Yes, the Moon's orbit around the Earth is considered stable on human timescales. The Moon orbits the Earth in a slightly elliptical path, and its motion is primarily governed by the gravitational attraction between the Earth and the Moon. This gravitational interaction results in a stable and predictable orbit.
However, it's important to note that the Moon's orbit is not entirely constant. Various factors can introduce small perturbations and influences on the Moon's motion over long periods of time. These include gravitational interactions with the Sun, as well as the gravitational effects of other planets in the solar system. These perturbations can cause slight variations in the Moon's orbit and its orbital parameters, such as its eccentricity and inclination.
Nonetheless, the overall stability of the Moon's orbit is well-understood and has been accurately modeled by scientists for many years. The variations caused by external influences are generally small and have been measured and accounted for in the study of lunar dynamics.
It's worth mentioning that over extremely long timescales (billions of years), the interactions between the Earth, Moon, and Sun can lead to gradual changes in the Moon's orbit. For example, tidal forces between the Earth and the Moon cause a slow transfer of angular momentum, resulting in the Moon gradually moving away from the Earth at a rate of about 3.8 centimeters per year. However, these long-term changes do not significantly affect the stability of the Moon's orbit within the context of human timescales.