New Zealand Scholarship Earth and Space Science cheat sheet

Earth's four spheres exchange matter and energy: geosphere (rock/soil), atmosphere (gas), hydrosphere (water), biosphere (life); a change in one sphere propagates through the others via feedbacks.

Negative feedback damps a perturbation and stabilises the system (e.g. silicate weathering draws down CO2 as temperature rises); positive feedback amplifies it (e.g. ice-albedo feedback, permafrost carbon release).

Residence time = reservoir size / flux through the reservoir; atmospheric CO2 residence times are short for exchange fluxes but long for the slow rock cycle, so perturbation lifetimes differ by reservoir.

Albedo feedback: ice and snow reflect ~0.6-0.9 of incident sunlight while open ocean reflects ~0.06; loss of cryosphere lowers planetary albedo and adds absorbed energy.

Carbon cycle fluxes: photosynthesis and respiration exchange on 1-10 year timescales; silicate weathering and volcanism operate on 10^5-10^7 year timescales.

Energy balance: incoming absorbed shortwave = outgoing longwave; greenhouse gases raise effective emission altitude, so surface temperature rises to restore balance.

Latent heat of vaporisation of water (~2.26 x 10^6 J/kg) links hydrosphere and atmosphere; evaporation cools the surface and releases heat on condensation.

Tipping elements (AMOC weakening, Amazon dieback, ice-sheet collapse) are thresholds where a subsystem shifts to a qualitatively different state, often irreversibly on human timescales.

Plate boundaries: divergent (new lithosphere, ridges, shallow quakes), convergent (subduction or collision, deep quakes, arc volcanism), transform (strike-slip, shallow quakes).

Mantle convection and slab pull drive plates; ridge push is minor. Subducting slabs are cold and dense, giving Benioff-Wadati seismicity to ~700 km depth.

Bowen's reaction series orders crystallisation from mafic (olivine, pyroxene, Ca-plagioclase) to felsic (quartz, K-feldspar, muscovite); it predicts mineral assemblages and melt composition.

Igneous texture records cooling rate: fine-grained/glassy = rapid cooling, coarse-grained = slow intrusive cooling, porphyritic = two-stage cooling.

Clastic sedimentary rocks are classified by grain size (gravel, sand, silt, clay); sorting and roundness indicate transport distance and energy.

Metamorphic grade is tracked by index minerals (chlorite, biotite, garnet, kyanite, sillimanite); foliation develops under directed stress.

Mineral identification uses hardness (Mohs 1-10), cleavage, lustre, streak and density; quartz has conchoidal fracture and hardness 7, calcite hardness 3 and fizzes in dilute acid.

Isostasy: crust floats on the mantle in gravitational balance; mountain roots and post-glacial rebound reflect density contrasts, not rigidity.

Relative dating principles: superposition, original horizontality, lateral continuity, cross-cutting relationships, inclusions, and faunal succession.

Radiometric dating: N = N0 e^(-lambda t), lambda = ln2 / half-life; closure of the mineral system is required for a valid age.

Zircon U-Pb dating is the benchmark for Precambrian ages; 238U half-life ~4.47 Ga, 235U ~0.704 Ga.

Geological timescale order: Hadean, Archean, Proterozoic, Phanerozoic; Phanerozoic eras are Palaeozoic, Mesozoic, Cenozoic.

Major extinctions: end-Ordovician (~444 Ma), Late Devonian (~372 Ma), end-Permian (~252 Ma, largest), end-Triassic (~201 Ma), end-Cretaceous (~66 Ma, Chicxulub impact, Ir anomaly).

Key transitions: Great Oxidation Event ~2.4 Ga; Cambrian explosion ~541 Ma; first land plants ~470 Ma; K-Pg boundary marks non-avian dinosaur extinction.

Index fossils are geographically widespread, abundant and short-ranging; graptolites, ammonites and trilobites are classic examples.

Isotopic and geochemical proxies (delta-18O, delta-13C, 87Sr/86Sr) reconstruct past climate and carbon cycling; negative delta-13C excursions mark carbon-cycle perturbations.

Kepler's third law: P^2 proportional to a^3 for bodies orbiting the same mass; Newtonian form P^2 = 4 pi^2 a^3 / (G(M+m)).

Stellar classification by spectral type OBAFGKM from hot to cool; luminosity class I-V distinguishes supergiants to dwarfs.

Hertzsprung-Russell diagram: main sequence, red giants, white dwarfs; main-sequence lifetime scales roughly as M^(-2.5) relative to the Sun.

Stellar fusion: pp chain dominates in Sun-like stars; CNO cycle dominates above ~1.3 solar masses; iron fusion is endothermic, triggering core collapse.

Doppler radial-velocity method gives minimum planet mass; transit method gives radius; combining both yields density and constrains composition.

Solar System architecture: terrestrial planets inside the frost line, giant planets outside; meteorites and asteroids sample early Solar System material.

Hubble's law v = H0 d; H0 ~70 km/s/Mpc; cosmic microwave background at z ~1100 has temperature 2.725 K.

Nucleosynthesis: Big Bang produced H, He, Li; heavier elements form in stellar cores and during supernovae and neutron-star mergers.

Thermohaline circulation is driven by density contrasts from temperature and salinity; North Atlantic Deep Water forms where surface water cools and sinks.

Coriolis parameter f = 2 Omega sin(latitude); geostrophic balance gives currents flowing with high pressure to the right in the Southern Hemisphere and left in the Northern Hemisphere.

Wind-driven surface circulation forms subtropical gyres; Ekman transport is 90 degrees to the right of wind in the Northern Hemisphere, driving upwelling at coasts.

Ocean acidification: CO2 + H2O -> H2CO3 -> H+ + HCO3-; rising pCO2 lowers pH and carbonate saturation, stressing calcifiers.

Atmospheric circulation: Hadley, Ferrel and polar cells; ITCZ marks the convergence zone near the thermal equator.

Adiabatic lapse rates: dry ~9.8 C/km, saturated ~6 C/km; environmental lapse rate determines stability.

El Nino-Southern Oscillation: weakened trade winds and warm eastern Pacific; La Nina is the cool phase; both shift global precipitation.

Relative humidity = actual vapour pressure / saturation vapour pressure; dew point is the temperature at which saturation occurs.

Distinguish precision (repeatability) from accuracy (closeness to true value); random error affects precision, systematic error affects accuracy.

Null hypothesis H0 states no effect; a p-value is the probability of data at least as extreme under H0, not the probability H0 is true.

Correlation does not establish causation; confounding variables and reverse causation must be excluded by design or analysis.

Uncertainty propagation: for sums, absolute uncertainties add in quadrature; for products, relative uncertainties add in quadrature.

Radiometric and proxy data carry age-model uncertainty; quote ages with 2-sigma ranges and avoid over-precise dates.

Proxy records (ice cores, tree rings, sediments) require calibration against instrumental data; calibration range limits extrapolation.

Spatial and temporal sampling bias can dominate apparent trends; check resolution, coverage and detection limits before interpreting patterns.

Model validity requires testing against independent observations; distinguish hindcast fit from predictive skill.

Exoplanet habitability links astronomy to Earth systems: stellar type sets insolation and UV flux, while atmosphere and magnetic field govern surface conditions.

Mass extinctions couple solid Earth (volcanism, impacts) to climate (aerosols, CO2) and biosphere (extinction, recovery), so evaluate multiple lines of evidence.

Snowball Earth hypotheses require feedback loops (ice-albedo runaway) plus geological evidence (glacial deposits at low palaeolatitude, cap carbonates).

Plate tectonics controls long-term climate via silicate weathering and volcanic CO2 outgassing; uplift of the Himalayas is implicated in Cenozoic cooling.

Ocean circulation changes link to palaeoclimate proxies (delta-13C, foraminifera) and to atmospheric CO2, so combine marine and ice-core records.

Impact hazard assessment combines orbital dynamics, atmospheric entry physics and geological crater records; risk is expressed as probability times consequence.

Tidal evolution and Moon recession link orbital mechanics to Earth's rotation and sedimentary tidal rhythmites.

Planetary energy budgets apply across bodies: a body's equilibrium temperature depends on stellar flux, albedo and greenhouse forcing.

Plate boundaries: divergent (new lithosphere, ridges, shallow quakes), convergent (subduction or collision, deep quakes, arc volcanism), transform (strike-slip, shallow quakes).

Mantle convection and slab pull drive plates; ridge push is minor. Subducting slabs are cold and dense, giving Benioff-Wadati seismicity to ~700 km depth.

Bowen's reaction series orders crystallisation from mafic (olivine, pyroxene, Ca-plagioclase) to felsic (quartz, K-feldspar, muscovite); it predicts mineral assemblages and melt composition.

Igneous texture records cooling rate: fine-grained/glassy = rapid cooling, coarse-grained = slow intrusive cooling, porphyritic = two-stage cooling.

Clastic sedimentary rocks are classified by grain size (gravel, sand, silt, clay); sorting and roundness indicate transport distance and energy.

Metamorphic grade is tracked by index minerals (chlorite, biotite, garnet, kyanite, sillimanite); foliation develops under directed stress.

Mineral identification uses hardness (Mohs 1-10), cleavage, lustre, streak and density; quartz has conchoidal fracture and hardness 7, calcite hardness 3 and fizzes in dilute acid.

Isostasy: crust floats on the mantle in gravitational balance; mountain roots and post-glacial rebound reflect density contrasts, not rigidity.

Earth's four spheres exchange matter and energy: geosphere (rock/soil), atmosphere (gas), hydrosphere (water), biosphere (life); a change in one sphere propagates through the others via feedbacks.

Negative feedback damps a perturbation and stabilises the system (e.g. silicate weathering draws down CO2 as temperature rises); positive feedback amplifies it (e.g. ice-albedo feedback, permafrost carbon release).

Residence time = reservoir size / flux through the reservoir; atmospheric CO2 residence times are short for exchange fluxes but long for the slow rock cycle, so perturbation lifetimes differ by reservoir.

Albedo feedback: ice and snow reflect ~0.6-0.9 of incident sunlight while open ocean reflects ~0.06; loss of cryosphere lowers planetary albedo and adds absorbed energy.

Carbon cycle fluxes: photosynthesis and respiration exchange on 1-10 year timescales; silicate weathering and volcanism operate on 10^5-10^7 year timescales.

Energy balance: incoming absorbed shortwave = outgoing longwave; greenhouse gases raise effective emission altitude, so surface temperature rises to restore balance.

Latent heat of vaporisation of water (~2.26 x 10^6 J/kg) links hydrosphere and atmosphere; evaporation cools the surface and releases heat on condensation.

Tipping elements (AMOC weakening, Amazon dieback, ice-sheet collapse) are thresholds where a subsystem shifts to a qualitatively different state, often irreversibly on human timescales.

Relative dating principles: superposition, original horizontality, lateral continuity, cross-cutting relationships, inclusions, and faunal succession.

Radiometric dating: N = N0 e^(-lambda t), lambda = ln2 / half-life; closure of the mineral system is required for a valid age.

Zircon U-Pb dating is the benchmark for Precambrian ages; 238U half-life ~4.47 Ga, 235U ~0.704 Ga.

Geological timescale order: Hadean, Archean, Proterozoic, Phanerozoic; Phanerozoic eras are Palaeozoic, Mesozoic, Cenozoic.

Major extinctions: end-Ordovician (~444 Ma), Late Devonian (~372 Ma), end-Permian (~252 Ma, largest), end-Triassic (~201 Ma), end-Cretaceous (~66 Ma, Chicxulub impact, Ir anomaly).

Key transitions: Great Oxidation Event ~2.4 Ga; Cambrian explosion ~541 Ma; first land plants ~470 Ma; K-Pg boundary marks non-avian dinosaur extinction.

Index fossils are geographically widespread, abundant and short-ranging; graptolites, ammonites and trilobites are classic examples.

Isotopic and geochemical proxies (delta-18O, delta-13C, 87Sr/86Sr) reconstruct past climate and carbon cycling; negative delta-13C excursions mark carbon-cycle perturbations.

Kepler's third law: P^2 proportional to a^3 for bodies orbiting the same mass; Newtonian form P^2 = 4 pi^2 a^3 / (G(M+m)).

Stellar classification by spectral type OBAFGKM from hot to cool; luminosity class I-V distinguishes supergiants to dwarfs.

Hertzsprung-Russell diagram: main sequence, red giants, white dwarfs; main-sequence lifetime scales roughly as M^(-2.5) relative to the Sun.

Stellar fusion: pp chain dominates in Sun-like stars; CNO cycle dominates above ~1.3 solar masses; iron fusion is endothermic, triggering core collapse.

Doppler radial-velocity method gives minimum planet mass; transit method gives radius; combining both yields density and constrains composition.

Solar System architecture: terrestrial planets inside the frost line, giant planets outside; meteorites and asteroids sample early Solar System material.

Hubble's law v = H0 d; H0 ~70 km/s/Mpc; cosmic microwave background at z ~1100 has temperature 2.725 K.

Nucleosynthesis: Big Bang produced H, He, Li; heavier elements form in stellar cores and during supernovae and neutron-star mergers.

Thermohaline circulation is driven by density contrasts from temperature and salinity; North Atlantic Deep Water forms where surface water cools and sinks.

Coriolis parameter f = 2 Omega sin(latitude); geostrophic balance gives currents flowing with high pressure to the right in the Southern Hemisphere and left in the Northern Hemisphere.

Wind-driven surface circulation forms subtropical gyres; Ekman transport is 90 degrees to the right of wind in the Northern Hemisphere, driving upwelling at coasts.

Ocean acidification: CO2 + H2O -> H2CO3 -> H+ + HCO3-; rising pCO2 lowers pH and carbonate saturation, stressing calcifiers.

Atmospheric circulation: Hadley, Ferrel and polar cells; ITCZ marks the convergence zone near the thermal equator.

Adiabatic lapse rates: dry ~9.8 C/km, saturated ~6 C/km; environmental lapse rate determines stability.

El Nino-Southern Oscillation: weakened trade winds and warm eastern Pacific; La Nina is the cool phase; both shift global precipitation.

Relative humidity = actual vapour pressure / saturation vapour pressure; dew point is the temperature at which saturation occurs.

Distinguish precision (repeatability) from accuracy (closeness to true value); random error affects precision, systematic error affects accuracy.

Null hypothesis H0 states no effect; a p-value is the probability of data at least as extreme under H0, not the probability H0 is true.

Correlation does not establish causation; confounding variables and reverse causation must be excluded by design or analysis.

Uncertainty propagation: for sums, absolute uncertainties add in quadrature; for products, relative uncertainties add in quadrature.

Radiometric and proxy data carry age-model uncertainty; quote ages with 2-sigma ranges and avoid over-precise dates.

Proxy records (ice cores, tree rings, sediments) require calibration against instrumental data; calibration range limits extrapolation.

Spatial and temporal sampling bias can dominate apparent trends; check resolution, coverage and detection limits before interpreting patterns.

Model validity requires testing against independent observations; distinguish hindcast fit from predictive skill.

Exoplanet habitability links astronomy to Earth systems: stellar type sets insolation and UV flux, while atmosphere and magnetic field govern surface conditions.

Mass extinctions couple solid Earth (volcanism, impacts) to climate (aerosols, CO2) and biosphere (extinction, recovery), so evaluate multiple lines of evidence.

Snowball Earth hypotheses require feedback loops (ice-albedo runaway) plus geological evidence (glacial deposits at low palaeolatitude, cap carbonates).

Plate tectonics controls long-term climate via silicate weathering and volcanic CO2 outgassing; uplift of the Himalayas is implicated in Cenozoic cooling.

Ocean circulation changes link to palaeoclimate proxies (delta-13C, foraminifera) and to atmospheric CO2, so combine marine and ice-core records.

Impact hazard assessment combines orbital dynamics, atmospheric entry physics and geological crater records; risk is expressed as probability times consequence.

Tidal evolution and Moon recession link orbital mechanics to Earth's rotation and sedimentary tidal rhythmites.

Planetary energy budgets apply across bodies: a body's equilibrium temperature depends on stellar flux, albedo and greenhouse forcing.

Plate boundaries: divergent (new lithosphere, ridges, shallow quakes), convergent (subduction or collision, deep quakes, arc volcanism), transform (strike-slip, shallow quakes).

Mantle convection and slab pull drive plates; ridge push is minor. Subducting slabs are cold and dense, giving Benioff-Wadati seismicity to ~700 km depth.

Bowen's reaction series orders crystallisation from mafic (olivine, pyroxene, Ca-plagioclase) to felsic (quartz, K-feldspar, muscovite); it predicts mineral assemblages and melt composition.

Igneous texture records cooling rate: fine-grained/glassy = rapid cooling, coarse-grained = slow intrusive cooling, porphyritic = two-stage cooling.

Clastic sedimentary rocks are classified by grain size (gravel, sand, silt, clay); sorting and roundness indicate transport distance and energy.

Metamorphic grade is tracked by index minerals (chlorite, biotite, garnet, kyanite, sillimanite); foliation develops under directed stress.

Mineral identification uses hardness (Mohs 1-10), cleavage, lustre, streak and density; quartz has conchoidal fracture and hardness 7, calcite hardness 3 and fizzes in dilute acid.

Isostasy: crust floats on the mantle in gravitational balance; mountain roots and post-glacial rebound reflect density contrasts, not rigidity.

Earth's four spheres exchange matter and energy: geosphere (rock/soil), atmosphere (gas), hydrosphere (water), biosphere (life); a change in one sphere propagates through the others via feedbacks.

Negative feedback damps a perturbation and stabilises the system (e.g. silicate weathering draws down CO2 as temperature rises); positive feedback amplifies it (e.g. ice-albedo feedback, permafrost carbon release).

Residence time = reservoir size / flux through the reservoir; atmospheric CO2 residence times are short for exchange fluxes but long for the slow rock cycle, so perturbation lifetimes differ by reservoir.

Albedo feedback: ice and snow reflect ~0.6-0.9 of incident sunlight while open ocean reflects ~0.06; loss of cryosphere lowers planetary albedo and adds absorbed energy.

Carbon cycle fluxes: photosynthesis and respiration exchange on 1-10 year timescales; silicate weathering and volcanism operate on 10^5-10^7 year timescales.

Energy balance: incoming absorbed shortwave = outgoing longwave; greenhouse gases raise effective emission altitude, so surface temperature rises to restore balance.

Latent heat of vaporisation of water (~2.26 x 10^6 J/kg) links hydrosphere and atmosphere; evaporation cools the surface and releases heat on condensation.

Tipping elements (AMOC weakening, Amazon dieback, ice-sheet collapse) are thresholds where a subsystem shifts to a qualitatively different state, often irreversibly on human timescales.

Relative dating principles: superposition, original horizontality, lateral continuity, cross-cutting relationships, inclusions, and faunal succession.

Radiometric dating: N = N0 e^(-lambda t), lambda = ln2 / half-life; closure of the mineral system is required for a valid age.

Zircon U-Pb dating is the benchmark for Precambrian ages; 238U half-life ~4.47 Ga, 235U ~0.704 Ga.

Geological timescale order: Hadean, Archean, Proterozoic, Phanerozoic; Phanerozoic eras are Palaeozoic, Mesozoic, Cenozoic.

Major extinctions: end-Ordovician (~444 Ma), Late Devonian (~372 Ma), end-Permian (~252 Ma, largest), end-Triassic (~201 Ma), end-Cretaceous (~66 Ma, Chicxulub impact, Ir anomaly).

Key transitions: Great Oxidation Event ~2.4 Ga; Cambrian explosion ~541 Ma; first land plants ~470 Ma; K-Pg boundary marks non-avian dinosaur extinction.

Index fossils are geographically widespread, abundant and short-ranging; graptolites, ammonites and trilobites are classic examples.

Isotopic and geochemical proxies (delta-18O, delta-13C, 87Sr/86Sr) reconstruct past climate and carbon cycling; negative delta-13C excursions mark carbon-cycle perturbations.

Kepler's third law: P^2 proportional to a^3 for bodies orbiting the same mass; Newtonian form P^2 = 4 pi^2 a^3 / (G(M+m)).

Stellar classification by spectral type OBAFGKM from hot to cool; luminosity class I-V distinguishes supergiants to dwarfs.

Hertzsprung-Russell diagram: main sequence, red giants, white dwarfs; main-sequence lifetime scales roughly as M^(-2.5) relative to the Sun.

Stellar fusion: pp chain dominates in Sun-like stars; CNO cycle dominates above ~1.3 solar masses; iron fusion is endothermic, triggering core collapse.

Doppler radial-velocity method gives minimum planet mass; transit method gives radius; combining both yields density and constrains composition.

Solar System architecture: terrestrial planets inside the frost line, giant planets outside; meteorites and asteroids sample early Solar System material.

Hubble's law v = H0 d; H0 ~70 km/s/Mpc; cosmic microwave background at z ~1100 has temperature 2.725 K.

Nucleosynthesis: Big Bang produced H, He, Li; heavier elements form in stellar cores and during supernovae and neutron-star mergers.

Thermohaline circulation is driven by density contrasts from temperature and salinity; North Atlantic Deep Water forms where surface water cools and sinks.

Coriolis parameter f = 2 Omega sin(latitude); geostrophic balance gives currents flowing with high pressure to the right in the Southern Hemisphere and left in the Northern Hemisphere.

Wind-driven surface circulation forms subtropical gyres; Ekman transport is 90 degrees to the right of wind in the Northern Hemisphere, driving upwelling at coasts.

Ocean acidification: CO2 + H2O -> H2CO3 -> H+ + HCO3-; rising pCO2 lowers pH and carbonate saturation, stressing calcifiers.

Atmospheric circulation: Hadley, Ferrel and polar cells; ITCZ marks the convergence zone near the thermal equator.

Adiabatic lapse rates: dry ~9.8 C/km, saturated ~6 C/km; environmental lapse rate determines stability.

El Nino-Southern Oscillation: weakened trade winds and warm eastern Pacific; La Nina is the cool phase; both shift global precipitation.

Relative humidity = actual vapour pressure / saturation vapour pressure; dew point is the temperature at which saturation occurs.

Distinguish precision (repeatability) from accuracy (closeness to true value); random error affects precision, systematic error affects accuracy.

Null hypothesis H0 states no effect; a p-value is the probability of data at least as extreme under H0, not the probability H0 is true.

Correlation does not establish causation; confounding variables and reverse causation must be excluded by design or analysis.

Uncertainty propagation: for sums, absolute uncertainties add in quadrature; for products, relative uncertainties add in quadrature.

Radiometric and proxy data carry age-model uncertainty; quote ages with 2-sigma ranges and avoid over-precise dates.

Proxy records (ice cores, tree rings, sediments) require calibration against instrumental data; calibration range limits extrapolation.

Spatial and temporal sampling bias can dominate apparent trends; check resolution, coverage and detection limits before interpreting patterns.

Model validity requires testing against independent observations; distinguish hindcast fit from predictive skill.

Exoplanet habitability links astronomy to Earth systems: stellar type sets insolation and UV flux, while atmosphere and magnetic field govern surface conditions.

Mass extinctions couple solid Earth (volcanism, impacts) to climate (aerosols, CO2) and biosphere (extinction, recovery), so evaluate multiple lines of evidence.

Snowball Earth hypotheses require feedback loops (ice-albedo runaway) plus geological evidence (glacial deposits at low palaeolatitude, cap carbonates).

Plate tectonics controls long-term climate via silicate weathering and volcanic CO2 outgassing; uplift of the Himalayas is implicated in Cenozoic cooling.

Ocean circulation changes link to palaeoclimate proxies (delta-13C, foraminifera) and to atmospheric CO2, so combine marine and ice-core records.

Impact hazard assessment combines orbital dynamics, atmospheric entry physics and geological crater records; risk is expressed as probability times consequence.

Tidal evolution and Moon recession link orbital mechanics to Earth's rotation and sedimentary tidal rhythmites.

Planetary energy budgets apply across bodies: a body's equilibrium temperature depends on stellar flux, albedo and greenhouse forcing.

Plate boundaries: divergent (new lithosphere, ridges, shallow quakes), convergent (subduction or collision, deep quakes, arc volcanism), transform (strike-slip, shallow quakes).

Mantle convection and slab pull drive plates; ridge push is minor. Subducting slabs are cold and dense, giving Benioff-Wadati seismicity to ~700 km depth.

Bowen's reaction series orders crystallisation from mafic (olivine, pyroxene, Ca-plagioclase) to felsic (quartz, K-feldspar, muscovite); it predicts mineral assemblages and melt composition.

Igneous texture records cooling rate: fine-grained/glassy = rapid cooling, coarse-grained = slow intrusive cooling, porphyritic = two-stage cooling.

Clastic sedimentary rocks are classified by grain size (gravel, sand, silt, clay); sorting and roundness indicate transport distance and energy.

Metamorphic grade is tracked by index minerals (chlorite, biotite, garnet, kyanite, sillimanite); foliation develops under directed stress.

Mineral identification uses hardness (Mohs 1-10), cleavage, lustre, streak and density; quartz has conchoidal fracture and hardness 7, calcite hardness 3 and fizzes in dilute acid.

Isostasy: crust floats on the mantle in gravitational balance; mountain roots and post-glacial rebound reflect density contrasts, not rigidity.

Earth's four spheres exchange matter and energy: geosphere (rock/soil), atmosphere (gas), hydrosphere (water), biosphere (life); a change in one sphere propagates through the others via feedbacks.

Negative feedback damps a perturbation and stabilises the system (e.g. silicate weathering draws down CO2 as temperature rises); positive feedback amplifies it (e.g. ice-albedo feedback, permafrost carbon release).

Residence time = reservoir size / flux through the reservoir; atmospheric CO2 residence times are short for exchange fluxes but long for the slow rock cycle, so perturbation lifetimes differ by reservoir.

Albedo feedback: ice and snow reflect ~0.6-0.9 of incident sunlight while open ocean reflects ~0.06; loss of cryosphere lowers planetary albedo and adds absorbed energy.

Carbon cycle fluxes: photosynthesis and respiration exchange on 1-10 year timescales; silicate weathering and volcanism operate on 10^5-10^7 year timescales.

Energy balance: incoming absorbed shortwave = outgoing longwave; greenhouse gases raise effective emission altitude, so surface temperature rises to restore balance.

Latent heat of vaporisation of water (~2.26 x 10^6 J/kg) links hydrosphere and atmosphere; evaporation cools the surface and releases heat on condensation.

Tipping elements (AMOC weakening, Amazon dieback, ice-sheet collapse) are thresholds where a subsystem shifts to a qualitatively different state, often irreversibly on human timescales.

Relative dating principles: superposition, original horizontality, lateral continuity, cross-cutting relationships, inclusions, and faunal succession.

Radiometric dating: N = N0 e^(-lambda t), lambda = ln2 / half-life; closure of the mineral system is required for a valid age.

Zircon U-Pb dating is the benchmark for Precambrian ages; 238U half-life ~4.47 Ga, 235U ~0.704 Ga.

Geological timescale order: Hadean, Archean, Proterozoic, Phanerozoic; Phanerozoic eras are Palaeozoic, Mesozoic, Cenozoic.

Major extinctions: end-Ordovician (~444 Ma), Late Devonian (~372 Ma), end-Permian (~252 Ma, largest), end-Triassic (~201 Ma), end-Cretaceous (~66 Ma, Chicxulub impact, Ir anomaly).

Key transitions: Great Oxidation Event ~2.4 Ga; Cambrian explosion ~541 Ma; first land plants ~470 Ma; K-Pg boundary marks non-avian dinosaur extinction.

Index fossils are geographically widespread, abundant and short-ranging; graptolites, ammonites and trilobites are classic examples.

Isotopic and geochemical proxies (delta-18O, delta-13C, 87Sr/86Sr) reconstruct past climate and carbon cycling; negative delta-13C excursions mark carbon-cycle perturbations.

Kepler's third law: P^2 proportional to a^3 for bodies orbiting the same mass; Newtonian form P^2 = 4 pi^2 a^3 / (G(M+m)).

Stellar classification by spectral type OBAFGKM from hot to cool; luminosity class I-V distinguishes supergiants to dwarfs.

Hertzsprung-Russell diagram: main sequence, red giants, white dwarfs; main-sequence lifetime scales roughly as M^(-2.5) relative to the Sun.

Stellar fusion: pp chain dominates in Sun-like stars; CNO cycle dominates above ~1.3 solar masses; iron fusion is endothermic, triggering core collapse.

Doppler radial-velocity method gives minimum planet mass; transit method gives radius; combining both yields density and constrains composition.

Solar System architecture: terrestrial planets inside the frost line, giant planets outside; meteorites and asteroids sample early Solar System material.

Hubble's law v = H0 d; H0 ~70 km/s/Mpc; cosmic microwave background at z ~1100 has temperature 2.725 K.

Nucleosynthesis: Big Bang produced H, He, Li; heavier elements form in stellar cores and during supernovae and neutron-star mergers.

Thermohaline circulation is driven by density contrasts from temperature and salinity; North Atlantic Deep Water forms where surface water cools and sinks.

Coriolis parameter f = 2 Omega sin(latitude); geostrophic balance gives currents flowing with high pressure to the right in the Southern Hemisphere and left in the Northern Hemisphere.

Wind-driven surface circulation forms subtropical gyres; Ekman transport is 90 degrees to the right of wind in the Northern Hemisphere, driving upwelling at coasts.

Ocean acidification: CO2 + H2O -> H2CO3 -> H+ + HCO3-; rising pCO2 lowers pH and carbonate saturation, stressing calcifiers.

Atmospheric circulation: Hadley, Ferrel and polar cells; ITCZ marks the convergence zone near the thermal equator.

Adiabatic lapse rates: dry ~9.8 C/km, saturated ~6 C/km; environmental lapse rate determines stability.

El Nino-Southern Oscillation: weakened trade winds and warm eastern Pacific; La Nina is the cool phase; both shift global precipitation.

Relative humidity = actual vapour pressure / saturation vapour pressure; dew point is the temperature at which saturation occurs.

Distinguish precision (repeatability) from accuracy (closeness to true value); random error affects precision, systematic error affects accuracy.

Null hypothesis H0 states no effect; a p-value is the probability of data at least as extreme under H0, not the probability H0 is true.

Correlation does not establish causation; confounding variables and reverse causation must be excluded by design or analysis.

Uncertainty propagation: for sums, absolute uncertainties add in quadrature; for products, relative uncertainties add in quadrature.

Radiometric and proxy data carry age-model uncertainty; quote ages with 2-sigma ranges and avoid over-precise dates.

Proxy records (ice cores, tree rings, sediments) require calibration against instrumental data; calibration range limits extrapolation.

Spatial and temporal sampling bias can dominate apparent trends; check resolution, coverage and detection limits before interpreting patterns.

Model validity requires testing against independent observations; distinguish hindcast fit from predictive skill.

Exoplanet habitability links astronomy to Earth systems: stellar type sets insolation and UV flux, while atmosphere and magnetic field govern surface conditions.

Mass extinctions couple solid Earth (volcanism, impacts) to climate (aerosols, CO2) and biosphere (extinction, recovery), so evaluate multiple lines of evidence.

Snowball Earth hypotheses require feedback loops (ice-albedo runaway) plus geological evidence (glacial deposits at low palaeolatitude, cap carbonates).

Plate tectonics controls long-term climate via silicate weathering and volcanic CO2 outgassing; uplift of the Himalayas is implicated in Cenozoic cooling.

Ocean circulation changes link to palaeoclimate proxies (delta-13C, foraminifera) and to atmospheric CO2, so combine marine and ice-core records.

Impact hazard assessment combines orbital dynamics, atmospheric entry physics and geological crater records; risk is expressed as probability times consequence.

Tidal evolution and Moon recession link orbital mechanics to Earth's rotation and sedimentary tidal rhythmites.

Planetary energy budgets apply across bodies: a body's equilibrium temperature depends on stellar flux, albedo and greenhouse forcing.

Plate boundaries: divergent (new lithosphere, ridges, shallow quakes), convergent (subduction or collision, deep quakes, arc volcanism), transform (strike-slip, shallow quakes).

Mantle convection and slab pull drive plates; ridge push is minor. Subducting slabs are cold and dense, giving Benioff-Wadati seismicity to ~700 km depth.

Bowen's reaction series orders crystallisation from mafic (olivine, pyroxene, Ca-plagioclase) to felsic (quartz, K-feldspar, muscovite); it predicts mineral assemblages and melt composition.

Igneous texture records cooling rate: fine-grained/glassy = rapid cooling, coarse-grained = slow intrusive cooling, porphyritic = two-stage cooling.

Clastic sedimentary rocks are classified by grain size (gravel, sand, silt, clay); sorting and roundness indicate transport distance and energy.

Metamorphic grade is tracked by index minerals (chlorite, biotite, garnet, kyanite, sillimanite); foliation develops under directed stress.

Mineral identification uses hardness (Mohs 1-10), cleavage, lustre, streak and density; quartz has conchoidal fracture and hardness 7, calcite hardness 3 and fizzes in dilute acid.

Isostasy: crust floats on the mantle in gravitational balance; mountain roots and post-glacial rebound reflect density contrasts, not rigidity.

Earth's four spheres exchange matter and energy: geosphere (rock/soil), atmosphere (gas), hydrosphere (water), biosphere (life); a change in one sphere propagates through the others via feedbacks.

Negative feedback damps a perturbation and stabilises the system (e.g. silicate weathering draws down CO2 as temperature rises); positive feedback amplifies it (e.g. ice-albedo feedback, permafrost carbon release).

Residence time = reservoir size / flux through the reservoir; atmospheric CO2 residence times are short for exchange fluxes but long for the slow rock cycle, so perturbation lifetimes differ by reservoir.

Albedo feedback: ice and snow reflect ~0.6-0.9 of incident sunlight while open ocean reflects ~0.06; loss of cryosphere lowers planetary albedo and adds absorbed energy.

Carbon cycle fluxes: photosynthesis and respiration exchange on 1-10 year timescales; silicate weathering and volcanism operate on 10^5-10^7 year timescales.

Energy balance: incoming absorbed shortwave = outgoing longwave; greenhouse gases raise effective emission altitude, so surface temperature rises to restore balance.

Latent heat of vaporisation of water (~2.26 x 10^6 J/kg) links hydrosphere and atmosphere; evaporation cools the surface and releases heat on condensation.

Tipping elements (AMOC weakening, Amazon dieback, ice-sheet collapse) are thresholds where a subsystem shifts to a qualitatively different state, often irreversibly on human timescales.

Relative dating principles: superposition, original horizontality, lateral continuity, cross-cutting relationships, inclusions, and faunal succession.

Radiometric dating: N = N0 e^(-lambda t), lambda = ln2 / half-life; closure of the mineral system is required for a valid age.

Zircon U-Pb dating is the benchmark for Precambrian ages; 238U half-life ~4.47 Ga, 235U ~0.704 Ga.

Geological timescale order: Hadean, Archean, Proterozoic, Phanerozoic; Phanerozoic eras are Palaeozoic, Mesozoic, Cenozoic.

Major extinctions: end-Ordovician (~444 Ma), Late Devonian (~372 Ma), end-Permian (~252 Ma, largest), end-Triassic (~201 Ma), end-Cretaceous (~66 Ma, Chicxulub impact, Ir anomaly).

Key transitions: Great Oxidation Event ~2.4 Ga; Cambrian explosion ~541 Ma; first land plants ~470 Ma; K-Pg boundary marks non-avian dinosaur extinction.

Index fossils are geographically widespread, abundant and short-ranging; graptolites, ammonites and trilobites are classic examples.

Isotopic and geochemical proxies (delta-18O, delta-13C, 87Sr/86Sr) reconstruct past climate and carbon cycling; negative delta-13C excursions mark carbon-cycle perturbations.

Kepler's third law: P^2 proportional to a^3 for bodies orbiting the same mass; Newtonian form P^2 = 4 pi^2 a^3 / (G(M+m)).

Stellar classification by spectral type OBAFGKM from hot to cool; luminosity class I-V distinguishes supergiants to dwarfs.

Hertzsprung-Russell diagram: main sequence, red giants, white dwarfs; main-sequence lifetime scales roughly as M^(-2.5) relative to the Sun.

Stellar fusion: pp chain dominates in Sun-like stars; CNO cycle dominates above ~1.3 solar masses; iron fusion is endothermic, triggering core collapse.

Doppler radial-velocity method gives minimum planet mass; transit method gives radius; combining both yields density and constrains composition.

Solar System architecture: terrestrial planets inside the frost line, giant planets outside; meteorites and asteroids sample early Solar System material.

Hubble's law v = H0 d; H0 ~70 km/s/Mpc; cosmic microwave background at z ~1100 has temperature 2.725 K.

Nucleosynthesis: Big Bang produced H, He, Li; heavier elements form in stellar cores and during supernovae and neutron-star mergers.

Thermohaline circulation is driven by density contrasts from temperature and salinity; North Atlantic Deep Water forms where surface water cools and sinks.

Coriolis parameter f = 2 Omega sin(latitude); geostrophic balance gives currents flowing with high pressure to the right in the Southern Hemisphere and left in the Northern Hemisphere.

Wind-driven surface circulation forms subtropical gyres; Ekman transport is 90 degrees to the right of wind in the Northern Hemisphere, driving upwelling at coasts.

Ocean acidification: CO2 + H2O -> H2CO3 -> H+ + HCO3-; rising pCO2 lowers pH and carbonate saturation, stressing calcifiers.

Atmospheric circulation: Hadley, Ferrel and polar cells; ITCZ marks the convergence zone near the thermal equator.

Adiabatic lapse rates: dry ~9.8 C/km, saturated ~6 C/km; environmental lapse rate determines stability.

El Nino-Southern Oscillation: weakened trade winds and warm eastern Pacific; La Nina is the cool phase; both shift global precipitation.

Relative humidity = actual vapour pressure / saturation vapour pressure; dew point is the temperature at which saturation occurs.

Distinguish precision (repeatability) from accuracy (closeness to true value); random error affects precision, systematic error affects accuracy.

Null hypothesis H0 states no effect; a p-value is the probability of data at least as extreme under H0, not the probability H0 is true.

Correlation does not establish causation; confounding variables and reverse causation must be excluded by design or analysis.

Uncertainty propagation: for sums, absolute uncertainties add in quadrature; for products, relative uncertainties add in quadrature.

Radiometric and proxy data carry age-model uncertainty; quote ages with 2-sigma ranges and avoid over-precise dates.

Proxy records (ice cores, tree rings, sediments) require calibration against instrumental data; calibration range limits extrapolation.

Spatial and temporal sampling bias can dominate apparent trends; check resolution, coverage and detection limits before interpreting patterns.

Model validity requires testing against independent observations; distinguish hindcast fit from predictive skill.

Exoplanet habitability links astronomy to Earth systems: stellar type sets insolation and UV flux, while atmosphere and magnetic field govern surface conditions.

Mass extinctions couple solid Earth (volcanism, impacts) to climate (aerosols, CO2) and biosphere (extinction, recovery), so evaluate multiple lines of evidence.

Snowball Earth hypotheses require feedback loops (ice-albedo runaway) plus geological evidence (glacial deposits at low palaeolatitude, cap carbonates).

Plate tectonics controls long-term climate via silicate weathering and volcanic CO2 outgassing; uplift of the Himalayas is implicated in Cenozoic cooling.

Ocean circulation changes link to palaeoclimate proxies (delta-13C, foraminifera) and to atmospheric CO2, so combine marine and ice-core records.

Impact hazard assessment combines orbital dynamics, atmospheric entry physics and geological crater records; risk is expressed as probability times consequence.

Tidal evolution and Moon recession link orbital mechanics to Earth's rotation and sedimentary tidal rhythmites.

Planetary energy budgets apply across bodies: a body's equilibrium temperature depends on stellar flux, albedo and greenhouse forcing.

Earth's four spheres exchange matter and energy: geosphere (rock/soil), atmosphere (gas), hydrosphere (water), biosphere (life); a change in one sphere propagates through the others via feedbacks.

Negative feedback damps a perturbation and stabilises the system (e.g. silicate weathering draws down CO2 as temperature rises); positive feedback amplifies it (e.g. ice-albedo feedback, permafrost carbon release).

Residence time = reservoir size / flux through the reservoir; atmospheric CO2 residence times are short for exchange fluxes but long for the slow rock cycle, so perturbation lifetimes differ by reservoir.

Albedo feedback: ice and snow reflect ~0.6-0.9 of incident sunlight while open ocean reflects ~0.06; loss of cryosphere lowers planetary albedo and adds absorbed energy.

Carbon cycle fluxes: photosynthesis and respiration exchange on 1-10 year timescales; silicate weathering and volcanism operate on 10^5-10^7 year timescales.

Energy balance: incoming absorbed shortwave = outgoing longwave; greenhouse gases raise effective emission altitude, so surface temperature rises to restore balance.

Latent heat of vaporisation of water (~2.26 x 10^6 J/kg) links hydrosphere and atmosphere; evaporation cools the surface and releases heat on condensation.

Tipping elements (AMOC weakening, Amazon dieback, ice-sheet collapse) are thresholds where a subsystem shifts to a qualitatively different state, often irreversibly on human timescales.

Plate boundaries: divergent (new lithosphere, ridges, shallow quakes), convergent (subduction or collision, deep quakes, arc volcanism), transform (strike-slip, shallow quakes).

Mantle convection and slab pull drive plates; ridge push is minor. Subducting slabs are cold and dense, giving Benioff-Wadati seismicity to ~700 km depth.

Bowen's reaction series orders crystallisation from mafic (olivine, pyroxene, Ca-plagioclase) to felsic (quartz, K-feldspar, muscovite); it predicts mineral assemblages and melt composition.

Igneous texture records cooling rate: fine-grained/glassy = rapid cooling, coarse-grained = slow intrusive cooling, porphyritic = two-stage cooling.

Clastic sedimentary rocks are classified by grain size (gravel, sand, silt, clay); sorting and roundness indicate transport distance and energy.

Metamorphic grade is tracked by index minerals (chlorite, biotite, garnet, kyanite, sillimanite); foliation develops under directed stress.

Mineral identification uses hardness (Mohs 1-10), cleavage, lustre, streak and density; quartz has conchoidal fracture and hardness 7, calcite hardness 3 and fizzes in dilute acid.

Isostasy: crust floats on the mantle in gravitational balance; mountain roots and post-glacial rebound reflect density contrasts, not rigidity.

Relative dating principles: superposition, original horizontality, lateral continuity, cross-cutting relationships, inclusions, and faunal succession.

Radiometric dating: N = N0 e^(-lambda t), lambda = ln2 / half-life; closure of the mineral system is required for a valid age.

Zircon U-Pb dating is the benchmark for Precambrian ages; 238U half-life ~4.47 Ga, 235U ~0.704 Ga.

Geological timescale order: Hadean, Archean, Proterozoic, Phanerozoic; Phanerozoic eras are Palaeozoic, Mesozoic, Cenozoic.

Major extinctions: end-Ordovician (~444 Ma), Late Devonian (~372 Ma), end-Permian (~252 Ma, largest), end-Triassic (~201 Ma), end-Cretaceous (~66 Ma, Chicxulub impact, Ir anomaly).

Key transitions: Great Oxidation Event ~2.4 Ga; Cambrian explosion ~541 Ma; first land plants ~470 Ma; K-Pg boundary marks non-avian dinosaur extinction.

Index fossils are geographically widespread, abundant and short-ranging; graptolites, ammonites and trilobites are classic examples.

Isotopic and geochemical proxies (delta-18O, delta-13C, 87Sr/86Sr) reconstruct past climate and carbon cycling; negative delta-13C excursions mark carbon-cycle perturbations.

Kepler's third law: P^2 proportional to a^3 for bodies orbiting the same mass; Newtonian form P^2 = 4 pi^2 a^3 / (G(M+m)).

Stellar classification by spectral type OBAFGKM from hot to cool; luminosity class I-V distinguishes supergiants to dwarfs.

Hertzsprung-Russell diagram: main sequence, red giants, white dwarfs; main-sequence lifetime scales roughly as M^(-2.5) relative to the Sun.

Stellar fusion: pp chain dominates in Sun-like stars; CNO cycle dominates above ~1.3 solar masses; iron fusion is endothermic, triggering core collapse.

Doppler radial-velocity method gives minimum planet mass; transit method gives radius; combining both yields density and constrains composition.

Solar System architecture: terrestrial planets inside the frost line, giant planets outside; meteorites and asteroids sample early Solar System material.

Hubble's law v = H0 d; H0 ~70 km/s/Mpc; cosmic microwave background at z ~1100 has temperature 2.725 K.

Nucleosynthesis: Big Bang produced H, He, Li; heavier elements form in stellar cores and during supernovae and neutron-star mergers.

Thermohaline circulation is driven by density contrasts from temperature and salinity; North Atlantic Deep Water forms where surface water cools and sinks.

Coriolis parameter f = 2 Omega sin(latitude); geostrophic balance gives currents flowing with high pressure to the right in the Southern Hemisphere and left in the Northern Hemisphere.

Wind-driven surface circulation forms subtropical gyres; Ekman transport is 90 degrees to the right of wind in the Northern Hemisphere, driving upwelling at coasts.

Ocean acidification: CO2 + H2O -> H2CO3 -> H+ + HCO3-; rising pCO2 lowers pH and carbonate saturation, stressing calcifiers.

Atmospheric circulation: Hadley, Ferrel and polar cells; ITCZ marks the convergence zone near the thermal equator.

Adiabatic lapse rates: dry ~9.8 C/km, saturated ~6 C/km; environmental lapse rate determines stability.

El Nino-Southern Oscillation: weakened trade winds and warm eastern Pacific; La Nina is the cool phase; both shift global precipitation.

Relative humidity = actual vapour pressure / saturation vapour pressure; dew point is the temperature at which saturation occurs.

Distinguish precision (repeatability) from accuracy (closeness to true value); random error affects precision, systematic error affects accuracy.

Null hypothesis H0 states no effect; a p-value is the probability of data at least as extreme under H0, not the probability H0 is true.

Correlation does not establish causation; confounding variables and reverse causation must be excluded by design or analysis.

Uncertainty propagation: for sums, absolute uncertainties add in quadrature; for products, relative uncertainties add in quadrature.

Radiometric and proxy data carry age-model uncertainty; quote ages with 2-sigma ranges and avoid over-precise dates.

Proxy records (ice cores, tree rings, sediments) require calibration against instrumental data; calibration range limits extrapolation.

Spatial and temporal sampling bias can dominate apparent trends; check resolution, coverage and detection limits before interpreting patterns.

Model validity requires testing against independent observations; distinguish hindcast fit from predictive skill.

Exoplanet habitability links astronomy to Earth systems: stellar type sets insolation and UV flux, while atmosphere and magnetic field govern surface conditions.

Mass extinctions couple solid Earth (volcanism, impacts) to climate (aerosols, CO2) and biosphere (extinction, recovery), so evaluate multiple lines of evidence.

Snowball Earth hypotheses require feedback loops (ice-albedo runaway) plus geological evidence (glacial deposits at low palaeolatitude, cap carbonates).

Plate tectonics controls long-term climate via silicate weathering and volcanic CO2 outgassing; uplift of the Himalayas is implicated in Cenozoic cooling.

Ocean circulation changes link to palaeoclimate proxies (delta-13C, foraminifera) and to atmospheric CO2, so combine marine and ice-core records.

Impact hazard assessment combines orbital dynamics, atmospheric entry physics and geological crater records; risk is expressed as probability times consequence.

Tidal evolution and Moon recession link orbital mechanics to Earth's rotation and sedimentary tidal rhythmites.

Planetary energy budgets apply across bodies: a body's equilibrium temperature depends on stellar flux, albedo and greenhouse forcing.

Plate boundaries: divergent (new lithosphere, ridges, shallow quakes), convergent (subduction or collision, deep quakes, arc volcanism), transform (strike-slip, shallow quakes).

Mantle convection and slab pull drive plates; ridge push is minor. Subducting slabs are cold and dense, giving Benioff-Wadati seismicity to ~700 km depth.

Bowen's reaction series orders crystallisation from mafic (olivine, pyroxene, Ca-plagioclase) to felsic (quartz, K-feldspar, muscovite); it predicts mineral assemblages and melt composition.

Igneous texture records cooling rate: fine-grained/glassy = rapid cooling, coarse-grained = slow intrusive cooling, porphyritic = two-stage cooling.

Clastic sedimentary rocks are classified by grain size (gravel, sand, silt, clay); sorting and roundness indicate transport distance and energy.

Metamorphic grade is tracked by index minerals (chlorite, biotite, garnet, kyanite, sillimanite); foliation develops under directed stress.

Mineral identification uses hardness (Mohs 1-10), cleavage, lustre, streak and density; quartz has conchoidal fracture and hardness 7, calcite hardness 3 and fizzes in dilute acid.

Isostasy: crust floats on the mantle in gravitational balance; mountain roots and post-glacial rebound reflect density contrasts, not rigidity.

Earth's four spheres exchange matter and energy: geosphere (rock/soil), atmosphere (gas), hydrosphere (water), biosphere (life); a change in one sphere propagates through the others via feedbacks.

Negative feedback damps a perturbation and stabilises the system (e.g. silicate weathering draws down CO2 as temperature rises); positive feedback amplifies it (e.g. ice-albedo feedback, permafrost carbon release).

Residence time = reservoir size / flux through the reservoir; atmospheric CO2 residence times are short for exchange fluxes but long for the slow rock cycle, so perturbation lifetimes differ by reservoir.

Albedo feedback: ice and snow reflect ~0.6-0.9 of incident sunlight while open ocean reflects ~0.06; loss of cryosphere lowers planetary albedo and adds absorbed energy.

Carbon cycle fluxes: photosynthesis and respiration exchange on 1-10 year timescales; silicate weathering and volcanism operate on 10^5-10^7 year timescales.

Energy balance: incoming absorbed shortwave = outgoing longwave; greenhouse gases raise effective emission altitude, so surface temperature rises to restore balance.

Latent heat of vaporisation of water (~2.26 x 10^6 J/kg) links hydrosphere and atmosphere; evaporation cools the surface and releases heat on condensation.

Tipping elements (AMOC weakening, Amazon dieback, ice-sheet collapse) are thresholds where a subsystem shifts to a qualitatively different state, often irreversibly on human timescales.

Relative dating principles: superposition, original horizontality, lateral continuity, cross-cutting relationships, inclusions, and faunal succession.

Radiometric dating: N = N0 e^(-lambda t), lambda = ln2 / half-life; closure of the mineral system is required for a valid age.

Zircon U-Pb dating is the benchmark for Precambrian ages; 238U half-life ~4.47 Ga, 235U ~0.704 Ga.

Geological timescale order: Hadean, Archean, Proterozoic, Phanerozoic; Phanerozoic eras are Palaeozoic, Mesozoic, Cenozoic.

Major extinctions: end-Ordovician (~444 Ma), Late Devonian (~372 Ma), end-Permian (~252 Ma, largest), end-Triassic (~201 Ma), end-Cretaceous (~66 Ma, Chicxulub impact, Ir anomaly).

Key transitions: Great Oxidation Event ~2.4 Ga; Cambrian explosion ~541 Ma; first land plants ~470 Ma; K-Pg boundary marks non-avian dinosaur extinction.

Index fossils are geographically widespread, abundant and short-ranging; graptolites, ammonites and trilobites are classic examples.

Isotopic and geochemical proxies (delta-18O, delta-13C, 87Sr/86Sr) reconstruct past climate and carbon cycling; negative delta-13C excursions mark carbon-cycle perturbations.

Kepler's third law: P^2 proportional to a^3 for bodies orbiting the same mass; Newtonian form P^2 = 4 pi^2 a^3 / (G(M+m)).

Stellar classification by spectral type OBAFGKM from hot to cool; luminosity class I-V distinguishes supergiants to dwarfs.

Hertzsprung-Russell diagram: main sequence, red giants, white dwarfs; main-sequence lifetime scales roughly as M^(-2.5) relative to the Sun.

Stellar fusion: pp chain dominates in Sun-like stars; CNO cycle dominates above ~1.3 solar masses; iron fusion is endothermic, triggering core collapse.

Doppler radial-velocity method gives minimum planet mass; transit method gives radius; combining both yields density and constrains composition.

Solar System architecture: terrestrial planets inside the frost line, giant planets outside; meteorites and asteroids sample early Solar System material.

Hubble's law v = H0 d; H0 ~70 km/s/Mpc; cosmic microwave background at z ~1100 has temperature 2.725 K.

Nucleosynthesis: Big Bang produced H, He, Li; heavier elements form in stellar cores and during supernovae and neutron-star mergers.

Thermohaline circulation is driven by density contrasts from temperature and salinity; North Atlantic Deep Water forms where surface water cools and sinks.

Coriolis parameter f = 2 Omega sin(latitude); geostrophic balance gives currents flowing with high pressure to the right in the Southern Hemisphere and left in the Northern Hemisphere.

Wind-driven surface circulation forms subtropical gyres; Ekman transport is 90 degrees to the right of wind in the Northern Hemisphere, driving upwelling at coasts.

Ocean acidification: CO2 + H2O -> H2CO3 -> H+ + HCO3-; rising pCO2 lowers pH and carbonate saturation, stressing calcifiers.

Atmospheric circulation: Hadley, Ferrel and polar cells; ITCZ marks the convergence zone near the thermal equator.

Adiabatic lapse rates: dry ~9.8 C/km, saturated ~6 C/km; environmental lapse rate determines stability.

El Nino-Southern Oscillation: weakened trade winds and warm eastern Pacific; La Nina is the cool phase; both shift global precipitation.

Relative humidity = actual vapour pressure / saturation vapour pressure; dew point is the temperature at which saturation occurs.

Distinguish precision (repeatability) from accuracy (closeness to true value); random error affects precision, systematic error affects accuracy.

Null hypothesis H0 states no effect; a p-value is the probability of data at least as extreme under H0, not the probability H0 is true.

Correlation does not establish causation; confounding variables and reverse causation must be excluded by design or analysis.

Uncertainty propagation: for sums, absolute uncertainties add in quadrature; for products, relative uncertainties add in quadrature.

Radiometric and proxy data carry age-model uncertainty; quote ages with 2-sigma ranges and avoid over-precise dates.

Proxy records (ice cores, tree rings, sediments) require calibration against instrumental data; calibration range limits extrapolation.

Spatial and temporal sampling bias can dominate apparent trends; check resolution, coverage and detection limits before interpreting patterns.

Model validity requires testing against independent observations; distinguish hindcast fit from predictive skill.

Exoplanet habitability links astronomy to Earth systems: stellar type sets insolation and UV flux, while atmosphere and magnetic field govern surface conditions.

Mass extinctions couple solid Earth (volcanism, impacts) to climate (aerosols, CO2) and biosphere (extinction, recovery), so evaluate multiple lines of evidence.

Snowball Earth hypotheses require feedback loops (ice-albedo runaway) plus geological evidence (glacial deposits at low palaeolatitude, cap carbonates).

Plate tectonics controls long-term climate via silicate weathering and volcanic CO2 outgassing; uplift of the Himalayas is implicated in Cenozoic cooling.

Ocean circulation changes link to palaeoclimate proxies (delta-13C, foraminifera) and to atmospheric CO2, so combine marine and ice-core records.

Impact hazard assessment combines orbital dynamics, atmospheric entry physics and geological crater records; risk is expressed as probability times consequence.

Tidal evolution and Moon recession link orbital mechanics to Earth's rotation and sedimentary tidal rhythmites.

Planetary energy budgets apply across bodies: a body's equilibrium temperature depends on stellar flux, albedo and greenhouse forcing.

Plate boundaries: divergent (new lithosphere, ridges, shallow quakes), convergent (subduction or collision, deep quakes, arc volcanism), transform (strike-slip, shallow quakes).

Mantle convection and slab pull drive plates; ridge push is minor. Subducting slabs are cold and dense, giving Benioff-Wadati seismicity to ~700 km depth.

Bowen's reaction series orders crystallisation from mafic (olivine, pyroxene, Ca-plagioclase) to felsic (quartz, K-feldspar, muscovite); it predicts mineral assemblages and melt composition.

Igneous texture records cooling rate: fine-grained/glassy = rapid cooling, coarse-grained = slow intrusive cooling, porphyritic = two-stage cooling.

Clastic sedimentary rocks are classified by grain size (gravel, sand, silt, clay); sorting and roundness indicate transport distance and energy.

Metamorphic grade is tracked by index minerals (chlorite, biotite, garnet, kyanite, sillimanite); foliation develops under directed stress.

Mineral identification uses hardness (Mohs 1-10), cleavage, lustre, streak and density; quartz has conchoidal fracture and hardness 7, calcite hardness 3 and fizzes in dilute acid.

Isostasy: crust floats on the mantle in gravitational balance; mountain roots and post-glacial rebound reflect density contrasts, not rigidity.