Astronomy
Telescopes and light
Aperture, diffraction limit, collecting area, seeing versus space telescopes.
Basics
Aperture
Aperture is the diameter D of the main lens or mirror. Larger D gathers more photons and, ideally, a finer image. Mirrors scale large apertures more cheaply than lenses. The focal ratio f/D shapes field and exposure feel. Mount, tracking, and dome can cost as much as the optic. Cheap eyepieces that only raise magnification just enlarge a blur.
Diffraction limit
A circular aperture’s theoretical resolution is near θ ≈ 1.22 λ / D (radians). Longer wavelength or smaller D thickens the image. A 1 m visible telescope is theoretically ~0.1″, but the atmosphere usually wins first on the ground. Radio needs much larger D for the same θ because λ is large. Interferometers stitch baselines from many apertures.
Collecting area
Collected light scales roughly with area π (D/2)². Double D and the same star yields about four times the photons. Faint galaxies and distant supernovae live or die by area. Spectroscopy still needs photons after the slit, or noise wins. Exposure time trades against area in the plan.
Seeing and space
Atmospheric turbulence that makes stars dance is seeing. Even on good mountains, visible seeing is often an arcsecond or more. Adaptive optics uses laser guide stars and fast mirrors to approach the diffraction limit. Space telescopes have no seeing and open UV/IR windows, at high launch and servicing cost. Huge ground apertures and space platforms complement each other.
Formulas
Diffraction limit (rough)
Radians; ×206265 for arcseconds.
Symbols
-
λwavelength -
Daperture diameter
Collecting area
First-order scale for photon rate.
Symbols
-
Aarea
Light and time (sketch)
Area, exposure, and bandpass raise S/N.
Symbols
-
texposure time -
Δλbandwidth
Key table
| Hubble vs giant ground | Hubble: no seeing. 30 m-class ground: area + AO compete |
|---|---|
| Seeing unit | stellar FWHM in arcseconds; 0.5″ is excellent |
| Central obstruction | a secondary blocking the centre tweaks contrast a little |
In this field
Solar system
Planets, Kepler, gravity, escape speed.
Stars
HR diagram, fusion, lifetimes, magnitude.
Galaxies and cosmology
Galaxies, Hubble, redshift, black holes.
Observing basics
Celestial sphere, coordinates, telescopes, spectra.
Exoplanets and life
Detection, habitable zone, a SETI sketch.
The Sun and space weather
Solar structure, spots, flares and CMEs.
Moon, tides, and eclipses
Lunar phases, tides, and solar and lunar eclipses.
Magnitudes and spectra
Apparent and absolute magnitude, distance modulus, colour and spectral type, Wien’s law.
Galaxies and Hubble
Galaxy shapes, rotation curves, the Hubble–Lemaître law, and a standard-candle sketch.
Stellar death
Red giants, supernovae, and sketches of white dwarfs, neutron stars, and black holes.