Abstract :Various gravitational laws are examined. Binary pulsars imply unusual behavior as evidence for gravitational waves in contrast to Newtonian gravity. Gravity’s intensity in the restricted three-body problem can significantly be reduced due to rotational centrifugal forces to explain short-comings usually mentioned to invent dark matter. Although libration points are distinct, they represent a suitable testing ground. The Trojan asteroids at the Sun-Jupiter stable triangular points do not demonstrate that millions of asteroids reside at a singular point but with a very large scatter and do not asymptotically congeal due to attraction to create planetoids, thereby suggesting Newtonian gravitation is not ample and has flaws. A phase-space trajectory methodology for an integral equation defines eigenvalues and a forcing function to test some different gravity laws. These findings indicate that a time-dependent law may not locally conserve energy and result in a celestial vibration, repulsive gravitation or produce gravitational waves. This provides insights for newer gravitational models possibly suitable for using warp drive concepts. Furthermore, this effort warrants placing more space probes at the triangular libration points as cosmic anomalies.