Mercury. Mercury 9/13/2017 PROBLEM SET 2 IS DUE TUESDAY AT THE BEGINNING OF LECTURE

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1 Mercury PROBLEM SET 2 IS DUE TUESDAY AT THE BEGINNING OF LECTURE 14 September 2017 ASTRONOMY 111 FALL Mercury Properties of Mercury Comparison of Mercury and the Moon Water on Mercury and the Moon Ice on the polar craters of Mercury and the Moon Tidal locking and Mercury s eccentric orbit Moment of inertia and differentiation in terrestrial planets Half Mercury, half Moon (Image from Mariner 10, NASA) 14 September 2017 ASTRONOMY 111 FALL

2 Mercury s vital statistics Mass 3.302x10 26 g (0.055M ) Equatorial radius x10 8 cm (0.383R ) Average density g cm -3 Albedo Average surface temperature Orbital semimajor axis K Orbital eccentricity Sidereal revolution period Sidereal rotation period 5.791x10 12 cm (0.387 AU) days days MESSENGER (JHU-APL/NASA) 14 September 2017 ASTRONOMY 111 FALL Visits to Mercury There have been two: NASA s Mariner 10 conducted three close fly-bys in NASA s MESSENGER (MErcury Surface, Space ENvironment, Geochemistry and Ranging) Satellite orbited with Mercury for about four years before crashing into the planet s surface on April 30, Mariner 10 MESSENGER displays its scientific instrument complement as it passes by (NASA/JHU-APL) 14 September 2017 ASTRONOMY 111 FALL

3 Moon vs. Mercury Moon Mercury Mass [g] 7.349x x10 26 Radius [cm] x x10 8 Mean density [g cm -3 ] Albedo Mean temperature [K] Orbital semimajor axis [cm] 3.844x x10 12 Orbital eccentricity Obliquity to Solar orbit Tidally-locked rotation? Yes Yes Mean surface magnetic field [G] 0 2.2x10-3 Atmosphere None < bar Surface visited? Yes No 14 September 2017 ASTRONOMY 111 FALL Moon v. Mercury (cont.) From the appearance, albedo, and reflectance spectra, we conclude that the surfaces are similar in composition: pyroxene bearing rocks (no feldspar) From the density, we conclude that Mercury has more than its share of iron in the form of a core with a radius about ¾ that of the planet. From the magnetic field, we conclude that Mercury s core is probably liquid for a dynamo mechanism to operate. Diagrams by UCAR (U. Michigan) 14 September 2017 ASTRONOMY 111 FALL

4 Tectonic activity: Mercury v. Moon From observations of rilles and scarps, we conclude that both have a plastic mantle, but that Mercury has been tectonically active and the Moon has not. Recently, volcanoes have been seen on Mercury within the giant Caloris impact basin. The moon has none. MESSENGER (JHU-APL/NASA) 14 September 2017 ASTRONOMY 111 FALL Water on airless Solar System bodies It is easy for hydrogen to escape from small bodies like the Moon and Mercury, and easy for sunlight to dissociate water into H and O. So is there any water at or just underneath the surface of Mercury and the Moon? There are two good reasons to think that there should be, despite the difficulties: 1. The solar wind. The Sun is constantly spewing out about M year -1 in the form of the Solar wind, mostly as protons and electrons. Travelling at high speeds, the protons bury themselves several cm below the surface of an airless they encounter. It does not take long for each proton to become H, nor for two of these to make water with a nearby O. This is probably the origin of the widespread water recently detected on the Moon by the NASA Deep Impact and ISRO Chandrayaan-1 spacecraft. Quantity: about one liter per ton of rock or regolith. What is closest to the surface seems to come and go with darkness and sunlight. 14 September 2017 ASTRONOMY 111 FALL

5 Moon temp, water content Temperature (left) and water concentration (right) on the Moon one quarter of a lunar day apart. From Jessica Sunshine and the EPOXI team. 14 September 2017 ASTRONOMY 111 FALL Polar ice: Mercury v. Moon 2. Comet and asteroid impacts. In principle, comets and asteroids could deliver larger amounts of water to the Moon and Mercury than the Solar wind can. It would not last long in the sunshine on either body it would evaporate, dissociate, and in short order the hydrogen would escape. But because the Moon and Mercury both have very small obliquity (tilt of rotation axis from the orbital axis), there are permanently shaded parts of craters near the north and south poles, where some of the delivered water can last in Mercury s case, practically forever. 14 September 2017 ASTRONOMY 111 FALL

6 Polar Ice: observations with Clementine The BMDO Clementine satellite passed over the poles of the Moon in early 1994 and took images that were interpreted as showing surface ice in polar craters. This would be of asteroidal/cometary origin, but the required amount was surprisingly large typically 5 m deep, 10 5 m 2 in area and the results remained controversial. Clementine was the DoD s first try at the faster better cheaper philosophy of spacecraft development. Images of the Moon s south pole from Clementine 14 September 2017 ASTRONOMY 111 FALL Polar ice: Lunar Prospector In 1998, NASA s Lunar Prospector satellite repeated the imaging observations, added neutron spectroscopy, and apparently confirmed the Clementine findings. Again plausible, but the low-energy neutron method of detecting water (hydrogen in the ice) had never been tried before under any conditions and was thus also controversial. Lunar Prospector was one of NASA s first tries at faster better cheaper. Like Clementine, there were difficulties in calibrating and interpreting its measurements. Lunar Prospector neutron-spectrometer scans during an orbit over both poles (Feldman et al. 1998) 14 September 2017 ASTRONOMY 111 FALL

7 Polar ice: observations with Arecibo In 1999, radar astronomers at Arecibo Observatory made a long-wavelength, radarpolarimetric study of the north pole of Mercury and found that the perpetuallyshadowed crater floors were very reflective in a way most easily explained by clean water ice. For ice detection, this technique is less controversial than the means employed by the Lunar satellites. But is was shocking nonetheless: ice on Mercury? Radar-reflectivity image of the north pole of Mercury (Harmon et al. 2001) 14 September 2017 ASTRONOMY 111 FALL Polar ice: Arecibo and the Moon Arecibo tried to confirm the Clementine and Lunar Prospector results. They were able to show that there is not any surface ice in the Moon s polar craters. Recently confirmed from space by the JAXA Kaguya/SELENE and NASA LRO satellites. Clementine-Prospector results were confounded by steep illumination angles, calibration difficulties. The you get what you pay for satellite development philosophy is making a comeback. Radar image of the Moon s south pole (N.J.S. Stacy, PhD dissertation, Cornell U.) 14 September 2017 ASTRONOMY 111 FALL

8 Polar ice: below the surface What about subsurface ice mixed with dirt in the Lunar polar craters? To expose this was the job of NASA s Lunar Crater Observation and Sensing Satellite (LCROSS) Make a small crater within a permanentlyshadowed region with the impact of a spent rocket stage. Analyze the composition of the ejecta from measurements by satellites directly overhead. A permanent shadow on the Moon (yellow contour) compared to neutron signal (blue) and the LCROSS impact site (red dot). (NASA and ISR/RAS) 14 September 2017 ASTRONOMY 111 FALL Polar ice: results from LCROSS Results show water ice present at the level of about 50 liters of water per ton of ejecta in this polar-crater floor. This would be on the high end of soil water content for the driest deserts on Earth, like the Sahara and Atacama. There is as much molecular hydrogen (H 2 ) in the soil as water ice, molecule for molecule. Much of the neutron signal was from this H 2. The water ice comes with very large amounts of other volatiles like CO, calcium, magnesium, and mercury. Species H 2 O 5.4 H CO 5.7 Hg 1.2 Ca 1.6 Mg 0.4 Abundance in ejecta (percent by mass) Colaprete et al. (2010), Gladstone et al. (2010) 14 September 2017 ASTRONOMY 111 FALL

9 Polar ice: comparison to previous results This is far less water than was claimed on the basis of the Clementine and Lunar Prospector results and is consistent with the Arecibo radar observations. There is enough to be scientifically interesting, and the mixture of volatiles will usefully constrain models of delivery and the thermal history of the crater floors. An entire permanently shaded region contains gallons, which would fill a large municipal water tower. This would go a long way toward the needs of a Lunar base. Has to be laboriously extracted and purified, though. 14 September 2017 ASTRONOMY 111 FALL Chemical composition of Mercury s surface Mercury formed from materials with less oxygen than those that formed other terrestrial planets Surface depleted in Fe and Ti by an order of magnitude Mg/Si ratio is 2-3 times higher than the Moon and other terrestrial planets Al/Si and Ca/Si are half as large Extremely high amount of S/Si (volatile) Surface chemistry maps (MESSENGER, JHU-APL/NASA) 14 September 2017 ASTRONOMY 111 FALL

10 Tidal locking and Mercury s orbit In celestial mechanics, tidal locking means that the heat dissipated during an orbit, by variations in the tidal forces, is minimized. Tidal forces are the gravitational force differences between one end and another of a body due to different distances away from a second body, and from one side to another of a body due to different directions toward the second body. The result is a stretch along the line between the two bodies and a compression in the perpendicular directions. We will derive formulas for tidal forces and much more on tides later this semester. 14 September 2017 ASTRONOMY 111 FALL An introduction to tidal forces Earth pulls all things toward its center, and pulls harder on things which are closer. To you, it seems as if you are stretched in the direction of the Earth s center and squeezed in the other direction. Figure from Thorne, Black holes and time warps 14 September 2017 ASTRONOMY 111 FALL

11 Tidal locking & Mercury s orbit (cont.) A body in circular orbit, with rotation period equal to revolution period, suffers no change in tidal forces as it travels its orbit. Thus, there is no heat dissipated from stretching and shrinking. The Moon s orbit about Earth has a fairly small eccentricity (0.055), so it can be considered circular to good approximation. The Moon s revolution and revolution periods are identical, so it is tidally locked. 14 September 2017 ASTRONOMY 111 FALL Mercury s elliptical orbit Mercury s orbit has a much larger eccentricity (0.2056) and thus is more distinctly elliptical. Reminder of the properties of ellipses: Equation x 2 a 2 + y2 b 2 = 1 Foci at x = ±c c = a 2 b 2 Eccentricity ε = c a = a2 b 2 Focal lengths (aphelion and perihelion distances) a f = a ± c = a 1 ± ε 14 September 2017 ASTRONOMY 111 FALL

12 ε = 0 (Circle) ε = (Mercury) Orbit comparison Drawn to scale, in units of semimajor axis length (a); coordinate axis origin on one focus. ε = (Moon) ε = September 2017 ASTRONOMY 111 FALL Mercury s orbit Since the distance between the Sun and Mercury varies by so much through an orbit, it is not possible to have no change in tides. Nevertheless, astronomers used to think that Mercury s rotation and revolution periods were equal (at 88 days) because that was what observations seemed to indicate and because it agreed with naïve expectations based on circular orbits. Aphelion a = AU f 2 = AU Sun b = AU f 1 = AU Perihelion 14 September 2017 ASTRONOMY 111 FALL

13 Mercury s orbit In the mid-1960s, though, radar astronomers at Arecibo Observatory showed that the rotation period of Mercury is actually closer to 59 days. Shortly thereafter, theoreticians realized that the minimum in tidal heating for Mercury s eccentric orbit was reached for an orbital period exactly 3/2 times the rotation period. In the mid-1970s, the fly-bys of Mariner 10 yielded the rotation period much more precisely and bore out this prediction. Mercury rotates exactly three times every two orbits. Like the Moon, the tidal forces to which it is subjected has made Mercury slightly oblong. The orbit is arranged so that the long axis always points toward the Sun at perihelion. This keeps the tidal stretching to a minimum, though the minimum is not zero. Other trivia: the perihelion of Mercury s orbit precesses slowly in a prograde direction. Long a mystery, the precise accounting for this orbital precession by warping of space by the Sun s gravity was one of the first triumphs of Einstein s general theory of relativity (1915). 14 September 2017 ASTRONOMY 111 FALL Moment of inertia and planetary differentiation For a given spin rate, different distribution of a given mass within the bounds of a planet would lead to different values of a planet s spin angular momentum. The relation between total angular momentum L and angular frequency ω is L = Iω where z r = r sin θ dm I = න r 2 dm θ r The moment of inertia can be measured from the fine details of a planet s gravitational field, as we will discuss in detail later this semester. x φ y 14 September 2017 ASTRONOMY 111 FALL

14 Moments of inertia Here are some simple spherical configurations of mass all with mass M and radius R and the corresponding moment of inertia. Constant-density sphere: I = 2 5 MR2 Spherical shell with constant mass per unit area: I = 2 3 MR2 Density maximum at center, declining linearly to zero at r = R: I = 4 15 MR2 = 0.267MR 2 The more strongly concentrated the mass is at the center, the smaller the leading factor in the expression for I. 14 September 2017 ASTRONOMY 111 FALL Moments of inertia & planetary differentiation (cont.) The Moon has I = 0.394MR 2, close enough to I = 2 5 MR2 that its density must be nearly constant. Mercury has I = 0.33MR 2, significantly smaller than the uniform-density value and probably reflective of a much larger density in the center than at the surface. An iron core, of the sort described above, would satisfy this. The moment of inertia and the average density can be used to calculate the properties of the core fairly confidently. A planet that is not concentrated at the center but tends to have a uniform density is called undifferentiated. The process of concentration of heavier minerals and metals at the center is called differentiation. 14 September 2017 ASTRONOMY 111 FALL