Answer:
Complex Question, actually, which leads, sadly, to a complex Answers.
First Answer (describing the irregular shape of the orbit of the moon): Yes. Unless, of course, it's moving toward the Earth.
The moon's orbit is not perfectly circular. Like all other planetary satellites, the moon's orbit describes an ellipse.
The closest point of approach is called the Perigee (approx) 360,000km., whereas its farthest point from earth (Apogee) averages (~) 405,000km.
In the larger, astrophysical sense, of course, the moon's orbit, as with all satellites, natural and artificial, is decaying. This means that, eventually, the moon will come close enough to the earth to impinge upon the upper atmosphere. What will happen then (guesses range from another million (or so) years to 'never', btw) is anybody's guess, as many Science Fiction authors' work will attest.
For more precise distances, please refer to the table contained in the (excellent, btw) website below.
http://www.fourmilab.ch/earthview/pacalc.html
Second Answer (describing the long term motion of the moon away from earth): Yes, over time the moon is gradually moving away from the earth. This is a result of Tidal forces.
As the earth spins, the gravity of the moon pulls water, air and even land up towards it in a bulge called the 'tide.' On the oceans, this tide often rises several feet. But the spinning earth pulls the tide 'ahead' of the moon. So the tide is not truly directly under the moon, but just east of it. Then the increased gravity effect from the tide, racing ahead of the moon, gradually, and ever so imperceptibly pulls the moon forward in its own orbit even faster.
The end result is a kind of tidal 'sling shot' effect that pulls the moon forward in its orbit, faster and faster over time, causing it to speed up. As it speeds up, it moves farther away from the earth. This is the mechanism that has caused the moon to 'recede' from the earth by many hundreds of thousands of kilometers, in the billions of years since it was formed, after the earth underwent a collision with another, Mars sized planet, in the early days of the solar system.
It is calculated that currently the orbit of the moon increases in diameter by about 3.8 cm (about 1 1/2 inches) every year, a surprisingly large amount, as a result of this tidal sling shot effect. Over millions and billions of years, this sling shot effect adds up.
The moon is currently moving away from the earth approximately 3 to 4 times faster than is has through much of its history, because the spacing of the major oceans and continents allows for a larger tidal-gravity sling shot effect than in the past. But it will not continue this way indefinitely. As the continents continue to drift (thus affecting the tides) the rate that the moon recedes will also change.
Someday, if the earth itself stops spinning, or if it loses all of its air and water and no longer has any significant tides, then the tidal sling shot effect will stop, and the moon's orbit will gradually start to decay. So the day may come when the moon might come crashing down upon the earth, but that day would certainly be billions of years in the future.
In fact, current calculations are that the moon would finally stop moving away from earth approximately 15 billion years from now, but the sun will likely develop into a red giant and incinerate both the earth and the moon before then, in only 6 or 7 billion more years.
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If this was true, then how can there be 2 high tides every day ? And how are there high tides on the opposite side of the earth from the moon ?