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Review Lecture 12 Moon-Earth distance = 3.8 x 108 m • 30 RE RM = 3.5 x 106 m • 1/3.7 RE Maria are seas of hardened magma, smooth, dark, younger rocks Highlands are densely cratered, 4-5 km above maria Craters are evidence of early bombardment Average density = 3.34 g/cc Atmosphere = none Surface temperature = 100 - 400 K Magnetic field = none Rate of Crater Formation The first 800 million years of the Moon’s history was dominated by frequent crater-making impacts. Near the end of this intense bombardment, several large impacts gouged out the mare basins. For the past 3½ billion years the impact rate has been quite low. The thermal history is terrestrial in nature, but much further advanced than Earth because of its relatively small size and heat loss. The Moon presents one face to us. This is called synchronous motion and results from the tidal evolution of the Moon. The Moon’s orbit is elliptical. In the figure below the slices formed by the dashed lines joining the Moon to the Earth are all equal according to Kepler’s Law of Areas. The arrow attached to the Moon rotates at a constant rate. When the Moon moves fastest on its orbit the rotation is unable to keep up with its orbital motion. Thus, the arrow drifts to the East and a little more of the Western side of the Moon becomes visible. Later the Moon is slowest and the rotation exceeds the orbital motion and the reverse is true. A total of 59% of the Moon is visible over a lunar month. This is called Libration of the Moon. Sidereal revolution = 27.3 days Lunar month = 29.5 days The shadow line caused by the Sun’s shadow is called the terminator. Earth tides are caused by the gravitational attraction on ocean water (a fluid) by the Moon and Sun. When the Moon and Sun are in alignment this produces extra large tides called Spring tides. When the Moon and Sun are at a 90o angle with respect to the Earth tides are at their lowest and called Neap tides. In the figure the arrows indicate the strength of the Moon’s gravity at different points on the Earth. The force is proportional to 1/r2, where r is the distance from the center of the Moon to location of the point on the Earth. The centripetal force necessary for each point to travel in uniform circular motion about the 2 Moon goes like ω r , where the angular velocity ω is the same for each mass point. At any location the tidal force equals the Moon’s gravitational pull minus the Earth’s reaction force (centrifugal force). Objects rigidly attached to the Earth are held in place by shear forces. Water moves with the forces causing bulges as shown. Tidal Recession Earth tides produce a torque on the Moon. Because of the Earth’s rapid rotation, Earth’s tidal bulge (MM’) gets dragged off the Earth-Moon line at an angle θ ahead of the Moon’s orbit. The resulting force F on the moon has a component FE contributing to the centripetal force on the Moon. The component FM accelerates the Moon ahead in its orbit causing it to spiral slowly outward at a rate of 4 cm/year. The reaction to the force adding energy to the Moon’s orbit is a drag on the Earth which slows the rotation rate of the Earth. Three billion years ago the oceans formed when the Earth day was 5-6 hours long and the lunar cycle was approximately 17 days long. The Roche limit is approximately 2.2 Rplanet . Inside this radius gravitational forces disrupt moon formation. Lunar formation theories: Co-accretion unlikely - too little iron in Moon Capture unlikely - dynamics for capture are rough Inelastic collision from second body a possibility