Which force law is used to derive the equations governing hyperbolic trajectories?

Newton's law of universal gravitation. The equations governing hyperbolic trajectories can be derived using Newton's law of universal gravitation. This law states that every mass attracts every other mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.Mathematically, it is expressed as:F = G (m1 * m2) / r^2where F is the gravitational force between two masses (m1 and m2), r is the distance between their centers, and G is the gravitational constant.By combining this law with Newton's second law of motion, which relates force, mass, and acceleration, it is possible to derive the equations describing the motion of objects following hyperbolic trajectories under the influence of gravity. These equations are essential for understanding and predicting the behavior of celestial bodies, spacecraft, and other objects moving through space.