Is it Possible for a Planet to Have a Stable Moon or a Double Planet Configuration Where the Orbital Period is Greater than the Orbits of Both Bodies Around the Star?

Short Answer: Highly Doubtful. If not physically impossible, then very close to it.

Longer Answer

I very highly doubt it. If we consider how orbits function, the size of the orbit determines the speed. The larger the orbit, the slower the objects must move. If the moon were to travel at a significantly faster speed while maintaining its current orbital distance, it would lose its circular orbit shape and may become elliptical or even collide with the planet itself. Conversely, if the moon were moving too slowly, it would be drawn closer to the planet, eventually either colliding with it or establishing a closer orbit.

Our solar system offers a clear example of different planetary speeds based on their distance from the sun. Jupiter, for instance, orbits the sun with a much larger distance than Earth, yet it still completes its orbit more quickly than Earth. This is due to the inverse square law of gravitational force, which means that gravity's strength decreases with the square of the distance between objects, thus speeding up objects in wider orbits.

Analysis of the Question

The question itself hinges on the concept of orbits being larger than those of the planets. For a moon to have an orbital period greater than the planet's own orbital period, it would need to have an orbit larger than the planet itself. This presents two primary challenges: gravitational stability and the interplay with other celestial bodies.

Firstly, for a moon to maintain a stable orbit around a planet that is itself orbiting a star, the moon's orbit must be much closer to the planet. The gravitational pull of the star would have a significant impact on the moon's orbit. If the moon were very far from the planet, it would likely either escape the planet's gravitational pull or be captured by the sun's much stronger gravitational force, resulting in its orbit becoming larger or falling closer to the planet.

Examples in Our Solar System

Looking at the moons in our solar system shows that very few, if any, have orbits larger than their respective planets. For example, the moons of Jupiter and Saturn are all significantly closer to their parent planets than the planets are to the sun. Io, one of Jupiter's moons, has an orbit much smaller than Jupiter's, and it stays in a stable orbit.

Potential Cases of Equal Orbits

While generally unlikely, there might be potential scenarios where the orbital periods of a moon and its planet are the same. This could occur in a binary system where both the planet and its moon orbit each other with the same period, leading to a double planet configuration. However, even in such a scenario, the actual orbital distances would still need to be much smaller than the orbital distance of the planet around the star.

A stable double planet configuration is rare and would require precise alignment and specific gravitational forces to maintain. Any significant influence from the star, or other nearby bodies, could disrupt this delicate balance and destabilize the system.

Conclusion

In conclusion, while we cannot definitively rule out the possibility of a planet with a moon or a double planet system where the moon's orbital period is greater than the planet's, the practical challenges and gravitational complexities make this extremely unlikely. The natural tendency of objects in orbit to move at speeds corresponding to their distance from the central body, and the influence of larger celestial bodies like stars, generally prevent such configurations from being stable and sustainable.