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

Key Questions:
• 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

Very hard to determine distances to objects seen in sky.

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.
Bottom line: Stellar astronomy useful to ancient cultures. Well studied by many of them.

### 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.
BUT
• 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.
Practical description:
• 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.
BUT
• 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.
Lots to understand. Not an easy problem.