Oops,
Looks like I used the velocity formula rather than the distance formula for the Eagle's Accleration.
Revised math:
assuming an initial veloctiy of 0 m/s when learing orbit (it would be higher, but then we are ignoring the time it takes to get to orbit), then:
s=1/2 at^2
s=2075610000m (the midpoint between the planet and Alpha)
t=83700 seconds (43 hors, 15 minutes or time to reach the midpoint)
the a=2s/(t^2)
a=4151220000/(83700^2)
a=4151220000/7,005690000
a=0.5925m/s
or mind bogglingly slow.
It looks like I have to look at the situation more as a fuel limitation than an acceleration limit. I'll go over a few of the other data points given on the show and see what can work out.