Download Review Lecture 12

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