Lecture #23: The Turning Tide


I. The cause of tides
-- tides on the Earth are the way an ocean rises and falls on a beach twice each day
-- they are caused by the oceans conforming to a football-like shape, and then the Earth rotates the beach through the "points" of the football, yielding two high tides (two points) per day
-- the football shape is partly caused by the fact that the Moon's gravity is weaker on the near part of the Earth as the far part, and partly by the way it pinches in on the sides of the Earth
-- neglecting any deformation in the Earth's shape due to its rotation, you can think of the football shape as being caused by the fact that the near side of the Earth is going at the same speed as the center of the Earth, but that's a little too slow to be in a circular orbit due to the Moon's gravity, so it tends to fall in toward the Moon. Meanwhile, the more distant point is going too fast to be in circular orbit, so it tends to fly away from the Moon. The Earth's center is in balance between the tendency to fall in and the tendency to fly away, so that's why we say the Earth and Moon are orbiting each other.
-- if you go back and include the Earth's rotation, it only causes an additional oblate bulge around the equator, it doesn't have any influence on the football shape that causes tides.
II. Spring and Neap Tides
-- the strength of a tide depends on the distance to the object causing the tides, and its mass, because it is a gravity effect
-- this means the Sun also has tidal effects on the Earth, because the Sun is so massive
-- the Moon is more important, so rules the tides, but the Sun augments the Moon's tides when the Sun and Moon align-- i.e., new and full Moon phases. This is called a spring tide, nobody knows why.
-- when the Sun is perpendicular to the direction to the Moon (quarter phases), the tides are weaker because the Sun fights the Moon, and we get neap tides
III. Tides revisited
-- tides on the Earth
-- tidal locking-- man in the moon, slowing of Earth rotation
-- conservation of angular momentum: when Earth's rotation slows, the Moon's orbit picks up angular momentum and pushes the Moon farther away from the Earth
IV. Geosynchronous orbits
-- orbits near the surface of the Earth have only 1.5 hour periods
-- the orbit of the Moon is almost a month
-- in between there is a special distance where a circular orbit takes exactly 24 hours, this is the "geosynchronous orbit"
-- guess why we have so many man-made satellites in geosynchronous orbit? So they don't appear to move in the sky.
v. Rings
-- tidal effects attempt to distort moons into football shapes
-- close enough to the planet (closer than the "Roche limit"), the tidal forces are so strong they rip the moon apart
-- moons inside the geosynchronous (or Saturn-synchronous!) distance will spin Saturn up a little, and lose energy in the process, causing their orbit to gradually decay until the fall inside the Roche limit
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