Suppose we want to use an asteroid to build a large space station. We could alter the course of a asteroid so that it will come very close to Earth, but the velocity relative to Earth will then be more than the escape velocity of 11.2 km/s. Presumably we must use aerobraking to let it lose enough energy to be captured. But then this must be done such that perturbations by the Sun or Moon will then change the orbit so that it doesn't move inside the atmosphere anymore. Can we capture a 10 km diameter asteroid this way?