Inspired by recent messages about tidal bulges, especially by those from
Donald Semanek, I took Interactive Physics and created a nice demo. It
does simulate tides withou rotation. My moon, M, is a square "nailed" to
the universe at x=y=0. My "earth", E, is also a square; it falls towards
M along the x axis (gravitational attraction). "Oceans", O1 (left) and
O2 (right), are column-like rectangles; they are attached to E with springs
and dampers, one set on each side. The bulges grow as the distance between
M and E decreases. I see this from the three position meters associated
with O1, M and O2.
I do not have time to optimize this very crude simulation system but it
does show TWO "bulges". Without springs and dampers O1 and O2 fall to E
before E hits M (sandwiching one ocean). Springs make oceans ocsillate
and I was forced to add dampers.
Ludwik Kowalski
WHAT FOLLOWS SHOULD BE CLEAR TO THOSE WHO ARE FAMILIAR WITH THE SOFTWARE
CALLED INTERACTIVE PHYSICS.
view size, 1.8*10^9 meters (all units are SI)
gravity was planetary, G=6.7*10^-7
air resistance was "none"; electrostatics, was "off".
Mass of the M was 10^27 (yes, much more than the mass of E)
Mass of E was 2*10^24, mass of each ocean 2*10^24 (yes, same as for E)
Spring constants (Hooke's law) were 10^22 each.
Damper constant (F=k*v) were 10^6 each.
Numbers and Units "4" and "SI"
Initial velocities zero
Initial position of O1 (center) x=5*10^8
Initial position of M (center) x=6*10^8
Initial position of O2 (center) x=7*10^8
Accuracy "accurate" and "1 second". (M is touched at t=600 s)
The initially "bilges", as shown above, were 10^8 m. At t=577 s (before
hitting M) the left bulge (closer to M) was 10.8*10^8 while the right
one was 10.4*10^8.