Lecture L04 - ASTC25 Physics of Tides Tides in the solar system Roche limit of tidal disruption.

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Presentation transcript:

Lecture L04 - ASTC25 Physics of Tides Tides in the solar system Roche limit of tidal disruption

Damped oscillator as a model equation of tidal wave braking Natural frequency of oscillations = sqrt( spring constant) Deformation (vertical, relative to sphere) Frequency of forcing = spin frequency = angular speed of planet forcing Free oscil.

?

Net torque = 0, stable resonance

c Phobos Phobos has only ~1 Gyr more to live… before a crash onto Mars

Io Europa Ganimede Callisto

Tidal flexing and heating of Io causes the most active volcanism in the Solar System

Roche limit: tidal forces destroy bodies which come too close to a source of gravitation through differential acceleration Consider an orbiting mass of fluid held together by gravity. Far from the Roche limit the mass is practically spherical. The body is deformed by tidal forces Within the Roche limit the mass' own gravity (self-gravity) can no longer withstand the tidal forces, and the body disintegrates. Particles closer to the primary orbit move more quickly than particles farther away, as represented by the red arrows. The varying orbital speed of the material eventually causes it to form a ring.

Jupiter disrupted tidally comet Shoemaker-Levy 9 (SL9)

Roche limit: Fluid limit: tides destroy a body bound by self-gravity within that minimum distance r_R Solid/rocky limit: the same but with additional binding (electromagnetic) forces of material strength Q: which limit is larger? First step in the computation is the estimation of the differential torque Édouard Roche (1820–1883)

Roche limit calculation

Comet Shoemaker-Levi SL-9 (1994) disintegrated after approach to Jupiter, and so do the sun-grazing comets. Roche limit [pron.: rowsh]

~2.2 R_p satellites generally outside the rings Roche limit for fluid satellite (~1849): Roche limit for rocky satellite: 1. 4

JupiterSaturn Uranus Neptune R_p 2R_p 3R_p =satellite rings 0 Roche limit is somewhere near 2 R_p: satellites destroyed if closer to their planets. Ring systems drawn to scale of their planets, but not to relative scale.