question: how the moon can drift away from earth despite earth’s immense gravity on the moon relative to other celestial objects
comment: The Moon's gravity causes tidal bulges on the Earth directly bellow it. Because the Earth spins faster than the Moon orbits, the Moon gets pulled along by the bulges causing it to speed up while the earth slows down. Because gravity decreases exponentially most of this effect already happened long ago when the Moon was closer. The Moon will not escape Earth during Sol's lifetime.
passages: The main visible effect (in longitude) of the variation of the Moon is that during the course of every month, at the octants of the Moon's phase that follow the syzygies (i.e. halfway between the new or the full moon and the next-following quarter), the Moon is about two thirds of a degree farther ahead than would be expected on the basis of its mean motion (as modified by the equation of the centre and by the evection). But at the octants that precede the syzygies, it is about two thirds of a degree behind. At the syzygies and quarters themselves, the main effect is on the Moon's velocity rather than its position.
   Asimov lists tug-of-war ratio for 32 satellites (then known in 1963) of the Solar System. The list below shows one example from each planet.
  
  Section::::The special case of the Moon.
  
  Unlike other satellites of the solar system, the solar attraction on the Moon is more than that of its primary. According to Asimov, the Moon is a planet moving around the Sun in careful step with the Earth.
   Considering the Earth–Moon system as a binary planet, its centre of gravity is within Earth, about or 72.6% of the Earth's radius from the centre of the Earth. This centre of gravity remains on the line between the centres of the Earth and Moon as the Earth completes its diurnal rotation. The path of the Earth–Moon system in its solar orbit is defined as the movement of this mutual centre of gravity around the Sun. Consequently, Earth's centre veers inside and outside the solar orbital path during each synodic month as the Moon moves in its orbit around the common centre of gravity.
   The notional tidal bulges are carried ahead of the Earth–Moon orientation by the continents as a result of Earth's rotation. The eccentric mass of each bulge exerts a small amount of gravitational attraction on the Moon, with the bulge on the side of Earth closest to the Moon pulling in a direction slightly forward along the Moon's orbit (because Earth's rotation has carried the bulge forward). The bulge on the side furthest from the Moon has the opposite effect, but because the gravitational attraction varies inversely with the square of distance, the effect is stronger for the near-side bulge. As a result, some of Earth's angular (or rotational) momentum is gradually being transferred to the rotation of the Earth–Moon pair around their mutual centre of mass, called the barycentre. This slightly faster rotation causes the Earth–Moon distance to increase at approximately 38 millimetres per year. Conservation of angular momentum means that Earth's axial rotation is gradually slowing, and because of this its day lengthens by approximately 23 microseconds every year (excluding glacial rebound). Both figures are valid only for the current configuration of the continents. Tidal rhythmites from 620 million years ago show that, over hundreds of millions of years, the Moon receded at an average rate of per year (2200 km or 0.56% or the Earth-moon distance per hundred million years) and the day lengthened at an average rate of 12 microseconds per year (or 20 minutes per hundred million years), both about half of their current values. The present high rate may be due to near resonance between natural ocean frequencies and tidal frequencies. See also tidal acceleration for a more detailed description.
   The Earth and its Moon are one example of this configuration. 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. Other examples are the Galilean moons of Jupiter (as well as many of Jupiter's smaller moons) and most of the larger moons of Saturn.
   Section::::Physics.:Dissipation.
  
  Earth's tidal oscillations introduce dissipation at an average rate of about 3.75 terawatts.
  
  About 98% of this dissipation is by marine tidal movement.
  
  Dissipation arises as basin-scale tidal flows drive smaller-scale flows which experience turbulent dissipation. This tidal drag creates torque on the moon that gradually transfers angular momentum to its orbit, and a gradual increase in Earth–moon separation. The equal and opposite torque on the Earth correspondingly decreases its rotational velocity. Thus, over geologic time, the moon recedes from the Earth, at about /year, lengthening the terrestrial day.
   A perfectly stable geostationary orbit is an ideal that can only be approximated. In practice the satellite drifts out of this orbit because of perturbations such as the solar wind, radiation pressure, variations in the Earth's gravitational field, and the gravitational effect of the Moon and Sun, and thrusters are used to maintain the orbit in a process known as station-keeping.
  
  Section::::Other geosynchronous orbits.
   Although the forces balance at these points, the first three points (the ones on the line between a certain large mass, e.g. a star, and a smaller, orbiting mass, e.g. a planet) are not stable equilibrium points. If a spacecraft placed at the Earth–Moon point is given even a slight nudge away from the equilibrium point, the spacecraft's trajectory will diverge away from the point. The entire system is in motion, so the spacecraft will not actually hit the Moon, but will travel in a winding path, off into space. There is, however, a semi-stable orbit around each of these points, called a halo orbit. The orbits for two of the points, and , are stable, but the halo orbits for through are stable only on the order of months.
   Because the Moon's mass is a considerable fraction of that of Earth (about 1:81), the two bodies can be regarded as a double planet system, rather than as a planet with a satellite. The plane of the Moon's orbit around Earth lies close to the plane of Earth's orbit around the Sun (the ecliptic), rather than in the plane perpendicular to the axis of rotation of Earth (the equator) as is usually the case with planetary satellites. The mass of the Moon is sufficiently large, and it is sufficiently close, to raise tides in the matter of Earth. In particular, the water of the oceans bulges out towards and away from the Moon. The average tidal bulge is synchronized with the Moon's orbit, and Earth rotates under this tidal bulge in just over a day. However, Earth's rotation drags the position of the tidal bulge ahead of the position directly under the Moon. As a consequence, there exists a substantial amount of mass in the bulge that is offset from the line through the centers of Earth and the Moon. Because of this offset, a portion of the gravitational pull between Earth's tidal bulges and the Moon is not parallel to the Earth–Moon line, i.e. there exists a torque between Earth and the Moon. Since the bulge nearer the moon pulls more strongly on it than the bulge further away, this torque boosts the Moon in its orbit and slows the rotation of Earth.
   However, because the 18.6-year cycle of standstills is so much longer than the Moon's orbital period (about 27.3 days) that the change in the declination range over periods as short as half an orbit is very small. The period of the lunar nodes precessing in space is slightly shorter than the lunar standstill interval due to Earth's axial precession, altering Earth's axial tilt over a very long period relative to the direction of lunar nodal precession. Simply, the standstill cycle results from the combination of the two inclinations.
  
  Section::::Apparent position of the Moon during standstill.
   The Moon differs from most natural satellites around other planets in that it remains near the ecliptic (the plane of Earth's orbit around the Sun) instead of Earth's equatorial plane. The Moon's maximum and minimum declination vary because the plane of the Moon's orbit around Earth is inclined about 5.14° with respect to the ecliptic plane, and the spatial direction of the Moon's orbital inclination gradually changes over an 18.6-year cycle, alternately adding to or subtracting from the 23.5° tilt of Earth's axis.
   At higher latitudes, there will be a period of at least one day each month when the Moon does not rise, but there will also be a period of at least one day each month when the Moon does not set. This is similar to the seasonal behaviour of the Sun, but with a period of 27.2 days instead of 365 days. Note that a point on the Moon can actually be visible when it is about 34 arc minutes below the horizon, due to atmospheric refraction.
   Using the simplified model where the orbit of the Moon around the Earth is circular, Schwaniger found that there exists a free-return trajectory in the plane of the orbit of the Moon which is periodic. After returning to low altitude above the Earth (the perigee radius is a parameter, typically 6555 km) the spacecraft would start over on the same trajectory. This periodic trajectory is counter-rotational (it goes from east to west when near the Earth). It has a period of about 650 hours (compare with a sidereal month, which is 655.7 hours, or 27.3 days). Considering the trajectory in an inertial (non-rotating) frame of reference, the perigee occurs directly under the Moon when the Moon is on one side of the Earth. Speed at perigee is about 10.91 km/s. After 3 days it reaches the Moon's orbit, but now more or less on the opposite side of the Earth from the Moon. After a few more days, the craft reaches its (first) apogee and begins to fall back toward the Earth, but as it approaches the Moon's orbit, the Moon arrives, and there is a gravitational interaction. The craft passes on the near side of the Moon at a radius of 2150 km (410 km above the surface) and is thrown back outwards, where it reaches a second apogee. It then falls back toward the Earth, goes around to the other side, and goes through another perigee close to where the first perigee had taken place. By this time the Moon has moved almost half an orbit and is again directly over the craft at perigee. Other cislunar trajectories are similar but do not end up in the same situation as at the beginning, so cannot repeat.
   The Moon makes a complete orbit around Earth with respect to the fixed stars about once every 27.3 days (its sidereal period). However, because Earth is moving in its orbit around the Sun at the same time, it takes slightly longer for the Moon to show the same phase to Earth, which is about 29.5 days (its synodic period). Unlike most satellites of other planets, the Moon orbits closer to the ecliptic plane than to the planet's equatorial plane. The Moon's orbit is subtly perturbed by the Sun and Earth in many small, complex and interacting ways. For example, the plane of the Moon's orbit gradually rotates once every 18.61 years, which affects other aspects of lunar motion. These follow-on effects are mathematically described by Cassini's laws.
   The mean semi-major axis has a value of . The time-averaged distance between Earth and Moon centers is . The actual distance varies over the course of the orbit of the Moon, from at the perigee to at apogee, resulting in a differential range of .
   Because the gravitational field created by the Moon weakens with distance from the Moon, it exerts a slightly stronger than average force on the side of the Earth facing the Moon, and a slightly weaker force on the opposite side. The Moon thus tends to "stretch" the Earth slightly along the line connecting the two bodies. The solid Earth deforms a bit, but ocean water, being fluid, is free to move much more in response to the tidal force, particularly horizontally. As the Earth rotates, the magnitude and direction of the tidal force at any particular point on the Earth's surface change constantly; although the ocean never reaches equilibrium—there is never time for the fluid to "catch up" to the state it would eventually reach if the tidal force were constant—the changing tidal force nonetheless causes rhythmic changes in sea surface height.
   Despite the Moon's rotational and orbital periods being exactly locked, about 59% of the Moon's total surface may be seen with repeated observations from Earth due to the phenomena of libration and parallax. Librations are primarily caused by the Moon's varying orbital speed due to the eccentricity of its orbit: this allows up to about 6° more along its perimeter to be seen from Earth. Parallax is a geometric effect: at the surface of Earth we are offset from the line through the centers of Earth and Moon, and because of this we can observe a bit (about 1°) more around the side of the Moon when it is on our local horizon.
   Classification of any one mechanism is mainly based on the circumstances in the disk that enable the mechanism to efficiently transfer energy and / or angular momentum to and from planetary orbits. As the loss or relocation of material in the disk changes the circumstances, one migration mechanism will give way to another mechanism, or perhaps none. If there is no follow-on mechanism, migration (largely) stops and the stellar system becomes (mostly) stable.
  
  Section::::Types of migration.:Disk migration.
   While gravitation causes acceleration and movement of the Earth's fluid oceans, gravitational coupling between the Moon and Earth's solid body is mostly elastic and plastic. The result is a further tidal effect of the Moon on the Earth that causes a bulge of the solid portion of the Earth nearest the Moon that acts as a torque in opposition to the Earth's rotation. This "drains" angular momentum and rotational kinetic energy from Earth's spin, slowing the Earth's rotation. That angular momentum, lost from the Earth, is transferred to the Moon in a process (confusingly known as tidal acceleration), which lifts the Moon into a higher orbit and results in its lower orbital speed about the Earth. Thus the distance between Earth and Moon is increasing, and the Earth's spin is slowing in reaction. Measurements from laser reflectors left during the Apollo missions (lunar ranging experiments) have found that the Moon's distance increases by per year (roughly the rate at which human fingernails grow).
   The Moon's rotation and orbital periods are tidally locked with each other, so no matter when the Moon is observed from Earth the same hemisphere of the Moon is always seen. The far side of the Moon was not seen until 1959, when photographs of most of the far side were transmitted from the Soviet spacecraft Luna 3.
  
  When the Earth is observed from the moon, the Earth does not appear to translate across the sky but appears to remain in the same place, rotating on its own axis.
   As a result of the Moon's synchronous rotation, one side of the Moon (the "near side") is permanently turned towards Earth, and the other side, the "far side", mostly cannot be seen from Earth. This means, conversely, that Earth can be seen only from the near side of the Moon and would always be invisible from the far side.
   The day-side magnetopause is compressed by solar-wind pressure—the subsolar distance from the center of the Earth is typically 10 Earth radii. On the night side, the solar wind stretches the magnetosphere to form a magnetotail that sometimes extends out to more than 100–200 Earth radii. For roughly four days of each month, the lunar surface is shielded from the solar wind as the Moon passes through the magnetotail.
   Gravitational Tides are caused by changes in the relative location of the Earth, sun, and moon, whose orbits are perturbed slightly by Jupiter. Newton's law of universal gravitation states that the gravitational force between a mass at a reference point on the surface of the Earth and another object such as the Moon is inversely proportional to the square of the distance between them. The declination of the Moon relative to the Earth means that as the Moon orbits the Earth during half the lunar cycle the Moon is closer to the Northern Hemisphere and during the other half the Moon is closer to the Southern Hemisphere. This periodic shift in distance gives rise to the lunar fortnightly tidal constituent. The ellipticity of the lunar orbit gives rise to a lunar monthly tidal constituent. Because of the nonlinear dependence of the force on distance additional tidal constituents exist with frequencies which are the sum and differences of these fundamental frequencies. Additional fundamental frequencies are introduced by the motion of the Sun and Jupiter, thus tidal constituents exist at all of these frequencies as well as all of the sums and differences of these frequencies, etc. The mathematical description of the tidal forces is greatly simplified by expressing the forces in terms of gravitational potentials. Because of the fact that the Earth is approximately a sphere and the orbits are approximately circular it also turns out to be very convenient to describe these gravitational potentials in spherical coordinates using spherical harmonic expansions.
   The changing distance separating the Moon and Earth also affects tide heights. When the Moon is closest, at perigee, the range increases, and when it is at apogee, the range shrinks. Every lunations (the full cycles from full moon to new to full), perigee coincides with either a new or full moon causing perigean spring tides with the largest "tidal range". Even at its most powerful this force is still weak, causing tidal differences of inches at most.
  
  Section::::Tidal constituents.:Other constituents.
   Constructions like those in Newton's diagram can be repeated for many different positions of the Moon in its orbit. For each position, the result is a perturbation vector like LS1 or LS2 in the second diagram. Shown here is an often-presented form of the diagram that summarises sizes and directions of the perturbation vectors for many different positions of the Moon in its orbit. Each small arrow is a perturbation vector like LS, applicable to the Moon in the particular position around the orbit from which the arrow begins. The perturbations on the Moon when it is nearly in line along the Earth-Sun axis, i.e. near new or full moon, point outwards, away from the Earth. When the Moon-Earth line is 90° from the Earth-Sun axis they point inwards, towards the Earth, with a size that is only half the maximum size of the axial (outwards) perturbations. (Newton gave a rather good quantitative estimate for the size of the solar perturbing force: at quadrature where it adds to the Earth's attraction he put it at of the mean terrestrial attraction, and twice as much as that at the new and full moons where it opposes and diminishes the Earth's attraction.)
  