Astronomy

Observing basics

Celestial sphere, coordinates, telescopes, spectra.

Basics

Celestial sphere

Right ascension and declination are sky longitude and latitude (equatorial). Altitude and azimuth are local horizontal coordinates. Earth’s rotation makes stars rise east and set west. The ecliptic is the Sun’s path, tied to the seasons.

Telescopes

Collecting area scales as aperture squared. Diffraction-limited resolution ≈ 1.22 λ / D. Seeing limits ground optical work. Radio, IR, and X-rays need special windows or space. Spectra give elements and Doppler speed.

Moon and eclipses

Synodic month ≈ 29.5 days. Eclipses happen near the nodes, when Sun, Moon, and Earth nearly align. A total solar eclipse has a narrow lunar shadow; a lunar eclipse can cover the whole Moon in Earth’s shadow.

Formulas

Diffraction limit

θ ≈ 1.22 λ / D (rad)

Larger D and shorter λ resolve finer angles.

Symbols

  • D aperture diameter

Radial velocity (non-rel.)

v_r / c ≈ Δλ / λ

Redshift means receding. Basis of the radial-velocity exoplanet method.

Symbols

  • Δλ wavelength shift

Small-angle size

θ ≈ s / d (rad)

Links angular size, physical size, and distance.

Symbols

  • s true transverse size
  • d distance

Key table

Polaris near the north celestial pole now — altitude ≈ latitude
Light pollution Cities drown faint nebulae and galaxies

In this field