Abstract-Virtual coordinate systems (VCS) provide accurate estimations of latency between arbitrary hosts on a network, while conducting a small amount of actual measurements and relying on node cooperation. While these systems have good accuracy under benign settings, they suffer a severe decrease of their effectiveness when under attack by compromised nodes acting as insider attackers. Previous defenses mitigate such attacks by using machine learning techniques to differentiate good behavior (learned over time) from bad behavior. However, these defense schemes have been shown to be vulnerable to advanced attacks that make the schemes learn malicious behavior as good behavior.We present Newton, a decentralized VCS that is robust to a wide class of insider attacks. Newton uses an abstraction of a real-life physical system, similar to that of Vivaldi, but in addition uses safety invariants derived from Newton's laws of motion. As a result, Newton does not need to learn good behavior and can tolerate a significantly higher percentage of malicious nodes. We show through simulations and real-world experiments on the PlanetLab testbed that Newton is able to mitigate all known attacks against VCS while providing better accuracy than Vivaldi, even in benign settings.