Notes from Independent Study Meeting
                      Feb 21, 2022

Present: Richmond, Dayal

  - Dayal shows results from calculations of sail + payload

          - basic calculation has small error in sign of gravitational
                 acceleration; please fix in future

          - assuming const acceleration, results are easy to do,
                 but not quite right
    
          - if try to solve varying accleration, hard to do analytically,
                 but can do it numerically
                 results pretty similar to "constant accel" assumption

  
  - the puzzle of orbits for a sail always face-on to Sun

          - Richmond said the results weren't right last week ...
                 but he was wrong.  Bad intuition!  
          
          - simulation was correct.  Good work!

          - the reason the orbit returns to starting place is that the
                 sail is always face-on to Sun, so force of photons
                 is always perpendicular to velocity.

          - in order to give (or take) energy to sail, the photon force
                 must have a component in same direction (or opposite 
                 direction) as the velocity

  - solution: tilt the sail

          - see Richmond's notes about forces on a tilted sail

          - only works if sail is REFLECTIVE.  That means basic force on
                 sail is twice as big as the purely absorbing sail

          - but there is also a term involving tilt angle "theta"
                 to account for decreased area of sail

          - and one must also compute the X and Y components of force
                 accounting for the tilt

          - Dayal modifies code to do so

          - first tests look okay

   

  - goals for next meeting (Thu, Feb 24): 
   
          - experiment with the thin-film sail, tilted at various angles
                 some positive theta
                 some negative theta

          - keep track of energy at end of simulation, compare to the
                 energy at start