IDENTIFICATION DIVISION
PROGRAM-ID Comet
VERSION 20240205
COMMENT A comet moves on a parabolic orbit in the gravitational field of the stationary sun.
COMMENT Its orbital plane coincides with the plane of the Earth's orbit, which is assumed to be circular.
COMMENT The perihelion distance is one third of the Earth's orbital radius R.E.
COMMENT How long does the comet move within the Earth's orbit?
COMMENT t(r)=root(2/(gamma*m(sun))*integral from 1/3RE to RE (r/root(r-1/3 RE)) dr

ENVIRONMENT DIVISION
ENGINE Anabrid-THAT
TIMEBASE 100ms # use SLOW on both integrators
REQUIRES COEFFICIENT 3, INTEGRATOR 2, COMPARATOR 1, SUMMER 1, OPEN-AMP 2, MULTIPLIER 2, INVERTER 1

DATA DIVISION
OUTPUT OUTPUT.X -xlimited
OUTPUT OUTPUT.Y result
COEFFICIENT.1 Factor # root(2/(gamma*m)), scaled to 0,142 10kd/Tm^3/2
COEFFICIENT.2 RE # Earth's orbital radius, scaled to 0,150 Tm
COEFFICIENT.3 1/3RE # note: dependent on RE, scaled to 0,05 Tm

PROGRAM DIVISION
+1 -> COEFFICIENT.RE -> RE
+1 -> COEFFICIENT.1/3RE -> 1/3RE

# obtaining x through integration of 1, starting at 1/3RE
+1, IC:1/3RE -> INTEGRATOR -> -x

# limiting x to the upper limit of the integral RE and set x=0 if beyond
A:-x, B:RE, GT0:-x -> COMPARATOR -> -xlimited

-xlimited, 1/3RE -> SUMMER -> -(-x+1/3RE)=x-1/3RE

# root of x-1/3RE
## first invert because the input of a root has to be negative
x-1/3RE -> INVERTER -> -(x-1/3RE)
## now make sure the input is never >0 (which causes the circuit to error)
A:-(x-1/3RE), LT0:-(x-1/3RE) -> COMPARATOR -> -(x-1/3RE)limited
## now calculate the root
-(x-1/3RE)limited, OA1 -> OPEN-AMP -> root
root, root -> MULTIPLIER -> OA1

# x/root
-xlimited, OA2 -> OPEN-AMP -> x/root
x/root, root -> MULTIPLIER -> OA2

# integral
x/root -> INTEGRATOR -> integral
integral -> COEFFICIENT.Factor -> result

OPERATION DIVISION
MODE REPEAT
OP-TIME 111ms