Download Lecture 5

The Sun and Planets
Lecture Notes 5.
Spring Semester 2017
Prof Dr Ravit Helled
Lecture 5
The Moon
Definitions
Escape Velocity
Escape velocity is the minimum speed needed for an object to escape a massive body.
The velocity depends only on the mass of the massive object and is independent of the
mass of the “escaping” object.
r
vesc =
2GM
R
where G is Newton’s gravitational constant, M is the mass of the body to be escaped,
and R is the distance from the center of mass of the body to be escaped and the escaping
object.
Surface gravity
The acceleration of a falling object at the surface of an object due to gravity. On Earth,
the gravitational acceleration is 9.8 m/s2 . When we talk about gravity beyond Earth’s
surface, we usually refer to the values relative to Earth’s surface gravity. For example,
the surface gravity on Mars is 3.71 m/s2 , which is 0.378 g (where g is short for “standard accelerations due to gravity on the surface of the earth”)—not to be confused with
Newton’s gravitational constant, G.
Albedo
The fraction of sunlight reflected by a surface. An albedo of A = 0 means that no light is
reflected (perfect absorption), whereas an albedo of A = 1 means that all light is reflected.
Atmospheric pressure
The surface pressure resulting from the overlying weight of the atmosphere. On Earth,
the atmospheric surface pressure is 1.01325 bars.
1
Eclipse
Occurs when one astronomical object casts a shadow on another object or crosses our
line-of-sight to another object.
Heavy bombardment
The period in the first few hundred million years—after the Solar System formed—during
which the tail end of planetary accretion created most of the craters found on ancient
planetary surfaces.
Impact basin
A very large impact crater often filled by a lava flow.
Impactor
The object responsible for an impact.
Synchronous rotation
Synchronous rotation is a term describing a body orbiting another, where the orbiting
body takes as long to rotate on its axis as it does to make one orbit; and therefore always
keeps the same hemisphere pointed at the body it is orbiting.
The Moon is in synchronous rotation about the Earth. Most major moons in the Solar
System have synchronous rotation due to tidal locking.
2
Moon Facts
• The Moon is Earth’s only natural satellite and the fifth largest satellite in the Solar
System.
• The Moon makes a complete orbit around the Earth every 27.3 days (the “orbital
period”). The periodic variations in the geometry of the Earth–Moon–Sun system are responsible for the phases of the Moon, which repeat every 29.5 days (the
“synodic period”).
• The Moon’s diameter is 3’474 km, and its volume is ∼2% that of the Earth. The
pull of gravity at its surface is about 17% of that at the Earth’s surface.
• The Moon is the only celestial body to which humans have traveled and upon which
humans have performed a manned landing. Several countries have announced plans
to return humans to the surface of the Moon in the 2020s.
• The Moon lacks an atmosphere. There are no clouds, vapour, wind, or rain.
• The Moon lacks oxygen or water to weather the rocks or alter its chemistry.
• Change on the Moon is slow. The footprints of the Apollo astronauts will still be
fresh a million years from now.
• The Moon is chemically different from asteroids or comets. It is differentiated and
not primitive; it lacks carbon and organic compounds.
• The Moon has a low density of ∼3.3 g/cm3 , which suggests that it lacks a metallic
core.
Lunar Maria
The dark and relatively featureless lunar plains are called maria (mare in the singular),
which is Latin for “sea(s)”, since they were believed by ancient astronomers to be filled
with water. These regions are large solidified pools of ancient basaltic lava. The majority
of these lavas erupted or flowed into the depressions associated with impact basins.
Maria are found almost exclusively on the near side of the Moon, with the far side having
only a few scattered patches covering ∼2% of its surface, compared with ∼30% on the
near side.
3
Lunar Highlands
The lighter-coloured regions of the Moon are called highlands since they are higher than
most maria. Several prominent mountain ranges on the near side are found along the
periphery of the giant impact basins, many of which have been filled by mare basalt.
These are believed to be the surviving ridges of the impact basin’s outer rims.
Figure 1: An image of the Moon depicting the lunar maria (the flat region) and lunar
highlands (the rough “mountainous” regions).
Impact Craters
The Moon’s surface is marked by impact craters. There are about a half million craters
with diameters greater than 1 km on the Moon. The lack of an atmosphere, weather, and
recent geological processes ensure that many of these craters have remained relatively well
preserved in comparison to those on Earth.
The largest crater on the Moon, which also has the distinction of the being one of the
largest known craters in the Solar System, is the South Pole-Aitken basin. This basin
is on the lunar far side, between the south pole and equator, and is some 2’240 km in
diameter and 13 km in depth.
4
Figure 2: A lunar topological map with the South Pole-Aitken basin shown in the center.
Notice the faint black line that traces the edge of the basin.
Impact crater formation model
1. Stage 1) Compression stage — Rocks are melted, vaporized or crushed, and shock
waves are sent out through the surface.
2. Stage 2) Excavation stage — Material excavated from the crater is distributed
radially as a blanket of fragmented debris or “ejecta”.
3. Stage 3) Post-cratering modification — “Isostatic” adjustment leads to the slumping of walls and the deep fracturing of the crater floor.
Figure 3: The stages of formation for an impact crater.
5
Moon internal structure
The Moon is differentiated, with three major layers: the crust, mantle, and core.
Figure 4: The internal layering of the Moon.
Lunar magnetic field
The Moon has an external magnetic field of the order of 1–100 nT (nanotesla). This is less
than one hundredth of Earth’s magnetic field strength, which is 30–60 µT (microtesla).
Other major differences are that the Moon does not currently have a dipolar magnetic
field (as would be expected from a geodynamo in its core), and the magnetizations that
are present are almost entirely crustal in origin.
Lunar atmosphere
The Moon has an atmosphere so thin as to be almost negligible. The total atmospheric
mass is less than 104 kg. The effective surface pressure of this atmospheric mass is
∼ 3 × 10−15 atm.
Lunar surface temperature
During the lunar day, the surface temperature averages 107◦ C. During the lunar night,
the surface temperature averages −153◦ C.
6
Origin of the Moon
The Moon is very large relative to the Earth (compared to other satellites). It’s density
is abnormally low, which implies that it is depleted in metals. Therefore it is expected to
either a small core or no core.
Several mechanisms have been suggested for the Moon’s formation. The formation of the
Moon is believed to have occurred about 4.527 billion years ago.
Hypotheses
1. Fission: Early speculation proposed that the Moon broke off from the Earth’s crust
because of centrifugal forces, leaving a basin—presumed to be the Pacific Ocean—
behind as a scar.
2. Capture: The Moon was formed elsewhere and subsequently captured by Earth’s
gravity. However, the conditions believed to be necessary for such a mechanism,
such as an extended atmosphere on Earth to dissipate the energy of the passing
Moon, are improbable.
3. Co-formation: The co-formation (also sometimes called “co-accretion”) hypothesis proposes that the Earth and the Moon formed together at the same time and
place from the primordial accretion disk. The Moon would have formed from material surrounding the proto-Earth, similar to the formation of the planets around
the Sun. However, this hypothesis may fail to explain the depletion of the metallic
iron in the Moon.
4. Giant Impact: The accepted hypothesis is that the Earth–Moon system formed
as a result of a giant impact. A Mars-sized body is believed to have hit the protoEarth, blasting sufficient material into orbit around the proto-Earth to form the
Moon through accretion. As accretion is the process by which all planetary bodies
are believed to have formed, giant impacts are thought to have affected most if
not all planets. Computer simulations modeling a giant impact are consistent with
measurements of the angular momentum of the Earth–Moon system, as well as the
small size of the lunar core. Unresolved questions regarding this theory concern
the determination of the relative sizes of the proto-Earth and impactor and of how
much material from these two bodies formed the Moon.
7