Most moons slowly move away from the planets they are orbiting because of the gravitational pull exerted by tidal bulges
. Earth's moon, for instance, is currently moving away at a rate of roughly 1.5 inches per year.
The tidal torque itself is proportional both to the height of the tidal bulge
and to the tidal field acting on it (which both raises the bulge and then pulls on it) and thus finally to [(tidal field).sup.2], hence varying as 1/[a.sup.6] where a= Earth-Moon distance; it is also proportional to sin 2[epsilon] where [epsilon] is the 'tidal offset' angle.
The torque causes an orbital acceleration of the Earth and Moon about their common center of mass; an equal and opposite torque exerted by the Moon on the tidal bulge
slows the Earth's rotation.
The tidal bulge, due to partial viscosity of the mantle and fluidity of the oceans, leads the direction to the acting force by a small angle [epsilon].
The Earth's deformation by tidal bulge is quite naturally time-dependent--both its orientation and magnitude depend on the position of the disturbing bodies, i.e.
Notably, Hoppa and Tufts's model works only if the tidal bulge
is sliding freely over the interior, a powerful argument that an ocean of water underlies Europa's crust.
The Moon pulls the tidal bulge
"backward," slowing the Earth, while the tidal bulge
pulls the Moon "forward," adding energy to its orbit and causing the orbit to expand.
The researchers also found that the moon's overall gravity field was no longer aligned with the topography, as it would have been when the tidal bulges
were frozen into the moon's shape.
and heartthrob boffin Professor Brian Cox is waffling on about tidal bulges
FIGURE B is a diagram of Earth with tidal bulges
and the Moon as seen from the same perspective as FIGURE A.
However, we get two high tides a day because the Earth has two tidal bulges
on opposite sides of the planet.