Astronomy 217


Prof. Andrew W. Steiner

Aug. 23, 2021

TA Bryce Fennig

Last Time

  • Syllabus
  • Office Hour
  • Scientific Notation
  • Units
  • Trigonometry
  • Applying to stars
  • Taylor series


  • Constellations
  • Clusters
  • Ecliptic
  • Alt-az coordinates
  • Equatorial coordinates
  • Circumpolar stars
  • Tropics and the polar tilt


  • Use in antiquity
  • Now 88 official regions in the sky
  • Borders follow lines of right ascension and declination
  • Shapes drawn out by stars are "asterisms"
  • Within constellations, stars are labeled with greek letters by brightness
  • Objects measured in radio or X-ray use a different naming scheme
  • Stars are not fixed in position, state, or brightness — though the "timescales" may be long

Night Sky as a 2D Projection

  • Stars which appear close in the sky may have no relationship to one another
  • Large objects at large distances and small objects at small distances may be indistinguishable


  • There are "associations" and clusters of stars which consist of many stars close to one another
  • Several types of clusters: open clusters, globular clusters, etc.


  • A single object has many different locations according to different coordinate systems
  • A convenient system for observation is altitude-azimuth, aka "alt-az" coordinates
  • Keywords: zenith, nadir, horizon, meridian
  • In alt-az system, One object has different coordinates for different observers
  • Also, altitude and azimuth change during the night
  • E.g., In North America, you can never see stars in the southern hemisphere (the corresponding altitude is negative)


  • Solar system lies nearly in a plane
  • All of the planets and the sun travel in a circle around the sky, the "ecliptic"
  • We can define a coordinate system using the ecliptic, "ecliptic coordinates" (less commonly used)

Equatorial Coordinates

  • Celestial sphere: extend the (geometric) poles and the equators outwards
  • Define a new coordinate system, "equatorial coordinates"
  • Two-dimensional coordinate system for three-dimensional universe
  • Planets' equatorial coordinates change rapidly
  • Stars also do not have fixed equatorial coordinates, but these changes are much slower

Polar Tilt

  • Poles tilted at 23.5 degrees with respect to the plane described by Earth's revolution around the sun
  • Impacts weather and our sky
  • Equinox marks passage of Sun across celestial equator
  • Solstice marks the sun's furthest distance from the celestial equator, causing the longest day or night

Right Ascension and Declination

  • "RA" and "Dec" form the equatorial coordinate system
  • Declination is similar to latitude, measured from celestial equator
  • Right ascension is like longitude, measured hours eastward from the sun's location at the vernal equinox
  • Hour angle is parallel to the right ascension, but measured in hours westward of the local zenith

Example of Sirius

Circumpolar Stars

  • Depending on your latitude, there are some stars which never set below the horizon, "circumpolar" stars
  • E.g. Polaris, the star which approximates the north pole
  • Near the north pole, most stars are circumpolar
  • For latitude \( \ell \), stars with declination \( > 90^{\circ} - \ell \) are circumpolar

The Tropics

  • Tilt of Earth's axis causes the declination of the sun to vary, from \( 23.5^{\circ} \) to \( -23.5^{\circ} \)
  • How does the Sun's altitude vary during the day?
  • At the summer solstice, the Sun is directly overhead at a latitude of \( 23.5^{\circ} \), the "Tropic of Cancer"
  • For latitudes above \( \ell = 90^{\circ} - 23.5^{\circ} = 67.5^{\circ} \), the sun is circumpolar at the summer solstice, this is the "Arctic Circle"

Motion in Circles

  • Circular motion in the solar system produces a length of time
  • Rotation around axis produces the day
  • Earth-Moon orbit produces the month
  • Revolution around Sun produces the year
  • Precession of the pole produces the Great Year

Solar Day

  • The rising and setting of the sun are natural markers for the day
  • However, the variation in the length of the day make sunrise and sunset make very irregular time keepers
  • The upper transit, the passage of the sun across the local zenith meridian, AKA noon, is a more reliable marker
  • The solar day is defined to be the length of time for the Sun to return to your celestial meridian