Resonances I. Orbital Resonances A. Definition: An orbital resonance occurs when two orbiting bodies exert a _______ and ________ gravitational influence on each other. This usually means that their orbital periods (i.e. the time it takes to make one orbit) are related by a ratio of two _____________. B. Orbital resonances result in greatly _________ effects. C. Examples: 1. Jupiter’s Moons: Ganymede_______ orbit Europa_______ orbits Io_______ orbits 2. Pluto and Neptune: Pluto_______ orbits Neptune_______ orbits

3. Saturn’s Rings: The Cassini Division, the ___________ in Saturn’s rings, between the inner B Ring and the outer A Ring, has been cleared by a _____ resonance with the moon ______.

4. Asteroid Belt: Gaps exist in the Asteroid Belt, known as the _____________. These are due to resonances with the massive planet ________. Some of the largest gaps occur at the 3:1, 5:2, 7:3 and 2:1 resonances. Asteroids have been ejected _____________ ______________ of Jupiter such that there are lanes almost empty of asteroids.

II. Spin-Orbit Resonances A. Definition: When sufficient _________ are exerted on a smaller body in orbit around a larger body, a spin-orbit resonance can exist with the smaller body. This is when the number of _________ and the number of _______ are related by a _______________________. B. Examples: 1. Moon: The Moon makes ___ rotation for every ___ orbit it makes. It is said to be in a ____ spin-orbit resonance. ________________ in the solar system are in a 1:1 spin- orbit resonance. 2. Mercury: Mercury is in a _____ spin-orbit resonance in its orbit around the Sun. This means it makes ___ rotations for every ___ orbits.