In this lab we will use the Orbit Simulator to study the motion 
of objects in orbit around one another.

Download the Simulator

   Startup MATLAB.

   Click on the link for orbit.m

   You can either use "Save As..." to save this in the work folder,
   or copy and paste it into a MATLAB m-file and save it in the
   work folder.  The name must be orbit.m

Running the Simulator

   Just type

      orbit

   and you will get a window with several fields you can fill out and
   two buttons.  To run a simulation, fill in the values
   for the fields and then click on "Go".  You will then see your
   objects in orbit.

   Explanation of Fields

      The fields in the upper-left-corner are for the ship.
      You can specify it initial position (X0,Y0) and initial
      Velocity and Angle (in degrees).  You can also specify
      the time-steps between calculations (leave it at 0.5 unless
      the results look too jumpy) and the total time of the
      simulation (start with 100, and increase it to see more).

      The big block of fields on the right are for the other objects:
      Planets.  You can use up to 10 planets for your ship to move around.
      For each planet you specify its radius (1 = radius of Earth),
      and its x and y position.  If you want it to move according to
      the law of gravity, you can make it movable (click on the button)
      and enter an initial velocity and angle.

      If the radius field is blank, then only the planets before that
      planet will be used.

   Try the Simulator with various values to get comfortable with
   how it works.

Assignments

   1. Use 1 planet, earth sized and start on the surface.  See what
      velocity and angle will get you off the surface.

   2. Use 1 planet, earth sized and start away from it.  Try to get
      starting values which produce an orbit.  If it doesn't make it
      all the way around, increase the max time.  Your orbit probably won't
      connect back to itself, but it might.

   3. Use 2 planets with the spaceship between them.  Try to get the ship to
      oscillate up and down, between the planets.

   4. Use 2 planets.  Try to get the spaceship to make an orbit like a 
      Figure 8.

   5. Use 2 planets, one smaller.  Make the smaller one moveable (like the
      Moon around the Earth).  Experiment with the spaceship to see if you
      can get some semi-stable orbits.

   6. Super Challenge Use up to 10 planets, have the spaceships path
      spell out your name.