# Astronomy 217

Aug. 23, 2021

TA Bryce Fennig

## Last Time

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

## Today

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

## Constellations

• 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

## Clusters

• 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.

## Coordinates

• 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)

## Ecliptic

• 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

## 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