Geography of Mars

Lecture Notes for the Midterm

• Mars in Space
  • See Viewgraphs: "Mars in space."
  • Orbital characteristics
    • Orbital Eccentricity
      • Orbits are slightly elliptical
        • The major focus of Mars' or Earth's orbit is inside the Sun
        • The plane of that orbit is called the plane of ecliptic or just the ecliptic
        • Mars' plane of ecliptic nearly parallels that of the earth (and most of the planets except Pluto, whooops, not a planet, so its 17° orbital inclination doesn't really count any more <G>)
          • This alignment of orbits along a common group ecliptic makes sense, since they all formed as gravitational accretions in the same solar disk of gasses and dust
          • This disk formed when the primordial proto-solar nebula, by rotating, generated centrifugal force that gradually flattened it
        • The diameter of the planet's orbit along its long axis is the major axis; half that distance (from the center of the orbit to the orbit itself where it crosses the major axis) is called the semi-major axis ("half axis")
        • The diameter of the planet's orbit along its short axis, 90° along the plane of ecliptic from the major axis, is called the minor axis
        • Half that is, of course, the semi-minor axis
      • Calculating eccentricity:
        • There are a few different ways of calculating eccentricty:
          • c and a -- If we measured the distance between the very center of the planet's orbit to the focus, or Sun (c on the slide), and then divided that distance by the semi-major axis (a on the slide), we would have the eccentricity of the planet's orbit. For your reference pleasure, c is roughly 21,250,000 km for Mars (and only 2,500,000 km for Earth). The semi-major axis, a, can be thought of as the average of the aphelion and perihelion distances or roughly 227,950,000 km for Mars (and 149,600,000 km for Earth).

            e = c/a

          • a and b or semi-major and semi-minor axes, respectively -- You can square both the semi-major and the semi-minor axes. Then, subtract the semi-minor axis square from the semi-major axis square. Now, divide the answer by the square of the semi-major axis. The last step is taking the square root of that answer. The semi-minor axis is a simple function of the semi-major axis if you know c: b = sqrt(a² - c²). For Mars, b is about 226,957,353 km (for Earth, it's 149,579,110).

            e = sqrt ( (a² - b²) / a² )

          • Aphelion and Perihelion -- This is probably the easiest way to go: few steps and readily available information. Take the perihelion distance between the planet in question and the sun and subtract it from the aphelion distance. Next, add the two distances together. Then, divide the former by the latter:

            e = (Da - Dp) / (Da + Dp)

        • For Mars, that eccentricity is 0.0934, one of the largest in the solar system at this time: Only Mercury and Pluto are more eccentric (for Earth, it's only 0.0167)
      • Changes in eccentricity
        • Planet's orbits change in shape through time, oscillating from nearly circular to more eccentric
        • Earth's varies from ~0.01 to ~0.05 over a period of roughly 100,000 years
        • Mars' varies from ~0.00 to ~0.14 over approximately 96,000 (Earth) years, and there is apparently another cycle under that, which runs about 2.2 million Earth years.
        • Mars' eccentricity is more unstable than Earth's because it is more readily influenced by the closer gravitation of Jupiter and the other outer solar system planets and it is a smaller body. It is currently becoming more eccentric, aiming for about 0.105 in about 24,000 years.
        • Changes in Mars' eccentricity would be a strong, quasi-rhythmic driver of climate change by altering insolation receipt and the behavior of wind, dust, temperature contrasts, frost and glaciation, atmospheric pressure, and the ability of liquid water to persist on the surface. Sediments of all kinds on Mars can be expected to document these effects, and the stack of sediments in the center of Gale Crater was a major reason for putting Curiosity there.
        • As if that weren't enough, the major axis itself precesses, which affects the alignment of perihelion/aphelion with solstices and equinoces. On Earth, the apsides are fairly close to the solstices (perihelion on January 3rd is just over a week after the northern winter solstice and aphelion on the 4th of July is not much later than the summer solstice, and that puts the most intense insolation in the watery hemisphere, which helps even things out). As the major axis of the orbit shifts, perihelion will shift into the Northern Hemisphere summer and seasonal differences will be exaggerated.
      • Eccentricity and distance from the sun at different times of year.
        • The semi-major axis is a representation of a planet's characteristic distance from the sun: For Mars, it's 227,936,640 km (compared with Earth's 149,597,890 km)
        • Perihelion distance: 206,700,000 km (Earth: 147,100,000 km). Perihelion distance is the distance between the planet and the focus at the point the planet crosses its orbit's semi-major axis at the closest approach to the Sun
        • Aphelion distance: 249,200,000 km (Earth: 152,100,000 km). Aphelion distance is the distance between the planet and the focus at the point the planet crosses its orbit's semi-major axis at the farthest approach to the Sun
        • Martian perihelion distance is only 82.9% of aphelion (for Earth, perihelion distance is 96.7% of aphelion)
        • Where the difference in energy receipt on Earth between perihelion and aphelion is trivial (at least as long as perihelion takes place during the more oceanic hemisphere's summer, around 3 January), it is a significant seasonal driver on Mars
          • Irradiance at the top of the atmosphere is a function of the sun's surface emissivity (62,900,000 joules/m²/s), its radius (~696,000 km), and the distance between it and a planet:

            I = E * (R/D)²
            Where:

            • I = Irradiance at the top of the atmosphere (j/m²/sec)
            • E = Surface Emmissivity of the sun (j/m²/sec)
            • R = Radius of the sun (km)
            • D = Distance between the sun and the planet in question (km)

          • So, I_Earth = 1,361 j/m²/s, while I_Mars = 587 j/m²/s, or only 43% of Earth's: This alone would make Mars pretty chilly, all else equal!
          • I_Earth at aphelion = 1,317 j/m²/s, while at perihelion, I_Earth = 1,408 j/m²/s. So, Earth's insolation at aphelion is fully 94% of the perihelion value. That shows you how Earth's orbital eccentricity is a trivial driver of seasonal differences between the two hemispheres.
          • I_Mars at aphelion = 491 j/m²/s, while at perihelion, I_Mars = 713 j/m²/s. So, Mars' insolation at aphelion is only 69% of the perihelion value! This is a major difference in insolation, and it means that the Southern Hemisphere has a more extreme seasonality than the Northern Hemisphere, because perihelion occurs during the Southern Hemisphere's summer and aphelion during its winter, exaggerating the seasonal contrasts.
  • Rotational characteristics
    • Obliquity or axial tilt:
      • Mars' axis of rotation is 25° 11' 24" (25.19°) from the vertical of the plane of ecliptic
      • Earth's is 23° 26' 24" or 23.44° from the vertical of the plane of ecliptic
      • So, Mars has a somewhat greater seasonal contrast than Earth does, simply because of its slightly greater axial tilt.
      • Where Earth's North Pole currently points to Polaris, Mars' North Pole points towards Deneb, one of the Summer Triangle stars (Deneb, Vega, Altair), which occupy Earth's Northern Hemisphere skies from east to overhead to west, depending on the time of summer.
    • Precession or change in the axial tilt
      • Mars takes 93,000 martian years or ~125,000 Earth years to precess 360°
      • Earth takes ~25,765 years to precess a full 360° or about 1 ° per 71.6 years
      • Precession of the axis causes the north and south poles of a planet to point to different "pole stars" through time. Earth's will gradually point away from Polaris (aka Alpha Ursæ Minoris) to Alrai or Gamma Cephei in about a thousand years!
    • Axial tilt and eccentricity combine to affect seasonal length
      • Since Earth's seasons are driven overwhelmingly by axial tilt and the effect of eccentricity is muted now that Earth has a more nearly circular orbit, we tend to think of our four seasons as equal in length, but they're not: In the Northern Hemisphere currently, winter is about 89 days long and summer is about 94 days long (95%), while fall is just under 90 days long and spring is not quite 93 days long, or 97% (just the opposite in the Southern Hemisphere). This reflects the acceleration and deceleration associated with Kepler's second law, as well as faint tugs by other planets' gravity.
      • For Mars, the seasons are much more asymmetrical in length, due to its greater eccentricity and the associated changes in velocity: The Northern Hemisphere spring (and Southern Hemisphere fall) is 194 sols (Mars days), while fall is only 142 sols (73%). Northern summer is 178 sols and northern winter is 154 sols (87%).
  • Size:
    • Equatorial radius: 3,396 km (Earth: 6,378 km)
    • North polar radius: 3,376 km vs. south polar radius: 3,382 km (Earth's average polar radius is 6,357 km, the south polar and north polar radii not being differentiated)
    • Equatorial circumference: 21,344 km (Earth: 40,075 km)
    • Volume: 163,140,000,000 km³ (Earth: 1,083,200,000,000 km³
    • Mass: 641.85 x 10¹⁸ metric tons (Earth: 5,973.70 x 10¹⁸ metric tons)
    • Equatorial surface gravity: 3.71 m/s² (Earth: 9.80 m/s²)
    • Escape velocity: 5.03 km/s (Earth: 11.19 km/s)
  • Shape
    • Markedly egg-shaped
    • Northern Lowlands drastically lower than the Southern Highlands (you saw that in Lab 2, where you used IDL and Gridview to create longitudinal profiles across the dichotomy at various longitudes on Mars)
    • Center of figure is offset from center of mass, leading to cartographic headaches
    • Possibly a huge impact knocked much of Mars' crust into space
    • Using the a and b version of the orbital calculation above and the equatorial and polar radii, we can calculate the ellipticity of the planet's shape:
      • For Earth, it's 0.08 (an oblate ellipsoid, or sphere flattened at the poles by the earth's rotation: Centrifugal force creates a slight bulge along the equator)
      • For Mars, it's 0.11, quite a bit more elliptical: Mars' ellipticity is greater and is quite asymmetric between the hemispheres (egg-shaped), with the north polar radius 6 km shorter than the south polar radius. Mars lost a lot of its northern end early on (likely due to a huge impact).
      • The distortion in shape and mass distribution means that Mars' center of mass is offset about 2.5 km - 3.0 km from its center of figure
      • This displacement is a cartographic headache, because geographic grids (parallels and meridians) are noticeably different for "planetographic" maps (based on the center of figure) and for "planetocentric" maps (based on the center of mass).
      • Here is a map showing both grids:
        http://planetarynames.wr.usgs.gov/images/mola_regional_boundaries.pdf
        • The red grid is planetographic, using "westings" from the Prime Meridian
        • The black grid is planetocentric, using "eastings"
  • Composition
    • As a terrestrial planet (inner solar system planet) like Earth, Mars is predominantly comprised of silicates and metals.
    • It is differentiated, like Earth, with an iron- and nickel-rich core and the lighter silicates pushed toward the surface
    • Differentiation is not as advanced as on Earth, so the core has more sulfur in it and the mantle has about twice the abundance of iron as found in Earth's mantle. There's also more potassium and phosphorous in the martian mantle than on Earth, where these are more abundant in the lithosphere/crust.
    • With a mean density of 3,933 kg/m³, Mars is about 71% the density of Earth (5,514 kg/m³), being more like our Moon (3,344 kg/m³) in that regard. This affects gravity on Mars, which is only 38% of Earth's, due both to the smaller size of the planet and its lower average bulk density.

  • Basic Internal Structure
    • Mars core is estimated to be 1,300 to 1,700 km in radius (Earth's is 3,845 km -- larger than the entire planet Mars!)
      • At present, it is not known whether the core is internally differentiated, like Earth's, into a solid inner core and a liquid outer core
      • If it's entirely solid now, that could help explain the loss of the planetary magnetic field
      • If there is an outer liquid core, the focus would then be on why it is not convecting and, thus, generating a magnetic field
      • The core is believed to be, like Earth's, largely iron with some nickel, which was drawn down to the center of the planet's gravity well by its early melting.
      • Mars' core is believed to have quite a bit of sulfur, perhaps as much as 14%. Earth's core is iron with 4% nickel and about 10% of other, lighter elements, including some sulfur. So, Mars may have noticeably more sulfur in its core than Earth.
    • Mars' mantle is somewhere between 1,590 km to 2,040 km thick, depending on estimates of the core radius and the crust.
      • Mars' mantle is enriched in iron, compared to Earth's, roughly twice as much.
      • It also has more potassium and phosphorus, which on Earth are depleted in the mantle and enriched in the crust.
      • It is in the mantle that silicate rock materials appear, segregated outwards during the differentiation of the planet. As on Earth, there's quite a variety of silicate minerals, depending on temperature and pressure conditions at a given depth.
      • Spinels are believed to dominate in the lower mantle with olivine, pyroxenes, and garnets higher up.
    • Mars' crust, while dominated by silicate rocks like Earth's is, differs from Earth's in being enriched in iron and mangesium (mafic, like Earth's ocean floor crust, and ultramafic).
      • It has not differentiated to the point of having silica and silicic/felsic minerals concentrated in the upper crust. Earth has, due partly to conservation of lighter, less dense materials at the surface by plate tectonics and their fractionation out in magma chambers.
      • The crust is thicker than Earth's. It ranges from about 100 km thick under Tharsis to about 10 km thick under Hellas Planitia. Generally, the Southern Highlands have a crustal thickness typically around 60-70 km, while the Northern Lowlands typically are around 35-45 km thick (though this isn't a perfect 1:1 correspondence). On Earth, crust is typically under 10 km thick under the ocean floor and 30-45 km thick under the continents, with the Andes and the Himalayas getting above 60 and 70 km, respectively.
  • Magnetism
    • Mars once had a planetary magnetic field, but it no longer exists.
    • It is believed to have collapsed around 4 billion years ago, perhaps sputtering back to life for a short while afterwards and then fizzing out for good.
    • Remanent magnetism is found on Mars, however.
      • This is the preservation of an ancient magnetic field's orientation in iron-rich rocks, the same way that Earth's record of magnetic field reversals is found in the basalts of the ocean floors.
      • When iron-bearing mineral matter melts and becomes magma or lava, as it solidifies or re-solidifies, the iron in the magma aligns with the then-current magnetic field as the minerals freeze out in the cooling mass.
      • These remanent magnetic fields were spotted by Mars Global Surveyor's MAGNETOMETER instrument as the spacecraft was ærobraking into Mars orbit in 1997.
      • Mars Express SPICAM instrument detected small auroræ in the areas that the MAGNETOMETER had found the magnetic anomalies: "auroralets" of a type never seen before!
    • Remanent magnetism is found associated with some really ancient craters on Mars and in areas that seem to be dikes, where magma was pushing its way to the surface along cracks and joints in the crustal rock but solidified in the cracks before reaching the surface.
    • Remanent magnetism is not found in the greatest craters, such as Hellas Planitia. These tremendous impacts would have melted rock into magma and most of the martian surface is covered with mafic rock, that is, containing iron. Yet, this iron-bearing magma did not show magnetic alignment! So, the planetary field must have collapsed by the time these bombs hit, which was during the Late Heavy Bombardment around 4.1 billion to 3.8 billion years ago.
    • So, Mars once had a relatively short-lived planetary magnetic field, evidenced by magnetic anomalies and auroræ today, but it had collapsed by the Late Heavy Bombardment.
    • Loss of the planetary magnetic field is linked with the subsequent erosion of the martian atmosphere, as the planet lost its protection from the solar wind and cosmic radiation and as hydrogen, especially, began to sputter away (taking any ocean or surface water with it).
      • Interestingly, like Mars, Venus has no intrinsic planetary magnetic field possibly because its retrograde rotation at 243 Earth days is too slow to induce convention in its core (it does have a weak field induced by interaction between its ionosphere and the solar wind, not one driven by an internal dynamo)
      • Even so, it has an extremely thick atmosphere, roughly 92 times as dense as Earth's and 9,200 times as dense as Mars'.
      • So, how come Venus retains its atmosphere and Mars wasn't able to, even though neither enjoys the protection of an intrinsic magnetic field against erosion by the solar wind?
      • Venus is considerably larger than Mars (its diameter at 12,100 km is similar to Earth's at 12,756, compared to Mars' at 6,792 km; Venus' average density is 5,243 kg/m³, much higher than Mars' at 3,933 kg/m³; this gives Venus more than twice the escape velocity of Mars at 10.4 m/sec² versus 5.0m/sec²).
      • So, while both planets are attacked by the solar wind and both have no protection from the planetary magnetic field, Venus' greater gravitation allows it to hang on to its atmosphere, especially the heavier constituents, such as carbon dioxide and, to a lesser extent, nitrogen.
      • Mars was less able to retain its atmosphere once the intrinsic magnetic field collapsed, especially against the much fiercer solar wind 4 billion years ago. Note, too, that it is the heavier carbon dioxide that dominates Mars' wispy atmosphere.
  • The moons of Mars: Phobos and Deimos
    • Cool video from Curiosity, showing Phobos eclipsing Deimos in August 2013: https://upload.wikimedia.org/wikipedia/commons/2/2f/PIA17352- MarsMoons-PhobosPassesDeimos-RealTime.gif
    • Both are similar to carbonaceous chondrite meteoroids and C-type asteroids.
    • Possible origins:
      • Perhaps they are captured Main Belt (between Mars and Jupiter) asteroids (but such capture generally leads to extremely elliptical orbits, so their nearly circular orbits around Mars pose a problem for that concept)
      • Because of the orbit issue, others speculate that they may have formed near Mars and orbited their near neighbor
      • Another idea is that they may be remnant debris from a large impact on Mars. Mars has a shallower gravity well, so the local accretion of impact debris is a possibility, given that some Mars debris has wound up in independent orbit around the Sun (and crashed onto Earth as meteorites).
    • Phobos:
      • About 22 km in diameter
      • Heavily cratered with a variety of crater sizes (Stickney Crater is 9 km wide!)
      • Orbits Mars at 9,377 km, every 7.66 hours, in a nearly circular orbit above Mars' equator (counterclockwise, if viewed over Mars' north pole)
      • Because it is so close to Mars and, therefore, orbits so fast, it rises in the west and sets in the east, because it is moving faster than Mars itself rotates
      • This means it is below the synchronous orbit radius, which exerts a tidal drag on it, slowing it down as some of its angular momentum is transferred to Mars
      • From Kepler's third law, then, we can expect slowing to reduce its ability to resist Mars' gravitation, shrinking the radius of its orbit.
      • So, the orbit is decaying: Phobos will eventually break up and crash into Mars, perhaps in 50 million years or so
      • Tidally locked, always presenting the same face towards Mars (as is the case with our Moon)
    • Deimos:
      • About 13 km in diameter
      • Has a smoother, less cratered surface than Phobos
      • Orbits Mars at 23,460 km every 30.35 hours
      • Rises in the east and sets in the west because it orbits more slowly than Mars rotates.
      • Like Phobos (and our own Moon), Deimos is also tidally locked to Mars
      • Because Mars rotates faster than Deimos revolves, Deimos is getting a gravitational boost from Mars, picking up angular momentum, gradually pushing it away from Mars (kind of like our own Moon is). It will eventually be more subject to the Sun's gravitation than Mars' and will enter independent solar orbit and leave Mars.