minute. Graph pos vs. time, velocity vs. time, total energy vs. time, (total energy - correct energy) vs. time. Include text and graphics. Use gnuplot to make graphs. Hand in hardcopy to my office by 5 PM, Thursday, Sep 18.
• Week 4: 2-D simulations; Earth in circular orbit around Sun.
  • Proper starting velocity to make circular orbit
  • Check over 1 orbit: in percentage terms ...
    • starting vs. ending position
    • starting vs. ending velocity
    • starting vs. ending total energy (KE + GPE)
    • choose timesteps of 1 day, 1 hour, 1 minute
  • hand in short report in hardcopy by Thursday at 5 PM
  • keep written notes in "time started ... time ended" for your work this week
• Week 5:
• Week 6:
• Re-write simulator from scratch, based on lessons learned so far; make more easily extensible
• Go to 3-D calculations
• make a series of tests with circular Earth orbits to verify that no new errors have crept in
• un-fix position of Sun
• make a series of tests with circular Earth orbits to verify that no new errors have crept in

(for next week??)

• add a third body
• make a series of tests with circular Earth orbits to verify that no new errors have crept in
• Week 7:
Using 3-D simulator with two bodies only (Earth and Sun), both of which are free to move
• write analysis program which reads in mass, position, velocity datafile
• make a series of tests with circular Earth orbits to verify that no new errors have crept in; use all 3 planes (x,y), (x,z), (y,z) orbits
• run for 100 or 1000 years;
  • compute change in total energy
  • compare singly-averaged method vs. doubly-averaged method

  Hand in hardcopy of status report by 5 PM on Thursday, Oct 16

  Hand in hardcopy of full report by 5 PM on Tuesday, Oct 21

  (for next week??)

• add a third body
• make a series of tests with circular Earth orbits to verify that no new errors have crept in
• Week 8:
• Week 9:
• Week 10: Presentation: Friday, Nov 7, 12:50 PM - 01:10 PM.
• Week 11: Paper due on Monday by 5 PM. Should be 5-7 pages long, and include a revised timeline for the Winter Quarter, with special attention for the first three weeks. All figures in the paper must either be produced by the student, or given full attribution with references. No figures from Wikipedia.

  Give paper hardcopy to advisor and to Cindy Drake by 5 PM, send electronic version to Franklin by 5 PM.

This page maintained by Michael Richmond. Last modified Sep 16, 2008.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.