PX283 - I7 - tides

• tidal interactions arise due to differential gravity across an object:

• the object becomes slightly elongated, exhibiting tidal bulges
• for earth $\simeq 10$ cm, and for moon $\simeq 20$ m

image: Carroll & Ostile, An Introduction to Modern Astrophysics (2007)

• bulges offset by rotations (ie earth spins faster, so its bulge leads the moon)

• then, the gravitational force acts to synchronize rotation with the orbit

• eg: earth's spin is slowing down ($\sim 1.6$ mins per century) and moon is spiraling out ($\sim 4$ cm per year) with transfer of angular momentum from rotation to orbit (moon is already synchronized)

• for a slowly spinning planet, the synchronization can spin up the planet and decay the orbit of the moon

• the tides depend very strongly on the orbital separation: $F_{tides}\propto \frac{1}{r^3{r}^2}\propto \frac{1}{r^5}$

• eccentric orbits still misalign tidal bulges after synchronization

• this leads to dissipation of energy and heating the planet/moon by internal friction - tidal heating

• this causes the circularization of the orbit (orbit loses energy at a constant average mass)

• it can stabilize mean motion resonances, eg. moons of jupiter and tidal heating of io and europa

• tides can lead to the break up of an object when tidal forces $>$ self gravity (roche limit)