There are two huge north-south barriers to the flow of the tides right now, the Americas in the western hemisphere and Afro-Eurasia in the eastern hemisphere. If something even funkier happens and the Moon recedes at any average rate of four centimeters per year over the next billion years, the Moon will be at a distance of , km from the Earth center to center. Even with that over-the-top recession rate, the Moon will not escape in the next billion years.
What about after a billion years? I chose a billion years because that's about when the Moon's recession should more or less come to a standstill. If the Earth hasn't already died before this billion year mark, this is when the Earth dies. Dwarf stars such as our Sun get progressively more luminous throughout their life on the main sequence. That should be enough to trigger a moist greenhouse, which in turn will trigger a runaway greenhouse. The Earth will become Venus II. All of the Earth's oceans will evaporate.
Water vapor will reach well up into what is now the stratosphere.
Ultraviolet radiation will photodissociate that water vapor into hydrogen and oxygen. The hydrogen will escape.
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Eventually the Earth will not only be bare of liquid water on the surface, it will be bare of water vapor in the atmosphere. Almost all of the Moon's recession is a consequence of ocean tides.
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Without oceans, that tunar recession will more or less come to a standstill. The Sun does not have nearly enough mass to become a supernova. Instead, it will swell to become a red giant , enveloping Mercury, Venus, and possibly Earth. After that, it will shed its outer layers as a planetary nebula , and settle down to become a white dwarf.
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Wikipedia , apparently, says the exact same things I had though of:. The Sun does not have enough mass to explode as a supernova. Instead it will exit the main sequence in approximately 5. It is calculated that the Sun will become sufficiently large to engulf the current orbits of the Solar System's inner planets, possibly including Earth.
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Still, that does put a deadline for the Earth and the Moon to evolve to the point you're looking for. Wikipedia addresses the possibility that the Earth and Moon survive:. Today, the Moon is tidally locked to the Earth; one of its revolutions around the Earth currently about 29 days is equal to one of its rotations about its axis, so it always shows one face to the Earth. The Moon will continue to recede from Earth, and Earth's spin will continue to slow gradually.
In about 50 billion years, if they survive the Sun's expansion, the Earth and Moon will become tidally locked to each other; each will be caught up in what is called a "spin—orbit resonance" in which the Moon will circle the Earth in about 47 days and both Moon and Earth will rotate around their axes in the same time, each only visible from one hemisphere of the other. So the Moon will certainly still be around by the time the Sun becomes a red giant, and for many billions of years after that. That's about one-seventh the current distance to the Moon - at its closest pass.
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Is this enough to make the Earth lose the Moon before the Sun goes into Supernova? Ahh, beat me to the calculations.
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