Tides VSI
Tides
- p14: 1 millibar decrease in pressure raises sea levels by 1 cm
- p21-22 Equilibrium tide model: The bulge going round the earth with the moon (why one on the other side) model = Newton’s model as if all ocean, accounts for about 50 cm = that seen in oceanic islands; theory fails
- p18-20: earth and moon rotating about their barycenter, causes bulge opposite moon (centripetal force)
- net effect is about 1 10millionth E gravity
- Real action is the force parallel to the E surface (not perp for the “bulge”) = tide generating force ; acts one way and then the other and it is all about resonance
- E-S and E-M have two sets of tide generating forces with different periods (24 hrs vs. 12 hrs 25 mins for moon (two sides) => tide moves 50 mins later per day [caused by motion of moon around the earth and the E rotates underneath: M moves 360/27.3 = 13.18 degrees/day, the earth rotates as 360/24= 15 degrees/hour, so the extra 13.18 degrees takes 13.18 / 15 * 60 = 52.74 mins] [length of moon’s orbit around E = 27.3 days = sidereal month; but moon to same spot in sky = 29.5 days = synodic month]
- Speed of wave in depth \(d\) water is \(\sqrt{g d}\)
- Forcing period \(T\) for resonance: must match time for wave to go back and forth across ocean, if \(L\) is width need \(T = 2L / \sqrt{g d}\). For T = 2 x 4000km wide / sqrt(10 4km deep} = [in m] = 2 x 4M / 200 = 40000sec = 11.11 hours; wave goes very fast!
- p48: Kelvin’s tide predication machine, combining circular displacements on a piece of string!
- Resonances against a wall and up a bay
- River bores
- Southampton has a double high tide
- p84: oldest recording of total eclipse is 720BC in Babylon: if E rotated at same rate (ss E, steady-state) vs actual (speeds up) then the actual moves ahead (east) of the ss E. If we know a particular time an eclipse was observed [you know when it happened from Newtonian mechanics, the point is it was visible] then the E must have made an additional 1/4 turn for that to happen. TODO deets!
- Io moon of Jupiter - see below
- Tidal coupling (see GPT below): Earth-Moon distance increases by 38 mm per year and length of day increases by 0.024 ms / year [GPT says 1.7ms / century]
GPT on tidal coupling and Io
The Earth’s rotation is gradually slowing down due to tidal forces exerted by the Moon. This process is known as tidal friction. According to the law of conservation of angular momentum, if the Earth loses angular momentum, this momentum must be transferred elsewhere in the Earth-Moon system.
The mechanism works as follows: the gravitational pull between the Earth and the Moon causes tidal bulges on Earth. Earth’s rotation tries to drag these bulges ahead of the Moon’s orbit. However, the gravitational pull between the bulges and the Moon acts as a torque, slowing Earth’s rotation. As Earth’s rotational angular momentum decreases, the angular momentum of the Moon’s orbit increases, causing the Moon to move to a higher orbit, gradually increasing its distance from the Earth.
This effect is measurable and results in the Moon moving away from Earth at an average rate of about 3.8 centimeters per year
Tidal locking occurs when an object’s orbital period matches its rotational period, causing one face of the object to always face the object it is orbiting. This is already the case with the Moon and the Earth; the Moon is tidally locked to the Earth, showing us only one side.
The process that is driving the Moon away from the Earth also works towards achieving a state where the Earth might one day become tidally locked to the Moon. However, this would take an extremely long time, far beyond current human timescales, due to the slow rate of the processes involved.
In such a scenario, the Earth would rotate once for each orbit the Moon makes around the Earth, meaning that one day on Earth would last as long as a month does now. However, this is a theoretical outcome projected to occur over billions of years, and other factors, such as the Sun’s life cycle, will likely intervene before tidal locking of the Earth to the Moon could be completed.
Io, one of Jupiter’s moons, is the most volcanically active body in the solar system. This intense volcanic activity is primarily due to the extreme tidal forces it experiences. Unlike the tidal forces on Earth, which are caused by the Moon and result in ocean tides, the tidal forces on Io result from its interaction with Jupiter and other Galilean moons (Europa, Ganymede, and Callisto).
Here’s how it works:
Orbital Resonance: Io is in an orbital resonance with Europa and Ganymede. This means that for every orbit Io completes around Jupiter, Europa completes about two orbits, and Ganymede completes about four. This resonance keeps Io’s orbit slightly eccentric (non-circular), ensuring that the tidal forces exerted by Jupiter vary in strength during Io’s orbit.
Tidal Heating: As Io moves closer to and farther from Jupiter, the immense gravitational pull of the planet causes Io’s shape to change slightly. This constant flexing generates internal friction, which heats Io’s interior, leading to its geological activity.
Volcanic Activity: The heat from tidal friction within Io causes widespread volcanic activity on its surface. Lava flows, volcanic eruptions, and sulfur geysers are common, dramatically altering Io’s landscape and replenishing its atmosphere.
Tidal Bulges: Unlike Earth’s water tides, Io’s “tides” are in its solid surface. The intense gravitational pull from Jupiter can create bulges up to 100 meters high on Io’s surface, compared to the meter-scale oceanic tides on Earth. [100m of the solid ground of Io!]
This tidal heating is so intense that it melts a significant portion of Io’s interior, leading to its volcanic activity being hundreds of times greater than that on Earth. The energy released by this tidal heating is much more significant than the energy Io receives from the Sun, making these tidal forces the dominant factor in Io’s geologic and atmospheric characteristics.
Io, one of Jupiter’s moons, is primarily composed of silicate rock surrounding a molten iron or iron sulfide core. Its surface is covered in sulfur and sulfur dioxide frost, giving it a colorful appearance with yellow, red, white, black, and green regions.
Deets
- David George Bowers and Emyr Martyn Roberts
- Volume 621
- Published 2019 (2)