Motions in the Heavens

Key Ideas: What is seen with the eye?

Daily Motions

Reflection of the Earth's Daily Rotation

Annual Motions

Reflection of the Earth's Orbital Motion
Ecliptic: The Path of the Sun

Bodies: The Sun, The Moon and its phases, The planets ("Wandering stars" that follow complex paths and retrograde motion near the Ecliptic.)

The Starry Night

From a dark site, about 6000 stars are visible to the naked eye on a moonless night.

This represents only a tiny fraction of the nearly 200 Billion stars that make up the Milky Way Galaxy in which we reside.

Constellations

From time immemorial, people have seen patterns and drawn figures in the sky by connecting the bright stars.

These starry figures are the Constellations

All peoples have populated the night sky with constellations.

Figures in the Sky

Most constellations are composed of bright stars that stand out from the others.

Many look like what they are named

Peoples greatly separated in distance and/or time often made the same connections. A few common examples:

Orion depicted as a male human
Scorpius called a scorpion by most desert peoples
Celestial Rivers and Snakes

[Look for Orion in the winter sky, it rises in the east/southeast around sunset beginning in late December].

The Classical Constellations

The oldest known constellations (Leo, Taurus, Scorpius) appear in cuneiform tables dating from 3000 BC, but may be older still.

The Greek constellations and associated star lore were described in the Phaenomena of Eudoxus of Cnidos (c. 366 BC), and likely derived from Babylonian (Assyrian?) lore of c. 1100 BC.

The Greek astronomer Ptolemy made a catalog of 48 "classical" constellations in the 2nd century AD:

All of the classical constellations are those visible from the middle latitudes of the northern hemisphere.

Stars are not fixed!
They move in the sky over long periods of time. In 20,000 years the Big Dipper will look noticably different than it does today. Why? The stars of our galaxy orbit in a plane, or sheet, in a plate-like disk geometry, and all orbit around the galaxy at roughly the same speed. But, just like care on the highway, they have motions relative to one another. They thus appear to move in the sky.

Daily Motions

Objects in the sky appear to rise in the East and set in the West each day. This apparent daily motion is a reflection of the Earth's rotation about its axis.

Earth rotates once a day (24 hours)
The sense of rotation is Eastward
Facing North, rotation is towards the Right.

The Sun-Earth orbital plane is called the ecliptic plane. This is the plane that we see the Sun move in. This is the path of the Sun from our perspective.

Annual Motion of the Sun

Over the course of a year, the Sun appears to move a little towards the East each day as seen with respect to the background stars . This daily eastward drift is about 1° per day (there are 365 days in a year, but 360° in a circle).

This apparent motion is a reflection of the Earth's annual orbit around the Sun. The fixed stars (at least on human timescales) apparently don't move. Over the course of the year we could look to see which stars are up in the east just before sunrise. We would find that over the course of the year the Sun's position on the sky with respect to those background stars changes. This is because, as we orbit around the Sun, our perspective on the Sun changes with respect to those background stars.

Our Nearest Celestial Neighbor

The Moon is a natural satellite of the Earth.

Its orbit around the Earth is elliptical:

~0.15% out of circular.
Tilted by 5º from the Ecliptic.
Mean Distance: 384,400 km
Perigee (Closest Approach): 363,300 km
Apogee (Maximum Distance): 405,500 km
Appears ~11% larger at Perigee than at Apogee

Synchronous Rotation

The Moon's rotation period is equal to its orbital period:

The Moon completes 1 rotation about its axis in the same time as it completes 1 orbit around the Earth.

As a consequence, the Moon always keeps the same face towards the Earth.

Near Side: hemisphere facing towards the Earth
Far Side: hemisphere facing away from the Earth

The synchronization of the Moon's rotation and orbit is caused by strong tidal forces from the Earth that effectively "locks" the Moon's orientation relative to the Earth.

[Note: The degree of synchronization is not perfect for two reasons. First, the Moon's orbit is elliptical rather than circular, so that the Moon's orbital speed is faster at perigee and slower at apogee. This mis-match in the exact orbital and rotation rates results in an apparent east-west "rocking" motion of the Moon by about 7.9 degress over the course of a month. The second is that the axis of the moon's rotation is tilted by about 7 degrees relative to its orbital plane (like the Earth's 23.5 degrees). This leads to an additional north-south nodding motion over the course of a month. The combined rocking and nodding motion motion is called "libration". You can see libration in the lunation movie below.]

Phases of the Moon

The Moon produces no visible light of its own

It shines only by reflected sunlight
Surface is very dark, only ~7% reflective

During the month, we see a complete cycle of Phases:

The sunward hemisphere is fully lit.
The opposite hemisphere is dark.

The phase of the Moon depends on the fraction of the sunlit hemisphere visible to us.

Graphical depiction of the phases (click to see full-size) (Graphic by R. Pogge)

[Lunation Movie (Graphic by R. Pogge). This movie shows one month of lunar phases. Note how the moon appears larger at perigee and smaller at apogee. Also note the apparent nodding and rocking motions due to "librations" as mentioned above.]

New Moon & Full Moon

New Moon:

Moon and Sun are on the same side of the sky.
Near side is in total darkness.
Moon and Sun rise together.

Full Moon:

Moon is opposite the Sun in the sky.
The near side is fully illuminated.
Moon rises as the Sun is setting.

Quarter Moon

Quarter Moons occur when the Earth, Moon, & Sun are at right angles:

Half of the near side is illuminated
Half of the far side is illuminated

First Quarter:

Quarter Moon between New Moon and Full Moon.

Last Quarter:

Quarter Moon between Full Moon and New Moon.
Sometimes also called "Third Quarter"

With New Moon and Full Moon, they help to divide the Lunar Month into quarters.

Waxing & Waning

Waxing: increasing illumination

Waxing Crescent: just after New Moon
Waxing Gibbous: just before Full Moon

Waning: decreasing illumination

Waning Gibbous: just after Full Moon
Waning Crescent: just before New Moon

Moonrise, Moonset...

You don't see all moon phases at all times

Never see a crescent moon at midnight.
Never see the last quarter moon at sunset.
Never see a full moon during the day.

Times of rising and setting depend on the details of the Earth-Sun-Moon configuration as viewed from the surface of the rotating Earth.

Moonrise and Moonset during Full Moon:

(Click on the image to view at full scale [Size: 28Kb])

Full Moon rises as the Sun sets.
The Full Moon is in mid-sky at Midnight.
Full Moon sets as the Sun rises.
Full Moon cannot be seen during the day.

Other examples were given in class (Better, work out the approximate moonrise and moonset times for the current phase of the Moon, and then go outside and see if your predictions are correct!)

The View from the Moon

Question: What would an astronaut on the Lunar near side see during one month?

Answer:

See the Earth neither rise nor set, but stay nearly fixed at the same position in the sky.
See the Earth rotate on its axis once every 24^h.
See the Earth go through phases.

The Naked-Eye Sky

Celestial objects visible to the naked-eye include

Sun:: Bright disk ~1/2° across
Moon:: Pale disk ~1/2° across that goes through monthly phases.
Stars:: Pinpoints of light that appear fixed relative to each other on the Celestial Sphere.
Planets: (Greek: planetai = "wanderers"): Points of light that move relative to the "fixed" stars.; Stay within a few degrees of the Ecliptic; Follow complex paths that take between 88 days (Mercury) and 30 years (Saturn) to complete a circuit across the sky.

Five Classical (those that can be seen with the naked eye) Planets:

Mercury, Venus, Mars, Jupiter, & Saturn

Inferior & Superior Planets

Early astronomers recognized that the 5 classical planets could be divided into two groups:

Inferior Planets: Mercury & Venus

Appear to follow the Sun across the sky.
<28° for Mercury, and <47° for Venus.

Superior Planets: Mars, Jupiter, & Saturn

All move along the Ecliptic on paths seemingly independent of the motions of the Sun.
All can appear in the sky any time (e.g., around midnight)

Retrograde Motion

In general, the planets move eastward relative to the "fixed" stars.

Called "Direct Motion".
Motion is non-uniform (not at the same speed).

Sometimes, however, the planets appear to

Slow down & stop!
Start moving westward, or RETROGRADE,
Slow down & stop again,
Resume moving eastward again.

[Click Here to see an image (16Kb) of the retrograde motions of Mars during 1994/95 when it made a particularly characteristic loop. A 688Kb QuickTime movie shows this figure in motion (beware! it is a large file)] (Graphic by R. Pogge)

Apparent retrograde motion is observed in all planets. In all cases the apparent paths followed by the planets as seen from the Earth are very complex. They make various loops and S-curves during their retrograde motions that are due to the tilts of their paths relative to the Ecliptic.

[Click Here to see an montage (18Kb) of the recent (1998-2000) retrograde motions of Mercury, Venus, Mars, Jupiter, and Saturn. Note that Jupiter & Saturn, currently visible after sunset high in the Eastern sky, are just now (Jan 18) ending a period of retrograde motion that started back in October of last year.](Graphic by R. Pogge)

Here is a composite picture of Mars undergoing retrograde motion from APOD.
Here is a movie showing retrograde motion for Jupiter and Saturn

Unlike all of the other motions we've seen thus far, planetary motions are dauntingly complex. The struggle to understand these motions took nearly 3000 years.

A Question of Approach

How do we explain the motions of the planets?

Two approaches have been taken:

Phenomenological Description

Find a way to compute the motions without worrying about the details of why they work this way.
Goal is to "preserve appearances" (i.e., make reliable predictions)

Physical Description

Discover the underlying physical principles behind the planetary motions (i.e., ask "why" they move).
Predictions of the motions should then follow from first principles