The effect of gas ejection on the structure and binding energy of newly formed stellar clusters is investigated. The star formation efficiency (SFE), necessary for forming a gravitationally bound stellar cluster, is determined. Two sets of numerical N‐body simulations are presented. As a first simplified approach we treat the residual gas as an external potential. The gas expulsion is approximated by reducing the gas mass to zero on a given time‐scale, which is treated as a free parameter. In a second set of simulations we use smoothed particle hydrodynamics (SPH) to follow the dynamics of the outflowing residual gas self‐consistently. We investigate cases where gas outflow is induced by an outwards propagating shock front and where the whole gas cloud is heated homogeneously, leading to ejection. If the stars are in virial equilibrium with the gaseous environment initially, bound clusters only form in regions where the local SFE is larger than 50 per cent or where the gas expulsion time‐scale is long compared with the dynamical time‐scale. A small initial velocity dispersion of the stars leads to a compaction of the cluster during the expulsion phase and reduces the SFE needed to form bound clusters to less than 10 per cent.

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This paper applies Bancroft's algorithm, which was developed for GPS, to the solution of aircraft multilateration surveillance equations. Results developed are equally applicable to two-dimensional hyperbolic surveillance and navigation. Bancroft's algorithm provides a closed-form position solution with a time tag.

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