Discussion of Spherical Trig. on P. 17 of C&O Is Optional

Note

Discussion of spherical trig. on p. 17 of C&O is optional. Celestial Coordinate Systems

We can specify where in the sky to ﬁnd an object, without knowing its distance. Thus most Celestial Coordinate Systems use only two angular coordinates. They differ depending on the axis of the system.

• Horizontal (altitude, azimuth) = (A,h) [observer’s axis] • Equatorial (right ascension,declination) = (α, δ) [Earth’s rotation axis] • Ecliptic (longitude, latitude) = (λ, β) [Earth’s orbital axis] • Galactic (longitude, latitude) = (l, b) [Galaxy’s rotation axis]

Coordinate systems also need a reference point:

Horizontal System: Due North = 0 degrees Equatorial: Celestial Equator = 0 degrees Ecliptic: Ecliptic = 0 degrees -Vernal Equinox (or “First Point in Ares”) = 0 deg. for both Eq&Ec Galactic System: Galactic center = 0 degrees. Two Planes in the Sky: Celestial Equator and Ecliptic Plane

• Earth’s axis is not perpendicular to the ecliptic. – It is tilted by 23.5º.

• The Celestial Equator is determined by Earth’s daily rotation

• The Ecliptic Plane is determined by the Earth’s annual orbital motion.

• These two planes in the sky intersect at the Equinoxes. Earth orbits the Sun in the Ecliptic Plane From Earth’s Perspective, the Sun appears to move along the Ecliptic Sun’s Apparent Annual “Motion” Sun’s Position in Equatorial System

The “Vernal Equinox” is also a point in space. It is the origin of of the Equatorial & Ecliptic Coordinate systems. Its Eq. coordinates are: α=0, δ=0 Historical Models of the Earth

! The fields of archeo-astronomy and cultural astronomy attempt to understand how ancient and modern people perceive the Earth & the universe. A few items from this field:

! Pythagoreans in 5th Cent. BC Greece said Earth is round ! What evidence could they have used? ! Some said the Earth rotated, others rejected the idea. ! Eratosthenes (c. 200 BC) measured the circumference of the Earth

! Humans have also observed the Sun & Moon for millennia. ! In addition to rising & setting: ! The Moon repeats its phases (Full, 3rd quarter, New, 1st qtr.) periodically ! Its “Synodic” period is 28.5 days ! The Sun ‘moves’ through 12 constellations in 1 year. Models of the Planetary System

! Also, humans have observed the planets since ancient times ! (Babylonian Venus tablets, c. 1600 BC) ! (Mayan Venus table in the ‘Dresden Codex’, c. 900 AD)

! Aristarchus of Samos (300 BC) said planets orbited the Sun

! However this heliocentric model was not widely accepted. ! Instead, by the 1st century AD, a geocentric model prevailed.

! Any model of planets must account for retrograde motion