Download General Proper es of the Terrestrial Planets

General Proper+es of the Terrestrial Planets •  The terrestrial planets are confined to the inner solar system: Mercury, Venus, Earth (or Earth–Moon), and Mars. •  Much more massive than the main belt asteroids •  Much less massive than the giant planets •  The rocky, central core of Jupiter is esCmated to be between 10 and 20 Earth masses, and if it became visible, might be considered the principal “terrestrial planet”. However, those rocky cores are under greater pressures than are the interiors of the terrestrial planets. •  For example, they are expected to be mixed with large quanCCes of ices, and this is true also for the smaller bodies of the outer solar system. •  Thus the natures of the planets of the inner solar system are sufficiently unique to be discussed as a separate group, the “inner” or “terrestrial” planets. •  The vast bulk of the rocky material of the terrestrial planets is in the interior, so much of what we know about the material of each planet comes mainly from its bulk properCes (i.e., the mean density, size, and mass) and the viewable surface. •  Only the Moon and Earth have yielded sufficient material for detailed laboratory analyses. •  The surfaces of Mars and Venus have been examined by on-­‐site probes and the composiCon has been invesCgated at a limited number of sites. •  Mercury has been seen only from fly-­‐by missions and remains largely unknown. Its similarity to Earth’s moon has made it a somewhat less well-­‐targeted desCnaCon. •  On the whole, the major planets are more spherical in shape than are the minor planets, comets, and meteoroids that permeate the larger solar system but none of them are precisely spherical. •  The approximate shape can be determined from ground-­‐based telescopes and, in most cases, those have been improved by direct imaging from space craV. •  The internal mass distribuCons can be and have been invesCgated by the perturbaCons on natural or arCficial satellite orbits for all the planets. •  The properCes of planetary interiors have been invesCgated primarily through seismic effects (for the Earth and the Moon), magneCc field effects (for some), and the bulk properCes such as radii, masses, mean densiCes, and surface densiCes (for all). •  The mean densiCes of the planets can be obtained simply from the bulk properCes of mass and radius. •  The mass is directly obtained by observaCon of the semi-­‐major axis of a moon in the case of most of the planets or from the acceleraCon of a space probe in the case of Mercury, Venus, (most) asteroids, or comets. •  In all the planets, impacts have played an important role in determining their physical and dynamical properCes. Planetary Surfaces 1.  Impacts •  The extensive cratering on the surfaces of the Moon or Mercury shows the effect of a long period of intense bombardment •  This may have been more intense for the Earth, Venus, and Mars because of their greater gravitaConal aXracCon •  The small populaCon of colliders that we know as meteors are destroyed in the atmospheres of the Earth or Venus, but much larger objects—meters or larger in diameter—explosively dissipate much or all of their material. •  The energy per unit mass arises ulCmately from the gravitaConal potenCal of the target body but more directly from the relaCve speed at impact: •  The effect of an impact depends criCcally on the velocity of the impact and the mass of the impactor. •  The mass of a meteoroid is unknown typically, but if its size can be determined, an esCmate of its density leads to a mass. •  The density ranges from 1000 kg/m3 for a “rubble pile” asteroid (an aggregaCon of loosely packed material) to solid nickel–iron, ∼8000 kg/m3. •  The speed of impact depends on the orbit of the impactor. •  If a meteoroid travels in a parallel path to the planet and has in effect no net speed with respect to it, the meteoroid will fall to the planet’s surface with the escape velocity of that planet: where Mp is the mass, Rp is the radius of the planet. •  This quanCty is 11.2 km/s for the Earth and only 5.01 km/s for Mars. •  A meteoroid of asteroidal origin is likely to have originated in the asteroid belt between Mars and Jupiter, although there is a relaCvely small populaCon of objects even within the orbit of the Earth. •  There is also a considerable populaCon of objects in the outer solar system, the “trans-­‐Neptunian objects,” which are more or less coplanar to the planets and travel in CCW orbits. These include the icy bodies of the Kuiper Belt. Finally, far beyond the 100 or so AU of this region is the spherically distributed Oort Cloud, from which we get the long-­‐period comets. •  A cometary object with a semi-­‐major axis, a, of 10,000 AU and perihelion distance, q, of 1 AU has an eccentricity: •  Therefore the speed of the comet at perihelion is just short of the escape velocity from 1 AU. The escape speed is: •  If the orbit is retrograde, the velocity is addiCve to the planet’s approximate speed, so that, for an encounter with Earth (orbital speed ≈ 30 km/s), the comet would impact with a speed of •  Here, we have computed a maximum case. The energy per unit mass involved in such a collision would be for Earth impact. •  Because the chemical energy released in a TNT explosion is 4.2 x 106 J/kg, such a cometary impact would be equivalent to ∼1000 kg of TNT per kg of impactor mass. •  Small impactors (meters across or less) ablate as they are passing through a planetary atmosphere, and fragments fall to the surface at the terminal velocity, not the escape velocity. •  Large objects (hundreds of meters to tens of kms, on the Earth), on the other hand, will not be slowed down very much and will impact with great violence, resulCng in a very large crater Meteorite impact crater in Arizona 2.  Observing Planetary Surfaces -­‐ Phase and Visibility •  The phase, f, of a planet is the fracCon of a planet’s diameter that appears illuminated by the Sun as viewed from the Earth. The phase angle, Φ, is the angle at the center of the planet between the direcCons to the Sun and to the Earth. The relaCon between f and Φ is: f = Note that when Φ = 0◦, the planet is fully illuminated. When Φ = 90◦, half the planet appears illuminated. •  At a phase angle of 180◦, f = 0. This is the case only at inferior conjuncCon, and is possible only for an interior planet •  Although all phase angles are possible for an interior planet (whether easily viewable or not!), this is not true for exterior planets. Phases of Venus •  For exterior planets, 0◦ ≤ Φ < 90◦, but even sharper constraints can be found, so that Φmax and fmin may be specified for a given planet. •  The phase angle of a planet can be calculated from the elonga-on, E (the angle between the Sun and the planet measured at the Earth, S⊕C in the figure) and the distances of the Earth from the Sun = r⊕, and of the Sun from the planet = rp, at any instant. (sin Φ)/r⊕=(sin E)/rp •  for given values of r⊕ and rp, the maximum phase angle, Φmax (and therefore minimum phase, fmin) of a superior planet occur at quadrature (E = 90◦): •  From the equaCons above, for superior planets, Φmax → 90◦ only if rp → r⊕. •  Mars has the smallest orbit beyond the Earth’s and therefore achieves the maximum separaCon from full phase that we see among the superior planets. •  The maximum possible value of Φmax for Mars occurs on the extremely rare occasion when the Earth is at aphelion at the same instant that Mars at quadrature (E = 90◦) at its perihelion. •  This leads to a minimum possible phase, fmin = 0.838. Because of the low probability of the required condiCons occurring, observed phases of Mars will almost always be greater than this. The Apparent Mo+on of Planets on the Celes+al Sphere •  All the planets revolve around the Sun in a counterclockwise (prograde) direcCon. As they move in their orbits, they also change their poisCon in the sky. •  The apparent moCon of the planets in the sky is called “retrograde” moCon. As it is seen from Earth, all the planets appear to change their posiCon in the sky periodically. •  It is because both their intrinsic moCon about the Sun and their reflex moCon, that is the reflecCon of the Earth’s rotaCon and orbital moCon in the sky. •  Because of Earth’s daily rotaCon, all stars and planets appear to move from east to west in the night sky. In addiCon, outer planets also show a slow eastward moCon (direct moCon) relaCve to the stars. The orbital speed of the planets causes the retrograde moCon since the orbital speed of Earth and the planets differs from each other. The apparent direct and retrograde moCon of an outer planet. The green planet is the earth, the red planet is any outer planet and the yellow curved line is the apparent path of the planet among the stars. The white lines are the lines of sight. Mars’s retrograde moCon. Planetary Heat Flow and Temperatures •  The surface temperatures of planets in our solar system currently depend basically on four quanCCes: 1. The luminosity of the Sun 2. The distance of the planet from the Sun 3. The planetary bolometric albedo 4. The heat welling up (rising) from the interior •  The first two of these determine the solar energy flux reaching the planet (the planet’s solar constant). •  And the third determines the energy flux actually absorbed by the planet. •  A planet’s surface temperature is determined by the equilibrium condiCon: the energy absorbed from the Sun + the energy welling up from the interior = the energy radiated by the planet. •  The total emiXed radiaCon of planets generally exceeds that absorbed from the Sun, some by significant amounts. •  Saturn, for example, radiates 78% more heat than it receives. The excess coming from internal heat sources. •  On the other hand, the internal heat sources in the terrestrial planets are far less important than solar radiaCon. •  For example, the average heat flux from Earth’s interior is 0.082 W/m2 (82 erg cm-­‐2 s-­‐1), and the total power radiated by the interior sources is 4.2 x 1013 W (4.2 x 1020 erg/s) . This compares to a radiaCve power of 1.09 x 1017 W (1.09 x 1024 erg/s) absorbed from the Sun. •  The temperature at the center of the Earth is determined as 6900 ± 1000 K by considering the average heat flux Solar Hea+ng •  The flux at distance r from the Sun’s center is •  (1) The power P, striking any cross-­‐secConal area α, normal to the direcCon of radiaCon (e.g., an area of a planetary surface with the Sun at the zenith, z = 0°) is Zenith (¤) (1) ¤(2) z x y α = x.y and the power absorbed over that area is •  where A is the bolometric albedo (effecCvely the raCo of reflected to incident bolometric flux). •  This power must be reradiated, because otherwise, the energy would increase conCnuously with Cme and the temperature would rise without limit (contrary to both observaCon and the laws of thermodynamics!). •  The reradiated or emiXed power for that area is similar to the luminosity of a star: where T is the equilibrium temperature. Sezng Pa = Pe, so that and we get the equilibrium temperature: •  (2) The power P, striking any cross-­‐secConal area α with the Sun at a z > 0° angle, and again, sezng the absorbed and emiXed power, Pa = Pe, equal, •  and designaCng the equilibrium temperature as Tα,0 and that of above derived for z > 0° as Tα,z , we get: •  we see that Tα,0 is the maximum possible temperature achievable during the day at the subsolar point, where the Sun is overhead. •  These temperatures are purely local temperatures, in the sense that every part of the planet can be thought of as having a different local temperature. If the Sun is not in the sky at all, the local temperature will decrease as the reradiated energy matches the reduced heat flux into the designated area. •  When we may make a similar calculaCon for the planet as a whole, we can have the mean equilibrium temperature for that planet. •  The reradiated power depends on how well the flux is distributed over the planet, i.e., it depends on the rotaCon as well as the atmospheric convecCon of the solar heat energy. Ignoring the laXer, we can discuss two cases: rapid and slow rota-ons. •  An example of the laXer would be a planet that is locked into its orbital angular rate so that the rotaCon period is equal to the revoluConary period (there is no such planet in the solar system). •  The mean equilibrium temperature for such a slowly rotaCng planet: •  The detecCon of some thermal radiaCon from the night side of Mercury in the 1960s proved conclusively that Mercury was not locked in a 1:1 spin–orbit coupling with the Sun; Doppler radar mapping later showed that the lock-­‐in rate is, rather 3ProtaCons = 2PrevoluCons •  So, if the planet is a rapid rotator, because all of the planet now contributes to the emission, on average the mean equilibrium temperature, •  Example: Earth’s mean equilibrium temperature? L = 3.83 x 1033 erg/s , F = 1.36 x 106 erg cm−2 s−1, A⊕ = 0.307, r⊕ = 1.49 x 1013 cm