Final answer:
Newton's law of universal gravitation expanded Kepler's laws by including the masses of celestial bodies, allowing refined calculations of orbits and masses. It also introduced orbits with varying eccentricities and the understanding of complex multi-body gravitational interactions. Planets orbit around the barycenter of a two-body system, which is often within the more massive body.
Step-by-step explanation:
How Newton's Law of Gravity Extends Kepler's Laws
Isaac Newton's law of universal gravitation built upon and extended Johannes Kepler's laws of planetary motion by introducing the role that mass plays in the gravitational force between two objects. This relation provided a foundation for explaining the orbital dynamics of celestial bodies. Newton's law considers the masses of both objects in the gravitational interaction, leading to the modified version of Kepler's third law: a³ = (M₁ + M₂) × P², which allows us to calculate the masses of astronomical objects.
New Orbital Paths Introduced by Newton's Law
Newton's law of gravitation explains the orbits that are not perfectly circular, such as those of comets, which often have high eccentricity. Moreover, it enables understanding the complex gravitational interactions in multi-body systems, permits predictions of Earth-crossing asteroids paths, and plays a crucial role in space vehicle navigation.
Orbiting Around an Imaginary Point
Planets and other orbiting objects actually revolve around the mass center of the two-body system they form with another object, often referred to as the barycenter. In most cases, this point is located within the more massive object, such as the Sun, for planets in our solar system. For systems where the mass is more evenly distributed, the barycenter may lie outside of both bodies.