Fifty-six original college-level destinations connect sky geometry and NASA image evidence to orbital inference, radiation, calibration, an actual SDSS spectrum audit and planetary and stellar inference, galaxies and calibrated cosmological evidence. A cumulative pair and retained whole-course project connect all six capability groups with actual source audits.
This is the course outline. Open a unit to choose a lesson; every lesson opens on its own page. Explanations and experiments live inside those lesson pages.
Preparation: Algebra, ratios, units and graph reading. Trigonometric coordinate and integration relationships are introduced with explicit definitions and worked examples; no telescope or outdoor viewing is required.
Course outcome: Infer astronomical mechanisms from geometry, calibrated images/spectra and conserved models while retaining source provenance, degeneracy and uncertainty. All six finite capability categories and the cumulative defense are authored; learner and practical completion require actual evidence.
All lessons are directly accessible. Reused foundation explanations are identified where relevant; completing a different course does not award this course's evidence. The 56 registered lessons keep separate predictions, captures, practice responses and reflections.
Transform celestial/local frames, distinguish seasonal/phase/eclipse mechanisms and design a reproducible accessible image comparison with source provenance.
Change latitude at fixed hour angle, then hour angle at fixed latitude. Retain east/north/up and verify their squared sum. Explain why a change in local altitude does not itself change the catalog declination.
At latitude 60°, compare declinations−60°,−30°,0°,30° and 60°. Retain both extrema and note the two grazing boundaries. Change latitude without changing declination and explain which evidence belongs to the observer.
Compare whole-day advances with extra-hour advances and retain both wrapped and unwrapped angles. Explain why a nearly four-minute daily difference accumulates but does not imply the star physically travels around Earth.
Compare opposite latitudes at fixed declination, then compare solstice/equinox at one latitude. Retain the integrated factor and duration rather than treating a noon snapshot as an entire-day average.
Hold elongation fixed while rotating the displayed north marker, then vary elongation at fixed orientation. Retain the difference between phase, orientation and brightness. Explain why a pixel-intensity sum would not directly measure the model’s area fraction.
Compare new/full at the sameu and retain the separate angular radii. Locate configurations with no overlap, partial overlap and containment. Explain why a geocentric result does not specify a safe local viewing location or an actual date.
Download the original JSON, selected CSV and provenance. Verify a timestamp/frame and all fields for one record, then compare two unchanged images and their diameter/distance ratios. Retain a changed-pair prediction and explain why agreement among derived source fields is not independent observational confirmation.
Reconstruct orbital position and mass from declared geometry, distinguish projected and relative records, and close specific energy, angular momentum, differential gravity and external work boundaries.
Hold eccentricity fixed and compare equal mean-anomaly steps. Reconstruct separation, swept-area fraction and speed, then compare with e=0. Identify an invariant that would reject a mistaken uniform-angle trajectory.
Change axis and period separately, retain the monotone endpoint calculation and explain the difference between relative, barycentric and projected axes. Identify a missing observation needed before applying this calculation to a real image pair.
Vary secondary mass fraction at fixed relative axis, then vary axis at fixed fraction. Close the radius sum, mass-weighted position and opposite momenta, and identify an observation that distinguishes barycenter from photocenter.
Hold fitted amplitudes fixed while changing inclination; retain projected and true mass separately. Then change phase without changing the fitted orbit and explain which new evidence could constrain inclination.
Hold speed fixed while changing the radial/tangential split. Reconstruct energy, angular momentum, eccentricity and turning radii; verify both energy and angular momentum at an apsis and explain what a missing finite apoapsis means.
Compare the second-impulse switch at fixed target radius. Retain arrival position, speed, transfer and post-arrival energy, then change target radius and explain why speed-change magnitude is not fuel mass.
Compare exact endpoint differences with the small-body approximation at different D and R. Retain common and relative accelerations separately, and identify the missing material information needed to predict deformation.
Vary final radius at fixed mass, then mass at fixed endpoints. Close ΔE and ΔL, compare their ratio with endpoint angular rates and identify the driver that a complete physical conservation argument would need to include.
Interpret photon/continuum/line quantities, separate collection and resolution, validate calibration and audit an actual public-domain spectrum with uncertainty, flags and source boundaries.
Change wavelength at fixed power, then power at fixed wavelength. Close photon energy times arrival rate against power, retain SI conversions and explain why detector efficiency would be an additional factor.
Compare temperature at a fixed selected wavelength. Retain Bλ units, peak, color ratio and integrated surface flux; explain why a normalized shape and one observed color do not uniquely determine a real source.
Hold distance fixed while changing optical depth, then hold transmission fixed while changing distance. Identify at least two compatible explanations for a low flux and a distinct observation that could discriminate them.
Compare diameter and one-exposure time separately. Retain area, expected source/background counts and each variance term; explain how an estimated sky background or repeated detector reads would change the assumptions.
Change aperture and wavelength separately, retain radians-to-arcseconds conversion and area, and explain which missing point-spread, sampling or contrast evidence prevents a guaranteed resolving claim.
Reconstruct slope and intercept, then evaluate the unused reference before trusting the target result. Change the common pixel offset and explain why the check residual persists; propose a discriminating additional reference.
Vary central optical depth and width separately. Retain depth, integrated area and the thin-limit comparison, then identify one omitted physical or instrumental factor that would affect a real abundance inference.
Compare both observed lines at changed shift and offset, reconstruct slope/intercept and retain the naive single-line error. Explain the evidence needed before interpreting the result as velocity rather than another shift mechanism.
Verify the exact FITS identity/hash and selected row values. Reconstruct wavelength and one uncertainty from source columns, compare the declared screens, retain all original flags and explain which source/model assumptions prevent a new astrophysical inference.
Compare physical planetary mechanisms and invert multiple supplied signals without hiding composition, history, contamination or survey-selection degeneracy.
Change core radius and mantle density separately. Retain all three fractions and the radial weighting of inertia; explain what additional measurement could discriminate two mass–radius-compatible interiors.
Close generation, loss and storage, then compare size at the same source age. Identify the fixed-flux assumption that prevents this snapshot from becoming a complete thermal history.
Compare two molar masses at the same temperature, keeping hydrostatic height, thermal speed and binding parameter distinct. Name a missing high-altitude or replenishment measurement before making a retention claim.
Retain separate surface, layer and top-boundary balances. Change emissivity at fixed incoming radiation; explain why temperature can change while top-boundary equilibrium output stays fixed.
Move luminosity and radius independently, reconstruct the threshold and mass inventory, then state two histories compatible with a present-day volatile signal.
Keep production, loss, observation time and patch reset separate. Compare the mixed density with both component densities and state why a single-age inversion hides geological history.
Compare depth and contact duration as separate observables. Change contamination at fixed radius, then radius at fixed contamination; identify what a second measurement constrains and what false-positive alternatives remain.
Invert the reflex relation, reconstruct its amplitude, then combine it with two different supported size ratios. Retain the stellar normalization and explain why a composition claim remains nonunique.
Reconstruct each selection factor and corrected fraction. Change short completeness without changing the true population; name an uncertainty or false-positive process omitted from the correction.
Connect distance, spectra and population diagrams with explicitly bounded stellar structure, energy and evolutionary models; distinguish a supplied trajectory from a population and a remnant diagnostic from a stability proof.
Invert both endpoints before subtracting the central value. Compare larger and smaller fractional parallax bounds, and distinguish hard limits from a probabilistic uncertainty claim.
Reconstruct distance with and without extinction, then verify the distance-ratio square against the inverse transmitted-flux fraction. State the fixed source-band assumption.
Change temperature at fixed luminosity, then luminosity at fixed temperature. Keep radius and the separately stipulated equal-mass density distinct from any actual mass inference.
Compute total energy and virial residual separately, then compare the density-dependent free-fall reference. Name one missing support or boundary term before describing a real cloud.
Check center, midpoint and surface pressure, then compare mass and radius scalings. Retain the separate structural, equation-of-state and energy-supply assumptions.
Retain total mass, accessible fuel, converted mass, energy and power as separate ledger stages. Change accessible fraction and explain why a luminosity evolution would change the timescale.
Compare mass at fixed exponent, then exponent at fixed mass. State the separate fuel and luminosity assumptions and identify a star category for which the rule should not be used.
Reconstruct emitting area and surface flux separately, then close the original shell-energy difference. State why the two packets do not by themselves supply an actual evolutionary timescale.
Compare mass and composition separately, retaining radius, density and limiting-mass quantities. Explain why the cold nonrelativistic law is not valid all the way to its separately quoted relativistic limit.
Reconstruct compactness and redshift while separating the material radius from the horizon radius. Name an equation-of-state or observational uncertainty absent from the model.
Identify the population turnoff and the separate equal-binary signal, then compare the supplied ordered evolutionary snapshots. Preserve the difference between a simultaneous ensemble and one star’s history, and do not infer durations from plot spacing.
Compare galaxy mass/light and lensing, propagate a distance ladder, and distinguish expansion, background-radiation and primordial-abundance evidence from their model assumptions.
Deproject speed before squaring it, retain kpc and km/s units, then separate the conditional mass discrepancy from a unique dark-matter identification. Name an independent geometry or mass probe.
Keep component masses, component luminosities and total mass-to-light ratio separate. Change the old population calibration and name a dust or active-nucleus alternative to a simple age interpretation.
Solve both signed roots and verify the original equation for each. Reconstruct sum/product before explaining what a more complex lens geometry would make uncertain.
Reconstruct the period-calibrated absolute magnitude and distance, then change only the shared zero point. Separate common systematic uncertainty from independent scatter.
Compare single-source, forced-origin and free-intercept slopes. State which nuisance was modeled and which real distance/velocity uncertainties remain outside the packet.
Close wavelength, energy, time and scale-factor ratios, then identify the additional expansion-history assumptions required for a distance.
Compare q and H/H 0 across redshift, then distinguish comoving distance, luminosity distance and lookback time. Retain the flatness and negligible-radiation assumptions.
Compare the two distance integrals before adding luminosity drift. Retain the model-only and combined residuals and propose an independent test of source evolution.
Reconstruct angle in radians before converting units, compare ruler and distance changes separately, and state what independent early-physics calibration is needed.
Count neutrons, protons, nuclei and baryons separately, then track unbound-neutron decay. Name a light-element or rate constraint missing from the endpoint model.
Propagate shared calibration across radiative and orbital quantities, discriminate competing explanations and defend all six capability groups with actual source audits and retained independent reasoning.
Change distance with contamination fixed, then change contamination with distance fixed. Retain every shared assumption and verify the radius and density cancellations algebraically before claiming they would survive real calibration uncertainty.
Preserve candidate ties, make unused predictions before reveal and audit the two actual source packets separately. Record source versions, transformations, permissions, uncertainty and prior pipeline/model exposure in the full-course workspace; then obtain substantive human review and a genuinely unfamiliar case.
Keep predictions before comparison, complete raw records and units, explain competing models and test a changed case. Supplied and simulated data are labeled in each lesson. A saved notebook is not proof of experimental technique or correct reasoning.
Evidence to retain: Retain east/north/up components, unit-vector invariant, both culmination extrema and unwrapped versus modulo rotation; test changed latitude/time without conflating reference frames.
Boundary: Original spherical geometric models, not actual telescope pointing, civil-clock conversion or terrain/refraction-corrected observation.
Evidence to retain: Compare hemispheric daily input integrals, phase area under display roll and separate solar/lunar angular overlap tests. Explain a changed boundary before public feedback.
Boundary: Original ideal geometry with explicit distances and radii, not weather, brightness photometry, local eclipse visibility or safe solar viewing.
Evidence to retain: Audit fixed weekly selection, timestamp/frame, original file hashes, all selected fields, orientation and media reuse; compare source diameter/distance and illumination without claiming independent observations.
Boundary: NASA scientific renderings and ephemeris-derived records, not direct photographs at each date, actual learner observations or independent ephemeris validation.
Evidence to retain: Retain equal-time versus equal-angle coordinates, swept area and speed, hard mass bounds and signed barycentric position/momentum closure.
Boundary: Original isolated two-body records, not actual astrometric data; deprojection and unit normalization explicit.
Evidence to retain: Separate fitted amplitudes from phase samples, projected from true mass, energy from angular momentum, and arrival radius from circularization velocity.
Boundary: Original circular/point-mass assumptions; no real stellar catalog fit, launch or mission-operation claim.
Evidence to retain: Compare exact endpoint accelerations with small-body gradients, then close orbital energy/angular-momentum changes and identify the missing external driver.
Boundary: No ocean height, material deformation or real migration prediction without the omitted physical response.
Evidence to retain: Retain SI photon-energy closure, B_lambda convention and normalization, gray-screen degeneracy, count/noise terms and separate angular/area scalings.
Boundary: Original source/instrument assumptions, not actual detector calibration, weather or safe instrument operation.
Evidence to retain: Fit two anchors then test an unused reference, separate depth/width/area and reconstruct common fractional versus additive shift. Keep alternative causes and missing physical evidence.
Boundary: Original exact calibration and absorbing-screen records; no universal abundance inference or cosmological-to-peculiar-speed conversion.
Evidence to retain: Verify exact raw FITS hash, source identity, all selected fields and fixed selection. Reconstruct wavelength and uncertainty from actual columns; preserve original masks and compare retained/empty windows without inventing a zero estimate.
Boundary: Actual coadded observation and disclosed pipeline labels; formal independent-pixel local mean is conditional, not a new redshift or continuum fit.
Evidence to retain: Retain radius/volume/mass and inertia weights, total generation/loss/storage, hydrostatic versus escape diagnostics and three radiative boundaries including disconnected-layer uncertainty.
Boundary: Original simplified spheres and layers, not actual internal profiles, escape lifetimes or climate forecasts.
Evidence to retain: Reconstruct condensation threshold and supplied solid inventory, then area-weight different crater histories before any single-age inversion. Name migration and preservation alternatives.
Boundary: No actual disk, crater catalog or surface chronology is supplied.
Evidence to retain: Separate diluted depth, contact geometry, exact reflex mass, density and selection factors; identify stellar/false-positive/uncertainty evidence missing from a real claim.
Boundary: Original synthetic signals and exact selection probabilities, not validated exoplanet discoveries or measured occurrence.
Evidence to retain: Invert positive parallax endpoints, retain band extinction and luminosity, infer radius from effective temperature and explicitly separate assumed mass.
Boundary: Original positive intervals and source properties, not a catalog posterior or unique chemical/evolutionary classification.
Evidence to retain: Distinguish total energy/virial relation/free-fall reference, integrate pressure, close accessible-fuel energy and compare envelope/core and lifetime quantities.
Boundary: Separate original approximations, not a self-consistent stellar-evolution calculation or actual thermal history.
Evidence to retain: Retain composition in degeneracy scaling, exterior compactness and stability limits, coeval turnoff, unresolved binary flux and a separate time-ordered schematic track.
Boundary: No actual remnant classification, full equation of state, measured cluster age or duration inferred from diagram spacing.
Evidence to retain: Deproject rotation before a conditional mass estimate, separate band light and mass fractions, and verify both signed lens solutions with source/model geometry.
Boundary: Original galaxy and point-lens records, not a measured dark-matter profile or unique actual formation history.
Evidence to retain: Propagate common zero-point shifts, fit nuisance offsets, close redshift ratios and distinguish time/distance integrals under declared backgrounds.
Boundary: No actual parameter fit, independent calibration sample or high-redshift peculiar-speed claim.
Evidence to retain: Separate luminosity drift from distance residual, comoving ruler from geometry and endpoint baryon conservation from abundance kinetics; state what cross-probe evidence adds.
Boundary: No actual supernova/CMB dataset, full early-universe network or model-free unique cosmology.
Evidence to retain: Propagate common distance/contamination assumptions, preserve candidate ties or rejected sets, and retain separate actual NASA image and SDSS spectral audits with source versions and unused predictions.
Boundary: Original integrated packet is fictional; published rendering and processed spectral observation have different provenance. Source inspection, human review and unfamiliar learner performance must actually occur.
Open the retained response and project workspaces. Practice, saved work and independently reviewed proficiency remain separate.
These 35 course-specific public tasks are practice, not a secure examination. Each retains up to three immutable written responses, known feedback exposure before each response, and human rubric critiques. Drafts remain editable. No text-length check or self-reported review certifies correctness, independence, laboratory skill or mastery.
For fixed declination +20° and hour angle 0, compare latitude 0° and 30°: altitude and north/south azimuth. Separately at the equator with declination +60°, determine both culmination altitudes and geometric duration. Using the uniform 365.25-day orbit, calculate same-solar-clock extra rotation after 30 days and explain why wrapped angle is not elapsed rotation count.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
At equator/equinox find noon altitude, day duration and daily mean normalized input. For elongation 270° and display roll 90°, give illuminated fraction and trend. At node offset 15°, compare lunar latitude 1.318351° with supplied solar/lunar overlap limits 0.525663°/0.944288°; is either overlap supported? State why no direct solar viewing follows.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Use the archived NASA SVS 5587 JSON/CSV and unchanged frames 505 and 673 (22 and 29 January 2026 at 00 UT). Verify all source fields and image hash/provenance, then calculate illumination change and compare angular diameter with inverse distance. Explain reference frame, shared ephemeris ancestry, reuse terms and why these are not photographs or a local observing log.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Before feedback, plan an unfamiliar pair of supplied sky images or source records. Name the coordinate/time frame, image orientation and selection rule; state a prediction, a reproducible measurement, an uncertainty and an alternative explanation. Preserve source reuse and assistance/exposure. Use screen-based records only; no Sun viewing or instrument aiming.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
For an original ellipse with axis 1, μ=1 and e=0.6, compare periapsis and apoapsis separation/speed and the area fraction reached at mean anomaly 90°. Separately use a circular binary total mass 4, relative axis 2 AU and equal component masses: calculate component radii, period and speeds. State why the two semimajor-axis meanings cannot be swapped.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Use relative axis 4±0.1 AU and period 4±0.1 years to obtain nominal total mass and hard bounds. In a separate abstract circular double-lined fit, K1=10, K2=20, P=2 and G=1: compare total mass at inclinations 90° and 30°, mass ratio and instantaneous velocities at phase 0°. Do not mix the two unit systems.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
At r=1, μ=1, speed 0.5 and tangent angle 90°, find ε, h, e and turning radii. Separately consider transfer from circular radius 1 to 4: calculate required two speed changes and compare post-arrival energy with/without the second impulse.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
At fixed small half-length R=0.2, halve center distance from 10 to 5: compare leading full endpoint differential acceleration and center acceleration. Separately move test mass 2 through a hypothetical circular-state sequence from radius 1 to 4 with μ=1: calculate ΔL, ΔE and their ratio, then compare final Ω times ΔL.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Before feedback, plan how an unfamiliar supplied orbit packet could distinguish a scale error, inclination ambiguity, phase-sampling mistake or missing torque. State the coordinate/time/units, a conservation or geometric check, at least two alternatives and the next discriminating observation. Preserve original reasoning and prior exposure.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Compare monochromatic 400 and 800 nm radiation at equal power 2 μW. Then double ideal blackbody temperature 3000→6000 K and state changes in wavelength-density peak and integrated surface flux. Separately use normalized luminosity 4π, true distance 3 and gray optical depth 2 to infer the distance an analyst would obtain while ignoring attenuation.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Use D=2 m, t=2 s, source/background arrival densities 100/20 photons/m²/s, efficiency 0.5 and one-read variance 25. Find expected electron counts and SNR. Separately at 800 nm compare ideal Rayleigh angles for diameters 1 and 2 m with a supplied pair 0.1 arcsec and separate width 0.08 arcsec. Explain why neither mean subtraction nor display enlargement removes missing information.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
For original anchors 400 nm at pixel 120 and 700 nm at 420, infer wavelength at pixel 200 and check the unused 550 nm line at pixel 275. Separately compare τ0=1 and 2 at width 0.2 nm in the supplied absorption screen. Finally observed lines 502/602 nm have rest wavelengths 500/600: recover common fractional shift and additive offset.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Open the actual archived SDSS DR17 plate358/MJD51818/fiber270 RUN2D26 FITS, full CSV and provenance. Verify hash and four fixed windows against COADD rows. Reconstruct row0 wavelength from LOGLAM rather than primary COEFF0; explain the trimmed-grid discrepancy. Compare positive-IVAR/zero-AND/zero-OR retained counts and formal means in windows0 and2000. Preserve units, original flags, release/reuse and pipeline-label exposure.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Before feedback, plan an unfamiliar supplied spectrum/image comparison. Specify coordinate and spectral-density conventions, calibration anchors plus unused validation, count/noise assumptions, source provenance/reuse and at least two explanations for a feature. Define a discriminating measurement and retain flags or missing data rather than forcing an estimate. No instrument operation is requested.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
An incompressible sphere has core radius fraction 0.6, core density 8 and mantle density 3 g/cm³. Find core volume/mass fractions and bulk density. Separately a radius 3 sphere has volumetric generation 10×2^−n, outward flux 5 and volumetric heat capacity 20; compare instantaneous temperature rates at n=0 and 2. Explain why neither calculation uniquely reconstructs a real planet.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
At fixed composition and gravity, double an isothermal ideal-gas temperature 200→400 K. State changes in scale height, rms speed and the fixed-escape-speed energy parameter. Separately use stellar irradiance 1200 W/m², albedo 0.3 and one-layer emissivity 0.5: reconstruct surface output, upward/downward layer output and top-boundary output. What becomes undetermined at emissivity zero?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Use T=280L^(1/4)/sqrt(r), threshold 170 K and refractory/ice inventories 10/20. Compare L=1 and 4 at r=3 AU. Separately a crater process has p=2,k=0.2, elapsed 6, with 40% of area reset at time 4. Reconstruct both component densities and the area mixture. State why neither a present orbit nor a mixed density uniquely identifies history.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A uniform full transit has radius ratio 0.15 and contaminating light fraction 0.5. Find measured depth and naive radius ignoring dilution. At fixed independently solved mass, halve radius and state density/gravity factors. Separately 10,000 stars have occurrence 0.5 in each disjoint bin, transit probabilities 0.1/0.02 and completeness 0.8/0.25. Reconstruct detections and corrected occurrences.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Before public feedback, plan an unfamiliar supplied planetary comparison. Choose at least two independent signals, state material/geometric/radiative assumptions and uncertainties, name two compatible histories or structures, and specify a discriminating observation. Include host-light or survey-selection limits when relevant. No physical observing procedure is requested.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
For original parallax 10±3 mas as hard limits, invert central and endpoint distances. Separately use m=14, M=5 and extinction A=2 in one band. Then a different source has effective temperature 6000 K and luminosity 100 relative to a 6000 K reference: infer radius and density only under a separately stipulated equal mass.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
For uniform isolated cloud G=1, M=1, R=2 and sound-speed squared 0.2, compute U, K, total energy and virial ratio. Separately integrate the uniform hydrostatic sphere with M=2,R=2,surface pressure zero: obtain central pressure, density and normalized ideal central temperature. Explain why neither calculation is a full evolving star.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
At total mass 2×10³⁰ kg, accessible fraction 0.1 and efficiency 0.007, find accessible and converted masses and released energy using exact c. Use fixed luminosity 3.8×10²⁶ W to estimate years. Separately a supplied main-sequence law has M=3 and exponent 4, reference lifetime 10 Gyr. Find its luminosity and lifetime without silently combining the two packets.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
An original expanded envelope has R=10,T=3000 K against a 6000 K unit-radius reference. Compute luminosity and shell-energy change for G=1,core mass 1,envelope 0.1 expanding from radius 1. Separately a cold nonrelativistic white-dwarf scaling at μe=2 changes mass 0.6→0.2 solar masses. Compare radius and density, and identify why a relativistic limiting mass is a separate approximation.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
For two solar masses and static radius 20 km, reconstruct Schwarzschild radius, compactness and gravitational redshift using the supplied constants. Separately a coeval population obeys lifetime 10/M³ Gyr and L=M⁴,T=6000sqrt(M). At age 2 Gyr and equal-binary fraction 0.25, find turnoff mass and mean luminosity per turnoff system. Explain why the four supplied ordered stage points are not a simultaneous isochrone or a duration-calibrated track.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Before feedback, choose an unfamiliar supplied stellar population or structure comparison. Define observables, calibration and at least two competing evolutionary/selection explanations. Predict a discriminating pattern, identify which relationships are conditional approximations, and retain source exposure and uncertainty. No direct observing is required.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
At radius 10 kpc and projected speed 100 km/s, compare spherical-approximation masses for inclinations 90° and 30° using the supplied G. Separately a 10¹⁰-solar-mass two-component population has young fraction 0.01, young band mass/light 0.1 and old ratio 2. Find young light fraction and state two assumptions that prevent a unique dark-matter or history claim.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Use normalized point lens M=1, source offset β=0.2. Solve both signed roots and recover sum/product. Separately change a shared variable-star absolute zero point from−0.2 to+0.2 mag at fixed period/apparent magnitude/extinction. Find the distance ratio and explain why adding sources does not erase this shared shift.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Original distances 10, 20, 40, 80 Mpc have velocities 70d−300 km/s. Compute the 20 Mpc ratio and forced-origin slope usingΣd 150,Σd²8500; identify the free-intercept fit. Separately use cosmological z=2 and emitted 400 nm to reconstruct observed wavelength, scale factor, energy/time ratios and reference radiation temperature.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
In flat Ωm 0.3/Λ0.7 at z=1, compute E² and q, and state the relation between luminosity and comoving distances. Explain why lookback time uses a different integrand. Separately change a candle luminosity drift−0.2→+0.2 mag at fixed redshift/background histories. What changes and what does not?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Compare comoving rulers 120 Mpc/10000 Mpc distance and 180 Mpc/15000 Mpc distance. Compute angular scale and acoustic proxy, explaining why it is not exactly the first CMB peak. Separately start protons 1, neutrons 0.1 and bind 80% of neutrons into He 4, then decay the remaining neutrons. Close nuclei and baryons.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Before feedback, choose a galaxy-mass or cosmic-distance claim. Identify two physically different probes, their shared versus independent calibrations, a competing explanation and a discriminating observation. Retain source/selection and model-parameter assumptions; do not label a synthetic packet actual observed cosmology.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Original packet: total-flux luminosity is one at 100 pc, host temperature equals the reference, contamination 0.5 in both bolometric and transit bands, transit depth 0.0075, relative binary axis 40 mas, period 8 yr and host mass fraction 0.75. At 80 pc calculate host luminosity/radius, corrected transit ratio, planet radius, total/host mass and host density. Then change distance to 120 pc and explain each scaling and the limits of cancellation.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Three original candidates share flux 0.0001: A(d100,L1,t1), B(d50,L0.25,t1), C(d50,L1,t0.25). Parallax 20 mas is supplied and transmission is unknown. Retain candidates, predict a transmission observation for each and then interpret unity. Separately explain parallax 10 mas with transmission 0.25. What uncertainty and omitted-model checks would a real source require?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Open the five actual NASA SVS 5587 frames and both source-packet downloads. Retain exact creator/release/frame/time/hash, reuse/credit and transformations. Verify the first selected Moon record and identify two visible changes without calling a rendering a photograph. Independently reconstruct the first actual SDSS wavelength from COADD LOGLAM, compare its raw FITS/full CSV, and audit both permissive and zero-OR-mask windows. State exposed ephemeris/pipeline labels and what agreement cannot independently validate.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Before public feedback, frame one astronomical claim and an alternative. Map sky/observation, orbits, light/calibration, planets, stars and cosmology to explicit evidence actions, using the actual source audits where relevant and labeling all fictional calculations. Retain a first report, actual human critique, justified revision and a genuinely unfamiliar reviewer-provided response before its solution is exposed. Which shared calibrations prevent treating two results as independent?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Reviewer identity and role are declarations, not authenticated credentials. Unsaved review fields below are lost on navigation. Review every criterion with an exact quotation, calculation or evidence citation and a next step.
A six-stage evidence project with actual NASA rendering and SDSS observation audits, original analytical packets and preserved earlier category histories. Authored completion is not learner, observing or credit completion.
Before feedback, state a claim and competing explanation; map all six capability groups. Reconstruct one observer/sky relation and inspect the actual NASA five-frame sequence with exact frame/time/source/version/credit. Distinguish a rendering and its common ephemeris from an independent photograph.
Evidence to retain: Original plan and predicted differences; frame-specific visible evidence and declared source-model exposure. Preserve earlier six category projects rather than replacing their snapshots.
Reconstruct an orbital/gravity conservation or binary comparison and the original integrated-scale packet. Propagate common distance, inclination and contamination assumptions, retaining bounds, alternative explanations and units.
Evidence to retain: Reproducible original arithmetic, powers of common calibration, rejected inference and explicit fictional-versus-observed boundary.
Open the unchanged SDSS FITS and full/selected CSV with provenance. Retain exact hash, release, units and conventions; reconstruct wavelength from COADD LOGLAM and compare quality screens including an empty window. Declare exposed source class/redshift and formal-error assumptions.
Evidence to retain: Actual source-specific audit and reproducible transformations, not a substituted invented spectrum or independent rediscovery. Separate NASA media conditions from SDSS data reuse terms.
Connect planetary interior/formation or selection alternatives, stellar H–R/support/fuel/endpoints and galaxy/cosmic distance evidence. Distinguish ensemble from evolutionary track, shared calibration from independent probes and observations from background-model predictions.
Evidence to retain: All remaining module mechanisms and changed calculations; explicit causal/model alternatives and limits. Do not pretend the NASA Moon or SDSS spectrum supplies every required measurement.
Submit an unchanged first report covering all six capability groups before critique. Obtain substantive actual human review, then retain a revision with reasons for accepting or rejecting each correction and assistance/exposure disclosure.
Evidence to retain: Original report, real reviewer identity/content, preserved category histories and reasoned revised report; no invented critique or automatic mastery approval.
Attempt a genuinely unfamiliar reviewer-assigned packet before its solution. Explain which inference survives changed calibration, selection or mechanism and which needs new observation. Record actual independent evidence and leave absent practical performance unmet.
Evidence to retain: Unfamiliar assignment and first response with exposure timing and review. Actual supervised observing, independent learner validation, institutional credit and professional authorization remain separate.
Retain raw-data identifiers, provenance, units, prior predictions, methods, calculations, competing explanations and safety boundaries. State explicitly when data are simulated, supplied or genuinely observed. This saved text cannot verify a real experiment; do not invent measurements or completed supervised work. Maximum 12,000 characters; retain larger evidence files separately and cite them.
A nonempty report is only a saved submission. First and revised reports remain separate and cannot be overwritten. A critique of the first report is required before retaining one revision.
A new source changes projection, spectral calibration, contamination, population selection, stellar-stage assumptions or distance-ladder covariance. Defend the revised inference without recycling an exposed answer as unfamiliar reasoning.
A human must supply the actual new task, evidence and conditions before the learner responds. The transfer-direction text is not itself an unseen assessment. Use the retained assignment form after the first project; exposed public task identifier: expanded-public:college-astronomy.
Science backups preserve each course's separate responses, exposure, rubric reviews and project history. Older backups do not reset attempts or erase known exposure. Divergent same-version immutable responses and incompatible same-version project histories are rejected rather than silently replaced; preserve both files for review.
Original LearnAI explanations and tasks use the references for scientific scope. Any attributed dataset or image has its own declared provenance. Laboratory or field activity requires an appropriate educator-approved protocol; no hazardous real-world operation is required by the guided path.
Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.
A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.
Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.
A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.
The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.
0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.
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