Secular Acceleration of Moon

In addition to the periodic irregularities the moon's motion mentioned above, prediction of the moon's position is further complicated by secular changes. A comparison of historical records of ancient eclipse with modern computerised timings of these same events show that, if the earth is constant, the moon is apparently accelerating in its orbit, advancing its position by about 10 seconds of arc per century.

The first explantion given for the acceleration was that planetary perturbations on the earth's orbit were causing its eccentricity to change. As a consequence, the effect of the sun's pull on the moon decreases and the moon accelerates. Subsequent detailed calculations however revealed that this theory can only account for just over half the observed acceleration. The most plausible explanation for the discrepancy which has emerged is that ocean tides dissipate energy in friction thereby slowing down the spin of the earth. The resultant secular increase in the length of the day ( 0.016 seconds per century ) resulte in a fictitious acceleration of the moon. This, however, is not the whole story.

For the angular momentum of the earth-moon system to be preserved the same tidal friction also causes the moon to recede from the earth, that is, its orbit increases and its orbital velocity decreases (Kepler's third law). In other words, tidal friction causes the moon to decelerate, which increases the length of the month. The apparent secular acceleration of the moon caused by the lengthening of the day is thus partially compensated by a secular deceleration due to the deformation of the moon's orbit. What is observed is the difference between the two effects.

Assuming the tidal friction theory is true, the moon will continue to recede to a distance where the period of rotation of the earth (the day) will equal the moon's period of revolution (the month). When this happens the earth and the moon will both keep the same sides continually towards each other (that is, only half of the earth will be able to see the moon). In fact, tidal forces are believed to have caused the slowing down of the orbital motion of the moon to a stage where the lunar period of rotation is equal to its period of revolution. One can also surmise from this theory that a long time ago the day was only a few hours long.

The theory futher predicts that when the month equals the day the lunar tide effect will then cease. However, tidal friction due to solar gravitation must persist. Solar tidal drag will decrease the angular momentum of the earth-moon system since it slows down the system's rotation. Consequently, the moon will slowly approach the earth once more.

Despite its interesting implications, tidal friction has been found to be an incomplete explanation to the lunar acceleration observed. Detailed calculations show that the loss of energy in the tides of the earth's main ocean is again too small to account for the observed acceleration. Other factors which may account for the slowing down of the earth's rotation have been suggested : interaction of the earth's magnetic field with interplanetary magnetic fields; progressive decrease in the force of gravitation, etc.

Whatever the reasons, it is accepted fact that the spin of the earth is slowing down causing an increase in the length of the day by about millisecond in a century and giving the moon a fictitious acceleration.