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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def crossing(b, component, time, dynamics_method='keplerian', ltte=True, tol=1e-4, maxiter=1000):
 """ tol in days """



    def projected_separation_sq(time, b, dynamics_method, cind1, cind2, ltte=True):
        """
        """
        #print "*** projected_separation_sq", time, dynamics_method, cind1, cind2, ltte


        times = np.array([time])

        if dynamics_method in ['nbody', 'rebound']:
            # TODO: make sure that this takes systemic velocity and corrects positions and velocities (including ltte effects if enabled)
            ts, xs, ys, zs, vxs, vys, vzs = dynamics.nbody.dynamics_from_bundle(b, times, compute=None, ltte=ltte)

        elif dynamics_method=='bs':
            ts, xs, ys, zs, vxs, vys, vzs = dynamics.nbody.dynamics_from_bundle_bs(b, times, compute, ltte=ltte)

        elif dynamics_method=='keplerian':
            # TODO: make sure that this takes systemic velocity and corrects positions and velocities (including ltte effects if enabled)
            ts, xs, ys, zs, vxs, vys, vzs = dynamics.keplerian.dynamics_from_bundle(b, times, compute=None, ltte=ltte, return_euler=False)

        else:
            raise NotImplementedError


        return (xs[cind2][0]-xs[cind1][0])**2 + (ys[cind2][0]-ys[cind1][0])**2


    # TODO: optimize this by allowing to pass cind1 and cind2 directly (and fallback to this if they aren't)
    starrefs = b.hierarchy.get_stars()
    cind1 = starrefs.index(component)
    cind2 = starrefs.index(b.hierarchy.get_sibling_of(component))

    # TODO: provide options for tol and maxiter (in the frontend computeoptionsp)?
    return newton(projected_separation_sq, x0=time, args=(b, dynamics_method, cind1, cind2, ltte), tol=tol, maxiter=maxiter)