In classical mechanics, if we consider only two astronomical objects isolated in space, their orbits would indeed last forever according to Newton's laws of motion and the law of universal gravitation. This concept is known as a two-body problem.
In such a scenario, assuming no external influences or perturbations, the two objects would continue to orbit around their common center of mass indefinitely. This is observed in celestial systems like Earth and the Sun, where the Earth's orbit around the Sun has been stable for billions of years.
However, in reality, celestial systems are not isolated, and additional factors can affect the long-term stability of orbits:
Perturbations from other objects: The presence of other celestial bodies can perturb and influence the orbits of objects within a system. For example, the gravitational interactions among planets in our Solar System can cause slight changes in their orbits over time.
Tidal effects: Tidal forces between astronomical objects can lead to energy dissipation and affect their orbits. This is seen in the case of tidal interactions between the Earth and the Moon, causing a gradual increase in the Moon's distance from the Earth and a corresponding decrease in Earth's rotation rate.
General Relativity: In extreme cases, the effects of general relativity can be significant. For instance, the predicted gradual inspiral of binary systems consisting of neutron stars or black holes due to the emission of gravitational waves.
While these factors can introduce long-term changes to orbits, they do not necessarily mean that orbits will "inevitably stop" in the sense of a complete cessation of motion. Rather, they can cause orbital evolution, altering the shape, size, and orientation of orbits over extremely long timescales.
In summary, in isolated systems, orbits can persist indefinitely. However, in real-world scenarios, external influences and factors like perturbations and tidal effects can introduce changes to orbits over extended periods, potentially leading to different outcomes over cosmic timescales.