Earth rotates, causing the apparent daily movement of the sky. An observation should record time, direction and location rather than assume all observers see the same view.
Grades 6–9Earth rotates, causing the apparent daily movement of the sky. An observation should record time, direction and location rather than assume all observers see the same view.
Grades 6–9The Sun is a star at the centre of the planetary system. Planets, moons, small bodies, gas and dust form a gravitationally interacting system.
Grades 5–9The Sun is a star at the centre of the planetary system. Planets, moons, small bodies, gas and dust form a gravitationally interacting system.
Grades 5–9Radio, infrared, visible, ultraviolet, X-rays and gamma rays are electromagnetic radiation. Astronomy uses more than the light visible to human eyes.
Grades 8–12Radio, infrared, visible, ultraviolet, X-rays and gamma rays are electromagnetic radiation. Astronomy uses more than the light visible to human eyes.
Grades 8–12A telescope collects light over an aperture. In a simple unobstructed comparison, collected power scales with diameter squared.
Grades 9–12A telescope collects light over an aperture. In a simple unobstructed comparison, collected power scales with diameter squared.
Grades 9–12Annual stellar parallax measures a small apparent angular displacement using Earth's orbital baseline. In the conventional units, d(pc)=1/p(arcsec).
UniversityAnnual stellar parallax measures a small apparent angular displacement using Earth's orbital baseline. In the conventional units, d(pc)=1/p(arcsec).
UniversityLuminosity is emitted power; flux is received power per area. For isotropic emission with negligible absorption, F=L/(4πd²).
UniversityLuminosity is emitted power; flux is received power per area. For isotropic emission with negligible absorption, F=L/(4πd²).
UniversityA hydrostatic star balances inward gravity with an outward pressure gradient. Equilibrium does not mean pressure is uniform.
UniversityA hydrostatic star balances inward gravity with an outward pressure gradient. Equilibrium does not mean pressure is uniform.
UniversityA star's mass and composition strongly influence its lifetime and later evolution. One single life-cycle diagram is not valid for every star.
UniversityA star's mass and composition strongly influence its lifetime and later evolution. One single life-cycle diagram is not valid for every star.
UniversityKeplerian orbits approximate isolated Newtonian two-body motion. Real trajectories can include perturbations, drag or relativistic corrections.
UniversityKeplerian orbits approximate isolated Newtonian two-body motion. Real trajectories can include perturbations, drag or relativistic corrections.
UniversityA mission trades measurement goals against mass, power, thermal control, communications and trajectory constraints. No single orbit is best for every goal.
UniversityA mission trades measurement goals against mass, power, thermal control, communications and trajectory constraints. No single orbit is best for every goal.
UniversityA planet crossing a star's visible disk can cause a periodic brightness dip. For an idealized small dark planet and uniform stellar disk, depth≈(Rp/Rstar)².
UniversityA planet crossing a star's visible disk can cause a periodic brightness dip. For an idealized small dark planet and uniform stellar disk, depth≈(Rp/Rstar)².
UniversityA simple equilibrium-temperature model balances absorbed stellar power and emitted thermal power. Albedo, redistribution and greenhouse effects require separate treatment.
UniversityA simple equilibrium-temperature model balances absorbed stellar power and emitted thermal power. Albedo, redistribution and greenhouse effects require separate treatment.
UniversityGalaxies contain stars, gas, dust and other gravitating components. Their morphology does not alone determine all their dynamical properties.
Advanced universityGalaxies contain stars, gas, dust and other gravitating components. Their morphology does not alone determine all their dynamical properties.
Advanced universityDefine z=(λobserved−λemitted)/λemitted. Redshift is dimensionless and can arise through different physical mechanisms.
Advanced universityDefine z=(λobserved−λemitted)/λemitted. Redshift is dimensionless and can arise through different physical mechanisms.
Advanced universityFor a nonrotating uncharged black hole, the horizon radius is rs=2GM/c². Rotation and charge require a different spacetime description.
Advanced universityFor a nonrotating uncharged black hole, the horizon radius is rs=2GM/c². Rotation and charge require a different spacetime description.
Advanced universityA detected sample is shaped by observing limits and selection criteria. It need not represent the full source population without correction.
Advanced universityA detected sample is shaped by observing limits and selection criteria. It need not represent the full source population without correction.
Advanced universityUse a positive parallax in arcseconds. Reciprocal inversion of noisy parallaxes needs additional statistical care.
UniversityUse a positive parallax in arcseconds. Reciprocal inversion of noisy parallaxes needs additional statistical care.
UniversityThe fluxes must refer to the same measurement band and calibration convention.
UniversityThe fluxes must refer to the same measurement band and calibration convention.
UniversityThis simplified model neglects extinction. Apparent and absolute magnitudes must use the same band.
UniversityThis simplified model neglects extinction. Apparent and absolute magnitudes must use the same band.
UniversityUse the effective-temperature blackbody luminosity model and compare the same reference quantities.
UniversityUse the effective-temperature blackbody luminosity model and compare the same reference quantities.
UniversityThis is the peak of spectral radiance per wavelength; a frequency-spectrum peak is a different definition.
Grades 9–12This is the peak of spectral radiance per wavelength; a frequency-spectrum peak is a different definition.
Grades 9–12Use the approximate AU-year-solar-mass two-body model with negligible companion mass.
UniversityUse the approximate AU-year-solar-mass two-body model with negligible companion mass.
UniversityAssume a dark small planet, central transit, no blending and uniform stellar brightness. Depth is a fraction, not a percentage.
UniversityAssume a dark small planet, central transit, no blending and uniform stellar brightness. Depth is a fraction, not a percentage.
UniversityThis exercise uses a constant distance and straight-line light travel, not a spacecraft maneuver model.
Grades 9–12This exercise uses a constant distance and straight-line light travel, not a spacecraft maneuver model.
Grades 9–12This measured wavelength ratio alone does not select a velocity-distance model.
Advanced universityThis measured wavelength ratio alone does not select a velocity-distance model.
Advanced universityApply the homogeneous expanding-universe cosmological-redshift model, not a local Doppler shift.
Advanced universityApply the homogeneous expanding-universe cosmological-redshift model, not a local Doppler shift.
Advanced universityAssume circular motion about a spherically symmetric mass distribution; this is not valid for all geometries.
Advanced universityAssume circular motion about a spherically symmetric mass distribution; this is not valid for all geometries.
Advanced universityAssume independent source and background Poisson noise and a background expectation known without extra uncertainty.
Advanced universityAssume independent source and background Poisson noise and a background expectation known without extra uncertainty.
Advanced university