MTLE Earth and Space Science (Grades 9-12) cheat sheet

Earth's mean radius is about 6,371 km; the crust ranges 5-10 km thick (oceanic) to 25-70 km (continental), and the mantle extends to ~2,900 km depth.

Seismic P-waves (compressional, fastest, travel through solids and fluids) arrive before S-waves (shear, solids only); the S-wave shadow zone beyond 103° proves a liquid outer core.

Plate boundaries: divergent (new crust, mid-ocean ridges, shallow quakes), convergent (subduction or collision, deep quakes, volcanoes), transform (lateral slip, shallow quakes, no volcanism).

Magnetic polarity stripes symmetric about mid-ocean ridges record seafloor spreading; reversal chronology calibrates spreading rates of a few cm/yr.

Relative dating laws: superposition, original horizontality, lateral continuity, cross-cutting relationships, and faunal succession; radiometric dating (e.g., K-Ar, U-Pb, C-14) gives absolute ages.

Rock cycle: igneous (crystallization), sedimentary (weathering, transport, deposition, lithification), metamorphic (heat and pressure); partial melting of mantle peridotite yields basaltic magma.

Milankovitch cycles (eccentricity ~100 kyr, obliquity ~41 kyr, precession ~23 kyr) plus albedo and greenhouse-gas feedbacks drive glacial-interglacial cycles.

Earth's orbital and rotational parameters: axial tilt 23.44°, rotation 23 h 56 min 4 s (sidereal), revolution 365.25 days; tilt causes seasons, not distance from the Sun.

Atmospheric layers by temperature gradient: troposphere (lapse rate ~6.5 °C/km), stratosphere (ozone heating), mesosphere, thermosphere; pressure decreases with altitude.

Coriolis effect deflects moving air right in the Northern Hemisphere and left in the Southern; it is zero at the equator and maximum at the poles.

Global circulation cells (Hadley, Ferrel, polar) produce prevailing easterlies, westerlies, and the ITCZ; El Niño–Southern Oscillation shifts Pacific pressure and rainfall patterns.

Relative humidity is the ratio of actual to saturation vapor pressure; dew point is the temperature at which air reaches saturation; rising air cools adiabatically.

Ocean circulation: surface currents driven by wind and Coriolis, deep thermohaline circulation driven by temperature and salinity; upwelling brings nutrient-rich water to the surface.

Hydrologic cycle fluxes: evaporation, transpiration, condensation, precipitation, runoff, infiltration, and groundwater flow; watersheds are bounded by drainage divides.

Weathering and erosion: mechanical (frost wedging, abrasion) vs. chemical (hydrolysis, oxidation, dissolution); running water, glaciers, wind, and gravity are erosional agents.

Climate proxies (ice cores, tree rings, sediment cores, corals) and the Keeling curve document rising CO2 and global temperature trends over the instrumental and proxy record.

Solar system structure: terrestrial planets (Mercury, Venus, Earth, Mars), gas giants (Jupiter, Saturn), ice giants (Uranus, Neptune); asteroid belt between Mars and Jupiter; Kuiper belt beyond Neptune.

Kepler's laws: orbits are ellipses with the Sun at one focus; equal areas in equal times; P² ∝ a³ (P in years, a in AU) - Newton's gravity explains these.

Nebular hypothesis: solar nebula collapses, spins, flattens into a disk; inner disk is hot (rocky planets), outer disk cold (ices and gas giants).

Stellar evolution: protostar → main sequence (H fusion) → red giant/supergiant → white dwarf (low mass) or supernova → neutron star/black hole (high mass); mass determines fate.

Hertzsprung-Russell diagram plots luminosity vs. temperature; main sequence runs from hot, bright O/B stars to cool, dim M dwarfs; the Sun is a G2 main-sequence star.

Cosmology: Hubble's law v = H₀d (H₀ ≈ 70 km/s/Mpc); cosmic microwave background at ~2.7 K; Big Bang ~13.8 billion years ago; redshift indicates expansion.

Moon phases and eclipses: phases depend on Sun-Earth-Moon geometry; solar eclipse at new moon, lunar eclipse at full moon; eclipses require near-alignment with the orbital nodes.

Earth-Moon-Sun motions: lunar synodic month 29.5 days (phases) vs. sidereal month 27.3 days; precession of Earth's axis has a ~26,000-year period.

Earth's energy budget: incoming shortwave solar radiation is balanced by reflected shortwave (albedo ~30%) plus outgoing longwave infrared; greenhouse gases absorb and re-emit IR.

Electromagnetic spectrum order by increasing frequency: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma; wavelength and frequency are inversely related (c = λf).

Doppler effect: approaching source shifts light blue (shorter λ), receding source shifts red (longer λ); used for stellar radial velocity and galaxy redshifts.

Spectroscopy: emission lines are bright at specific wavelengths of each element; absorption lines appear dark against a continuum; each element has a unique spectral fingerprint.

Newton's laws and gravity: F = Gm₁m₂/r²; weight depends on local g; orbital velocity and escape velocity depend on mass and radius of the central body.

Rock and mineral identification: minerals are identified by hardness (Mohs 1-10), cleavage/fracture, luster, streak, and color; silicates dominate the crust.

Plate tectonics evidence: matching continental margins and fossils, paleomagnetic stripes, seafloor age patterns, and GPS-measured plate motion (~2-10 cm/yr).

Natural hazards: earthquakes measured by magnitude (logarithmic) and intensity; volcanoes at subduction zones and hotspots; floods, landslides, and hurricanes tied to climate and topography.