The Sun and Planets Lecture Notes 5. Spring Semester 2019 Prof Dr Ravit Helled 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. It is given by GM g= 2 R and on Earth it 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
Facts about the Moon 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/cm 3, 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. 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. 3
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 10 4 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 proto- Earth, 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
Mercury Orbits (review) The perihelion is the point in the orbit of a celestial body where it is nearest to its orbital focus, generally a star. It is the opposite of aphelion, which is the point in the orbit where the celestial body is farthest from its focus. The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. Orbital inclination measures the tilt of an object s orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. Mercury Mercury is the smallest and least massive of the eight planets in the Solar System, as well as the closest to the Sun. It is one of the four so-called terrestrial planets, i.e. a rocky body similar to the Earth. However, the similarities with Earth largely end there. Mercury has a number of unusual characteristics (relative to the other planets). The most notable of these unusual characteristics are Mercury s high density and large iron core, it s 3:2 spin-orbit resonance configuration, and its anomalous perihelion precession. Atmospheric Characteristics At first glance, Mercury appears to be a dry, airless planet. However, it actually hosts a (very!) tenuous atmosphere composed mostly of heavier elements: oxygen (42%), sodium (29%), hydrogen (22%), helium (6%), potassium (0.5%). The atmospheric surface pressure on Mercury is incredibly low, measuring only 10 14 bar! The atmospheric pressure at Earth s surface is 1.013 bar, for reference. Surface Characteristics Mercury s surface is dominated by impact craters. Volcanism does not play as important a role on Mercury as it does on the Moon. Tectonic activity on Mercury has produced large scarps (shrinkage cracks) across the surface. Mercury has the most extreme temperatures in the Solar System, reaching 425 C on the day side and 210 C on the night side. In 2012, NASA confirmed that images taken by the MESSENGER spacecraft show water ice in craters near Mercury s north pole. 8
Internal Structure Mercury consists of approximately 70% metallic and 30% silicate material. Mercury s density is the second highest in the Solar System at 5 400 kg/m3. It has a large iron core that accounts for an astonishing 42% of its volume. Layer Crust Mantle Core Thickness (km) 100 300 600 1800 Figure 5: The interior structure of Mercury. Unusual Features High Density / Large Core Mercury has a large iron core that accounts for 42% of its volume. This is not what we expect, given what we know about planet formation. There are three main theories that seek to explain this anomalous high density: 1. Giant impact Early in the Solar System s history, Mercury may have been struck by a planetesimal of approximately 1/6 its mass and several thousand kilometres across. The impact would have stripped away much of the original crust and mantle, leaving the core behind as a relatively major component. 2. Evaporation Much of Mercury s surface rock could have been vaporized at early stages when the Sun was extremely hot leading to the formation of a rock vapor atmosphere which was then carried away by the solar wind. 9
3. Drag The solar nebula causes drag on the particles from which Mercury was accreting, which meant that lighter particles were lost from the accreting material and not gathered by Mercury. 3:2 spin-orbit resonance Mercury completes three spins about its rotational axis for every two orbits that it completes. This means that Mercury rotates 1.5 times around its axis every orbit. The orbital period is 88 days, while the spin period is 56 days. Perihelion precession Newtonian physics can describe the motion of the planets in the Solar System nearly perfectly, but it can not explain the rate of Mercury s perihelion precession. It wasn t until Einstein developed the Theory of General Relativity that the mystery of Mercury s perihelion precession was solved. Because it s distance to the Sun is small, its orbital velocity is much faster than that of the other planets. It is therefore significantly affected by relativistic effects that are not accounted for in Newtonian physics. Missions to Mercury Mariner 10 Three flybys in 1973 and 1974. Mapped half of the planet. MESSENGER Orbited Mercury between 2011 and 2015. Mapped 100% of the planet. Figure 6: The surface of Mercury as mapped by the MESSENGER spacecraft. 10