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Cell["\<\
System of differential equations 
for motion of a planet along the axis 
of a binary star with small eccentricity ecc and initial phase phi0.
Choose units for which 2 G M = 1, average radius of orbits of stars is 1\
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Cell["\<\
Time parameters:
binary star year
number of years to evolve the system,
number of positions to save during each year\
\>", "Subsection",
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Cell["\<\

Binary star with circular orbit\
\>", "Subtitle",
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Cell["\<\
Values of parameters
Initial conditions for planet in the plane of the binary star (zstart = 0) \
with specified velocity zdotstart\
\>", "Subsection",
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Cell["\<\
Solve the system of differential equations numerically one year at a time for \
a total of  Nyear years,
saving the position z(t) of the planet Nsave times during each year.
Keep track of  each time the planet crosses the orbital plane of the binary \
star.\
\>", "Subsection",
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Cell["\<\
List the times when the planet crosses the plane of the binary star,
the time interval between crossings, 
and the maximum time interval.\
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Cell["\<\
Find the escape velocity (zdotstart) for ecc = 0 to 3 digits accuracy.
Plot the position of the planet as a function of time for a velocity above \
and a velocity below the escape velocity.
Show your results to the instructor.\
\>", "Subsection",
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Cell["\<\

Binary star with elliptical orbit with small eccentricity\
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Cell["\<\
Change the eccentricity to ecc = 0.1.
Set the initial velocity equal to the escape velocity for ecc = 0.
Plot z(t) as a function of t for 6 values of the initial phase phi0 ranging \
from 0 to 2 Pi.\
\>", "Subsection",
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Cell["\<\
Vary the initial phase phi0 and the initial velocity zdotstart, 
looking for solutions for which the time interval between the planet crossing \
the orbit of the binary star is as large as possible 
and for solutions for which the final crossing of the planet before escaping \
is as large as possible.  
Report your record values to  the instructor.
Note the extreme sensitivity to initial conditions.\
\>", "Subsection",
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