SUB EulerRichardson(pos(),vel(),t,GM,dt,kick_flag$,xsave,ysave)
    DIM accel(2),velmid(2),posmid(2)
    GET MOUSE x,y,s
    IF s = 2 then
       LET xsave = x              ! save position where mouse clicked
       LET ysave = y
       LET kick_flag$ = "on"
    END IF
    IF (kick_flag$ = "on") then
       LET diffx = abs(pos(1) - xsave)
       LET diffy = abs(pos(2) - ysave)
       ! wait until orbit reaches point where mouse clicked
       IF (diffx < 0.02) and (diffy < 0.02) then
          LET v2 = vel(1)*vel(1) + vel(2)*vel(2)
          LET v = sqr(v2)
          LET impulse = 0.1*v     ! magnitude of impulse/mass
          LET vel(2) = vel(2) + impulse     ! vertical kick
          LET kick_flag$ = "off"
       END IF
    END IF
    ! compute acceleration at beginning of interval
    CALL acceleration(pos(),accel(),GM)
    FOR i = 1 to 2
        LET velmid(i) = vel(i) + 0.5*accel(i)*dt
        LET posmid(i) = pos(i) + 0.5*vel(i)*dt
    NEXT i
    ! compute acceleration at middle of interval
    CALL acceleration(posmid(),accel(),GM)
    ! position and velocity at end of interval
    FOR i = 1 to 2
        LET vel(i) = vel(i) + accel(i)*dt
        LET pos(i) = pos(i) + velmid(i)*dt
    NEXT i
    LET t = t + dt
END SUB