vanvleck 2001$ calc
* @constants.cal
* ? gn*msun*year^2/au^3
    39.47534117074645    
* ? sqrt(Res)
    6.282940487601840    
* ? 2*pi
    6.283185307179586    

problem #2
a=20, seek half a period
* ? .5*20^1.5
    44.72135954999580    

problem #3:
T (in years)=[a (in AU)]^(3/2)
* ? 75.7^(2/3)
    17.89495399936801 
peri distance =a*(1-e); e=1-peri/a
* ? 1-.587/res
    .9671974568908793    

problem #6
from Eq 2.4-5: (v/(2*pi))^2=2/r -1/a
1/a=2/r-(v/(2*pi))^2
* ? 2/1.6-(1.2/2/PI)^2
    1.213524373888758    
* ? 1/RES
    .8240460772909602    
* let a=res
h=2*pi*sqrt(a(1-e^2))
(h/2/pi)^2/a=1-e^2
e=sqrt(1-(h/2/pi)^2/a)
h=L/m=rvsin(60deg)

* ? (1.2*1.6*SIN(pi/3)/2/pi)^2/a
* ? sqrt(1-res)
    .9565631198354961    
(1 + e cos(p))=a(1-e^2)/r
cos(p)=(a(1-e^2)/r-1)/e
* let ecc=.9565631198354961
* ? (a*(1-ecc^2)/1.6-1)/ecc
   -.9996509679684875    
* ? acos(res)*180/pi
    178.4861497898665