Astronomy 263

Lecture 14

The Tide is High

Quiz 5 and Answers

The Moon has an orbital period around the Earth of 27.3 days (note this is a different period than that of the lunar phases). The rotation of the Moon on its own axis (its spin period) is also 27.3 days. The Moon is therefore in synchronous rotation around the Earth. The lunar orbit is tilted about 5o from the Earth's orbital plane and, in addition, is tilted with respect to the Earth's equatorial plane. This is very unusual and indicates that our Moon probably has an origin different than most of the moons around planets in the solar system. Another peculiarity of the Moon is the fact that its mass is about 1/81st that of the Earth compared to the largest moons of Jupiter and Saturn which are about 1/1000th of their parent planet. The Moon is therefore the largest moon in the solar system in proportion to its parent planet.

Prior to the Apollo lunar missions in the 60's and 70's there were 3 prevalent theories for the origin of the Moon. In the first theory, the Moon was a small inner planet which was captured by the Earth's gravity (capture theory). This leads one to infer that the lunar composition could be very different from the Earth since the Moon started out as a different planet completely. The second model was a twin formation theory where both the Earth and the Moon formed side-by-side from the same pre-planetary material. In this scenario the composition of the Earth and the Moon would be expected to be very similar. Finally there was the fission theory where the Moon was once thought to be part of the Earth but broke off the surface when the Earth was young and spinning very rapidly (coincidentally, the volume of the Moon and the Pacific ocean are about the same!). In the case of fission theory the composition of the Moon should be identical to the Earth. When the Apollo astronauts brought back lunar samples it was found that none of the hypotheses seemed to match the composition. It was similar in some ways and very different in others (e.g. the Moon has a high abundance of high melting-point materials and a small abundance of low melting-point materials relative to the Earth). A new theory was needed.

Present day astronomers believe that the Moon was a result of the impact of a large body with the Earth when the Earth was very young (an impact theory). The Moon formed out of debris which was blasted from the Earth's surface and ejected into orbit around the Earth. The present day Moon later formed, under the influence of gravity, into the body we see today. This model explains many of the peculiar features of the Moon: the lack of low melting-point materials (they were vaporized) and the abundance of high melting-point materials, the low iron content of lunar material (the core of the Earth was undisturbed by the impact), the mixed composition (Earth-like and not Earth-like) since the Moon is a mixture of 2 objects, and the peculiarities of the lunar orbit (determined by the details of the impact).

One phenomenon associated with the Moon are the tides, the change in height of the oceans which occurs on a daily basis. The tidal force is due to the difference between the gravitational force on the near side of the Earth and the attraction of the Earth to the Moon. Since gravity depends on the inverse square of the distance (see Newton's Laws) this differential force results in a tidal bulge, drawing the water in the oceans toward the Moon. On the side of the Earth away from the Moon the force is smaller than the attraction of the Earth to the Moon and this results in a tidal bulge half way around the globe. One quarter of the way around the globe of the Earth the net force is toward the center of the Earth and this causes a tidal depression, or low tide. As the Earth rotates then there are succesively high tides and low tides seperated by approximately six hours twice a day. There is also a solar tide but due to the Sun's large distance it is never more than about half the size of the lunar tide. However, when the alignment is favorable the combination of solar and lunar tides lead to large tides (oft called spring tides), while very low tides occur when the alignment of Sun and Moon are at right angles (referred to as neap tides).

In addition to the obvious effect on the oceans the tides also have an influence on the rotation of the Earth and the Moon. This phenomenon, called tidal braking, is a result of friction between the oceans and the solid part of the Earth which result on a force which brakes the Earth in its rotation. When the rotation of the Earth slows the Moon is forced to accelerate in its orbit and move farther from the Earth (conservation of angular momentum). The tidal force of the Earth on the Moon is responsible for the fact that the Moon always faces the Earth. The braking of the lunar rotation by the tidal force of the Earth has locked the rotation and the orbit of the moon. In fact, in the distant future these same forces will ultimately lock the Earth's roation with the lunar orbit and the Moon will always stay on one side of the Earth!