Praxis Earth and Space Sciences cheat sheet

Earth's layers by composition: crust (oceanic ~5-10 km, basaltic; continental ~30-70 km, granitic), mantle (peridotite), core (Fe-Ni); by rheology: lithosphere, asthenosphere, mesosphere, outer core (liquid), inner core (solid).

Seismic waves: P waves (compressional, fastest, travel through solids and fluids) refract away from the core; S waves (shear, slower) cannot pass through liquid, producing the S-wave shadow zone beyond ~103 degrees.

Moho discontinuity separates crust from mantle; Gutenberg discontinuity (~2900 km) separates mantle from core; Lehmann discontinuity marks the inner-core boundary.

Density and pressure increase with depth; geothermal gradient averages ~25 degrees C per km in the crust, driven by radioactive decay of U, Th, K and residual accretion heat.

Relative dating principles: superposition, original horizontality, lateral continuity, cross-cutting relationships, inclusions, and faunal succession; unconformities are angular, disconformity, or nonconformity.

Absolute dating: half-life T1/2 = ln2/lambda; decay equation N = N0 e^(-lambda t); useful parent-daughter pairs include U-Pb (zircon), K-Ar, Rb-Sr, and C-14 (short range, <~50 kyr).

Geologic time scale order: Hadean, Archean, Proterozoic, Phanerozoic (Paleozoic, Mesozoic, Cenozoic); major extinctions at end-Ordovician, end-Devonian, end-Permian (~252 Ma, largest), end-Triassic, and end-Cretaceous (~66 Ma).

Plate tectonics evidence: matching continental margins, paleomagnetic striping and apparent polar wander, seafloor age symmetry at ridges, Wadati-Benioff zones, and hotspot chains (Hawaii-Emperor bend).

Isostasy: crustal blocks float on the mantle; Airy model (root thickness varies with density) versus Pratt model (density varies); postglacial rebound records mantle viscosity.

Mineral identification: Mohs hardness 1-10 (talc, gypsum, calcite, fluorite, apatite, orthoclase, quartz, topaz, corundum, diamond); cleavage versus fracture; streak is more reliable than color.

Bowen's reaction series: discontinuous branch olivine, pyroxene, amphibole, biotite; continuous branch Ca-plagioclase to Na-plagioclase; then muscovite, quartz, K-feldspar at lowest temperature.

Igneous classification by silica: felsic (granite, rhyolite), intermediate (diorite, andesite), mafic (gabbro, basalt); intrusive textures are coarse (phaneritic), extrusive fine (aphanitic) or glassy/vesicular.

Sedimentary rocks: clastic (conglomerate, sandstone, shale) by grain size; chemical (limestone, chert, rock salt); biochemical (coal, chalk); sorting, rounding, and cement indicate transport history.

Metamorphic grade indicators: slate, phyllite, schist, gneiss; index minerals chlorite, biotite, garnet, staurolite, kyanite, sillimanite; foliation versus non-foliated (quartzite, marble).

Weathering: mechanical (frost wedging, exfoliation, abrasion) versus chemical (hydrolysis of feldspar to clay, oxidation, carbonation/dissolution of limestone); higher temperature and rainfall accelerate chemical weathering.

Mass wasting classification by material and motion: creep, slump, debris flow, mudflow, rockfall, lahar; slope failure triggered by water saturation, undercutting, and vegetation loss.

Stream erosion and deposition: competence and capacity; V-shaped valleys in uplands, meanders, point bars, cut banks, oxbow lakes, and deltas in lowlands; base level controls incision.

Glacial features: U-shaped valleys, cirques, aretes, horns, moraines, drumlins, eskers, kettle lakes; till is unsorted, outwash is sorted; Milankovitch cycles drive glacial-interglacial cycles.

Ocean water composition: ~3.5% salinity dominated by Na+ and Cl-; salinity controlled by evaporation minus precipitation plus river input and sea-ice formation; residence times of ions vary widely.

Thermohaline circulation is driven by temperature and salinity (density); North Atlantic Deep Water forms near Greenland and drives the global conveyor belt; upwelling brings cold nutrient-rich water to shelves.

Surface currents are wind-driven and deflected by the Coriolis effect: Ekman transport ~90 degrees to the right in the Northern Hemisphere, producing coastal upwelling and gyres.

Tides: semidiurnal, diurnal, or mixed; spring tides at new and full moon, neap tides at quarter phases; tidal range amplified in narrow estuaries and bays.

Wave dynamics: wave speed c = sqrt(gd) in shallow water; refraction bends waves toward shore; longshore drift and rip currents shape coastlines.

Ocean zones: intertidal, neritic (to ~200 m), pelagic (epipelagic, mesopelagic, bathypelagic, abyssalpelagic), benthic; photic zone depth limited by light attenuation.

Water cycle reservoirs: oceans ~97%, ice caps and glaciers ~2%, groundwater ~0.6%, surface freshwater <0.02%, atmosphere tiny; residence times longest for deep groundwater and oceans.

Groundwater: porosity versus permeability; water table, confined versus unconfined aquifers, artesian wells, cone of depression; Darcy's law Q = K A (dh/dL).

Watershed concepts: drainage divide, hydrograph lag, base flow, stormflow; urbanization increases peak discharge and decreases lag time.

Atmospheric composition: N2 ~78%, O2 ~21%, Ar ~0.9%, CO2 ~0.04%; variable constituents include water vapor, ozone, and aerosols; ozone absorbs UV in the stratosphere.

Vertical structure by temperature trend: troposphere (decreasing), stratosphere (increasing due to ozone), mesosphere (decreasing), thermosphere (increasing); tropopause averages ~12 km.

Lapse rates: dry adiabatic ~10 degrees C/km, saturated adiabatic ~6 degrees C/km, environmental average ~6.5 degrees C/km; instability when environmental lapse rate exceeds saturated adiabatic.

Pressure and wind: pressure gradient force drives flow, Coriolis deflects (right in NH), friction slows and turns flow near the surface; geostrophic balance aloft.

Global circulation: Hadley, Ferrel, and Polar cells; trade winds, westerlies, polar easterlies; ITCZ near the thermal equator; jet streams at tropopause boundaries.

Cloud formation requires condensation nuclei and saturation; cloud types: cirrus, stratus, cumulus, cumulonimbus; precipitation types: rain, snow, sleet, freezing rain, hail.

Air masses classified by source: cP, cT, mP, mT; fronts: cold (steep, fast, narrow), warm (gentle, broad), occluded, stationary; midlatitude cyclones form at polar front.

Severe weather: thunderstorms require moisture, instability, lift; tornadoes from supercells with rotating updrafts; hurricanes need sea-surface temperature >26 degrees C, low shear, and Coriolis.

Climate controls: latitude, altitude, proximity to water, ocean currents, prevailing winds, and topography; greenhouse effect raises surface temperature ~33 degrees C above blackbody.

Kepler's laws: orbits are ellipses with the Sun at one focus; equal areas in equal times (angular momentum); P^2 proportional to a^3 (with P in years, a in AU).

Newton's gravitation F = G m1 m2 / r^2 explains orbits; escape velocity v = sqrt(2GM/r); orbital velocity v = sqrt(GM/r) for circular orbits.

Solar system formation: solar nebula collapse, accretion disk, planetesimals, differentiation into terrestrial (rocky, dense, small) and Jovian (gas/ice giants, massive) planets; frost line explains composition.

Solar structure: core (fusion of H to He via proton-proton chain), radiative zone, convective zone, photosphere (~5800 K), chromosphere, corona; sunspots follow an ~11-year cycle.

Stellar classification: OBAFGKM by temperature; main sequence, giants, supergiants, white dwarfs; Hertzsprung-Russell diagram plots luminosity versus temperature.

Stellar evolution: protostar, main sequence, red giant, planetary nebula plus white dwarf (low mass) or supernova plus neutron star or black hole (high mass); mass determines lifetime.

Galaxies: spiral, elliptical, irregular; Milky Way is a barred spiral ~100,000 light-years across with a central supermassive black hole; Hubble's law v = H0 d supports expansion.

Moon and tides: synchronous rotation, lunar phases every ~29.5 days synodic versus 27.3 days sidereal; solar and lunar eclipses require alignment near nodes.

Planetary data: terrestrial planets have few or no moons; Jupiter and Saturn have many; Venus has runaway greenhouse; Mars has thin CO2 atmosphere; Mercury has no atmosphere and extreme temperature range.

Earth's energy budget: incoming solar ~1361 W/m^2 at top of atmosphere; albedo ~30%; absorbed shortwave balanced by outgoing longwave; greenhouse gases trap infrared.

Milankovitch cycles: eccentricity (~100 kyr), obliquity (~41 kyr, 22.1-24.5 degrees), precession (~23 kyr); these modulate glacial-interglacial timing.

Solar activity influences: variations in irradiance, solar wind, and cosmic rays; geomagnetic storms from coronal mass ejections affect satellites, power grids, and communications.

Magnetosphere: generated by the geodynamo in the liquid outer core; shields Earth from solar wind; auroras occur where charged particles funnel along field lines at high latitudes.

Earth-Moon system: tides slow Earth's rotation and increase lunar distance (~3.8 cm/yr); Moon stabilizes axial tilt, moderating climate.

Carbon cycle: reservoirs include atmosphere, oceans, biosphere, soils, and rocks; ocean uptake and silicate weathering act as long-term sinks; fossil fuel combustion adds ~10 Gt C/yr.

Plate tectonics and climate: uplift increases weathering and CO2 drawdown; volcanic eruptions release CO2 and aerosols; supercontinent assembly alters ocean circulation.

Natural hazards and systems: El Nino-Southern Oscillation (ENSO) shifts precipitation and temperature patterns globally; La Nina generally cools the tropical Pacific.

Remote sensing and Earth observation: satellites monitor land cover, sea level, ice extent, and atmospheric composition; geostationary versus polar orbits serve different purposes.

Scientific method: observation, question, hypothesis, prediction, controlled experiment or field study, data analysis, conclusion, peer review, and replication; hypotheses must be falsifiable.

Variables: independent (manipulated), dependent (measured), controlled (held constant); confounding variables threaten validity; random assignment reduces bias.

Measurement: accuracy versus precision; significant figures reflect instrument uncertainty; percent error = |measured - accepted| / accepted x 100.

Graphing: line graphs for continuous change, bar charts for categories, scatter plots for correlation; slope and units carry meaning; label axes and include units.

Statistics: mean, median, mode, range, standard deviation; correlation does not imply causation; sample size and representativeness affect inference.

Geologic data: maps, cross sections, stratigraphic columns, and seismic records; contour lines connect equal elevation; gradient = change in field value / distance.

Models and inquiry: physical, conceptual, and mathematical models have assumptions and limits; use evidence to revise models; distinguish observation from inference.

Instructional design: 5E model (Engage, Explore, Explain, Elaborate, Evaluate); inquiry-based labs; formative versus summative assessment; misconceptions should be elicited and addressed.

Safety and ethics: lab safety rules, proper disposal of chemicals, field trip risk management, and ethical use of data; cite sources and avoid fabrication.

Scientific method: observation, question, hypothesis, prediction, controlled experiment or field study, data analysis, conclusion, peer review, and replication; hypotheses must be falsifiable.

Variables: independent (manipulated), dependent (measured), controlled (held constant); confounding variables threaten validity; random assignment reduces bias.

Measurement: accuracy versus precision; significant figures reflect instrument uncertainty; percent error = |measured - accepted| / accepted x 100.

Graphing: line graphs for continuous change, bar charts for categories, scatter plots for correlation; slope and units carry meaning; label axes and include units.

Statistics: mean, median, mode, range, standard deviation; correlation does not imply causation; sample size and representativeness affect inference.

Geologic data: maps, cross sections, stratigraphic columns, and seismic records; contour lines connect equal elevation; gradient = change in field value / distance.

Models and inquiry: physical, conceptual, and mathematical models have assumptions and limits; use evidence to revise models; distinguish observation from inference.

Instructional design: 5E model (Engage, Explore, Explain, Elaborate, Evaluate); inquiry-based labs; formative versus summative assessment; misconceptions should be elicited and addressed.

Safety and ethics: lab safety rules, proper disposal of chemicals, field trip risk management, and ethical use of data; cite sources and avoid fabrication.