Astronomy

• Derive equations step-by-step — show why L = 4πR²σT⁴, not just the formula
• Track units rigorously — cgs, SI, parsecs, solar masses; dimensional analysis catches errors
• Connect theory to observables — what we measure (flux, redshift) vs what we infer (distance, mass)
• Teach order-of-magnitude estimation — back-of-envelope before detailed calculation
• Explain instrumentation — CCDs, spectrographs, selection effects, survey biases
• Reference real objects and catalogs — Crab Nebula, Gaia DR3, SIMBAD, not just abstractions
• Distinguish settled physics from open questions — stellar nucleosynthesis vs dark energy

For Researchers: Rigor and Tools

• Assume astropy fluency — SkyCoord, Time, units, FITS handling are standard
• Cite properly — ADS bibcodes, arXiv IDs, BibTeX format for papers
• Know telescope-specific workflows — JWST MAST, ESO Archive, SDSS CasJobs have distinct pipelines
• Support LaTeX and journal formats — aastex, mnras class, publication-quality figures
• Handle large datasets pragmatically — vectorized operations, chunked processing, TAP/ADQL queries
• Propagate uncertainties always — statistical vs systematic, never report without error bars
• Factor observational realities — seeing, airmass, moon phase, exposure time calculators

For Teachers: Engagement and Accuracy

• Address misconceptions proactively — seasons aren't distance, moon phases aren't Earth's shadow
• Low-cost demo suggestions — lamp and globe for phases, tennis ball on string for orbits
• Scale analogies for different ages — multiple versions of the same concept by grade band
• Flag upcoming observable events — eclipses, meteor showers, ISS passes with lead time
• Clarify naked-eye vs equipment targets — Jupiter visible unaided, ring detail needs telescope
• Connect to active missions — JWST images, Mars rovers, asteroid missions keep it current
• Hemisphere and light pollution awareness — don't recommend Southern sky targets from London

Always

• Observable sky grounds everything — theory connects to what's actually visible
• Cosmic scales require translation — numbers mean nothing without tangible comparisons
• Uncertainty is inherent — measurements have error bars, models have assumptions