Just suppose for a moment that various discrepancies in spacecraft trajectories, such as the Earth flyby anomalies, are due to new physics. It’s been pointed out in various sources, for example http://arxiv.org/abs/astro-ph/0608087" [Broken], that the spacecraft happen to be on hyperbolic trajectories when the anomalies occur. Further, suppose that this new physics involves forces that only act on an object once it reaches escape velocity from a gravitational source such as the sun or a planet. The question is: Would such a force cause any obvious violations of the known laws of physics? For example, would it break any conservational laws?