What are mean motion orbital resonances?

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Welcome, my name is Phil, and in this video I discuss what mean motion orbital resonances are.
Mean motion resonances (MMRs) are a type of orbital resonance that occur when two orbiting bodies, such as planets, moons, or asteroids, exert regular, periodic gravitational influences on each other due to their orbital periods being in a ratio of small integers. This means that for every orbit completed by one body, the other body completes a specific, integer number of orbits. These resonances can lead to a variety of dynamical effects, including stabilizing the orbits of the bodies involved or causing significant changes in their orbits over time.
Here are some key aspects of mean motion resonances:
Orbital Period Ratio: MMRs are characterised by simple ratios of the orbital periods of the two bodies. For example, a 2:1 resonance means that one body completes two orbits in the same time it takes the other body to complete one orbit.
Gravitational Influence: When bodies are in MMR, their gravitational interactions can lead to periodic gravitational forces that can affect their orbits. These interactions are often more pronounced than those experienced in non-resonant orbits.
Stability: MMRs can contribute to the long-term stability of orbits. For example, many of the moons of Jupiter and Saturn are in mean motion resonances, which helps maintain their stable orbits over long periods.
Asteroid Belts and Gaps: In the asteroid belt, certain mean motion resonances with Jupiter create gaps known as Kirkwood gaps. Asteroids that would be in these resonances are perturbed by Jupiter's gravity and are either ejected from these regions or moved to different orbits.
Planetary Systems: MMRs are also observed in exoplanetary systems. Some pairs of exoplanets are found in resonances, which provides clues about the history of planetary migration and the dynamics of the system.
Examples in the Solar System:
Pluto and Neptune: Pluto is in a 3:2 resonance with Neptune, meaning that for every three orbits Pluto makes around the Sun, Neptune makes two.
Jupiter's Moons: The Galilean moons Io, Europa, and Ganymede are in a 4:2:1 resonance. Io orbits Jupiter four times for every two orbits of Europa and every one orbit of Ganymede.
MMRs play a crucial role in the dynamics and evolution of many celestial systems, influencing the behavior and distribution of planets, moons, and smaller bodies within those systems.

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