LECTURE 2: MOTIONS OF THE STARS, SUN, MOON, AND PLANETS

• How do stars "move" on the sky over the course of a night, and the course of a year?
• How does the Sun move relative to the stars, nightly and yearly?
• How does the Moon move, nightly and monthly?
• How do the motions of the planets compare to those of the stars, the Sun, and the Moon?

EMPIRICAL DESCRIPTION OF ASTRONOMICAL MOTION

We see angular motions on the sky, not 3-d motions.

For this lecture, we will focus on empirical description of how celestial objects move on the sky. Leave interpretation in terms of true 3-d positions and motions until later.

DAILY MOTION OF THE STARS

Constellations: Patterns of stars on the sky, help to identify particular stars. Not true 3-d groupings.

Follow motion of the stars over the course of the night. Find:

• One bright star, Polaris, doesn't move. A.k.a. north star.
• Other stars appear to move in perfectly circular arcs.
• Circumpolar stars circle entirely above horizon, centered on Polaris.
• Other northern stars circle partly below horizon. Rise in east, set in west.
• Southern stars circle south pole instead of north pole. From northern hemisphere, mostly or entirely below horizon.
• Height of a given star above horizon depends on observer's latitude on Earth.
• Paths of stars depend on observer's latitude.

YEARLY MOTION OF THE STARS

• Stars complete daily circle in 23 hours, 56 minutes.
• After 24 hours (1 day), move 4 minutes into next circle.
• 4 minutes per day = (1/15 hour)/(24 hour) ~ 1/360.
• After 1 year: At same position at same time of night.

A useful practical description:

• Stars fixed to a "celestial sphere," a giant imaginary sphere that encircles the Earth.
• Celestial sphere rotates once per 23h56m.
• Only see stars at night, so see different parts of sphere at different times of year.
• (We now know that) this model is not physically accurate, but it is still useful as a description of celestial motions.
• Positions of stars on celestial sphere can be described by coordinates called right ascension and declination, analogous to longitude and latitude.

USING THE STARS

Four applications of stars:

• Simple calendar: tell time of year from positions of stars at Sunset.
• Night time clock: stars move at 15 degrees per hour.
• Compass: Polaris always north.
• More general navigation tool: Height of stars above horizon depends on observer's latitude. E.g., Polaris is overhead at north pole, near horizon at equator.

MOTION OF THE SUN

Daily motion of the Sun almost like a star.

• Rises in east, sets in west.
• Moves in circle centered on north or south pole.

• Daily cycle takes 24 hours, not 23h56m.
• Thus, position against background stars changes over time.
• Also, height of Sun above horizon changes with season.
• Summer: day is long, Sun high in sky at noon. Path like northern star.
• Winter: day is short, Sun low in sky at noon. Path like southern star.

• Sun moves nearly with celestial sphere, but position on sphere changes over year.
• Moves along a great circle called the ecliptic, inclined 23.5 degrees relative to equator.
• Constellations along ecliptic are called the "Zodiac" signs. Constellation opposite Sun depends on time of year.
• Behaves like northern star half the year, like southern star the other half.
• Completes circle every 365.24 days. One year is almost, but not quite, 365 days.

MOTION OF THE MOON

Motion of the moon sort of like sun.
Follows celestial sphere each day, but moves relative to stars along a great circle.
Differences:

• Completes circuit once a month, not once a year.
• Specifically: returns to same position against stars every 27.3 days.
• Slightly different path, inclined 5 degrees to ecliptic.
• Goes through phases: new, 1st quarter, full, 3rd quarter, new.

MOTION OF PLANETS

To naked eye, planets look like stars, but they move around in the sky.
Greeks called them "wandering stars" (asterai planetai).

Motion somewhat like sun and moon:

• Circle with celestial sphere from night to night.
• Roughly follow great circle path through stars over time.
• These paths are close to the ecliptic, but slightly inclined.

• Planets get noticeably brighter and fainter over time.
• Each planet has its own period for path through stars.
• Planets' motions along these paths are far from uniform --- sometimes move fast, sometimes slow.
• Planets sometimes reverse course relative to stars, retrograde motion.
• Planets brightest when in retrograde motion.