1. Resonances

2. 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. Resonances I. Orbital Resonances regularperiodic small integers A. Definition: An orbital resonance occurs when two orbiting bodies exert a _regular_ and _periodic_ 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 _small integers_. 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

4. Resonances I. Orbital Resonances regularperiodic small integers A. Definition: An orbital resonance occurs when two orbiting bodies exert a _regular_ and _periodic_ 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 _small integers_. enhanced B. Orbital resonances result in greatly _enhanced_ effects. C. Examples: 1. Jupiter’s Moons: Ganymede_______ orbit Europa_______ orbits Io_______ orbits 2. Pluto and Neptune: Pluto_______ orbits Neptune_______ orbits

6. Resonances I. Orbital Resonances regularperiodic small integers A. Definition: An orbital resonance occurs when two orbiting bodies exert a _regular_ and _periodic_ 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 _small integers_. enhanced B. Orbital resonances result in greatly _enhanced_ effects. C. Examples: 1. Jupiter’s Moons: Ganymede_______ orbit Europa_______ orbits Io_______ orbits 2. Pluto and Neptune: Pluto_______ orbits Neptune_______ orbits

7. Resonances I. Orbital Resonances regularperiodic small integers A. Definition: An orbital resonance occurs when two orbiting bodies exert a _regular_ and _periodic_ 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 _small integers_. enhanced B. Orbital resonances result in greatly _enhanced_ effects. C. Examples: 1:2:4 1. Jupiter’s Moons: 1:2:4 1 Ganymede___1___ orbit 2 Europa___2___ orbits 4 Io___4___ orbits 2. Pluto and Neptune: Pluto_______ orbits Neptune_______ orbits

9. Resonances I. Orbital Resonances regularperiodic small integers A. Definition: An orbital resonance occurs when two orbiting bodies exert a _regular_ and _periodic_ 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 _small integers_. enhanced B. Orbital resonances result in greatly _enhanced_ effects. C. Examples: 1:2:4 1. Jupiter’s Moons: 1:2:4 1 Ganymede___1___ orbit 2 Europa___2___ orbits 4 Io___4___ orbits 2. Pluto and Neptune: Pluto_______ orbits Neptune_______ orbits

10. Resonances I. Orbital Resonances regularperiodic small integers A. Definition: An orbital resonance occurs when two orbiting bodies exert a _regular_ and _periodic_ 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 _small integers_. enhanced B. Orbital resonances result in greatly _enhanced_ effects. C. Examples: 1:2:4 1. Jupiter’s Moons: 1:2:4 1 Ganymede___1___ orbit 2 Europa___2___ orbits 4 Io___4___ orbits 2:3 2. Pluto and Neptune:2:3 2 Pluto___2___ orbits 3 Neptune___3___ orbits

11. 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 ______.

12. 3. Saturn’s Rings: The Cassini Division, the _largest gap_ in Saturn’s rings, between the inner B Ring and the outer A Ring, has been cleared by a _2:1_ resonance with the moon _Mimas_.

13. 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.

14. 4. Asteroid Belt: Kirkwood Gaps Jupiter due the repeated gravitational tug Gaps exist in the Asteroid Belt, known as the _Kirkwood Gaps_. These are due to resonances with the massive planet _Jupiter_. Some of the largest gaps occur at the 3:1, 5:2, 7:3 and 2:1 resonances. Asteroids have been ejected _due the repeated gravitational tug _ of Jupiter such that there are lanes almost empty of asteroids.

15. 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.

16. II. Spin-Orbit Resonances A. Definition: tidal forces rotationsorbits ratio of two small integers When sufficient _tidal forces_ 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 _rotations_ and the number of _orbits_ are related by a _ratio of two small integers_. 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.

17. II. Spin-Orbit Resonances A. Definition: tidal forces rotationsorbits ratio of two small integers When sufficient _tidal forces_ 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 _rotations_ and the number of _orbits_ are related by a _ratio of two small integers_. B. Examples: 11 1:1 Most major moons 1. Moon: The Moon makes _1_ rotation for every _1_ orbit it makes. It is said to be in a _1:1_ spin-orbit resonance. _Most major moons_ 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.

18. II. Spin-Orbit Resonances A. Definition: tidal forces rotationsorbits ratio of two small integers When sufficient _tidal forces_ 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 _rotations_ and the number of _orbits_ are related by a _ratio of two small integers_. B. Examples: 11 1:1 Most major moons 1. Moon: The Moon makes _1_ rotation for every _1_ orbit it makes. It is said to be in a _1:1_ spin-orbit resonance. _Most major moons_ in the solar system are in a 1:1 spin- orbit resonance. 3:2 3 2 2. Mercury: Mercury is in a _3:2_ spin-orbit resonance in its orbit around the Sun. This means it makes _3_ rotations for every _2_ orbits.

19. Resonances