Outline - Jan. 21, 2010

• Seasons (pgs. 28-30, 36-40)

• Phases of the Moon (pgs. 42-43, pgs. 45-48)

• Angular Sizes (pg. 31)

• Planetary motions (pgs. 49-51)

• Stellar parallax (pg. 52)

To get the notes, go to

http://firedrake.bu.edu/AS102/AS102.html

and click on “Class Notes”

Be sure to use the correct case (upper/lower) for the letters!!

Be sure to “refresh” your browser to see the latest version of the pages!!

Hypothesis & Prediction(science in action!)

Hypothesis: The cause of the seasons on earth is due to the changing distance between the earth and the sun over the course of a year.

If this hypothesis were correct, what would you expect to observe? (i.e., what predictions does the hypothesis make?)

What do we actually observe when it comes to the seasons?

Changing Earth-Sun distance is not the cause of the seasons

Over the course of the year in Boston, what will you notice about:

1. The height of the sun at noon

2. The rising and setting points of the sun (i.e., is it always due east and due west, respectively?) **note typo correction

Day after day, the sun appears to take a slightly different track in the sky, and the track correlates with the seasons.

Path of the Sun at Different Times of Year

From March 21-22 (spring equinox) to September 22-23 (autumnal equinox), the sun rises and sets north of due east/due west, so the days are long.

From September 22-23 to March 21-22, the sun rises and sets south of due east/due west, so the days are short.

Equniox = equal night

The height of the sun at noon and its rising/setting point depend upon your latitude on earth. The poles are truly extreme (constant day/night for months).

Midnight Sun

Near the earth’s poles, the sun never sets during mid-summer (= late June for the North Pole, = late December for the South Pole).

You pay for all this summer sun by never seeing the sun in mid-winter!

Tilt of the Earth Relative to the Sun’s Rays

The earth is inclined at 23.5o to the plane of its orbit around the sun. Notice how the angle at which sunlight hits the earth is different at different latitudes. This is the true cause of the seasons.

What season is it in South America in the picture?

What season is it in North America in the picture?

Solar “Irradiance”

equator mid-latitude (similar to Boston)

polar climates

The greater is the angle between the surface of the earth and the sun’s rays, the more power per unit area the surface of the earth receives.

Seasons and the Earth’s Orbit

You experience winter when your hemisphere is pointed away from the direction of the sun, and summer when your hemisphere is pointed toward the direction of the sun.

Precession of the Equinoxes

Like a spinning top, the earth’s rotation axis “precesses”, constantly changing the direction of the North pole with respect to the sky.

This “minor motion” is very slow (takes 26,000 years to complete), but is important to navigation by the stars!

Right now, the North Star is “Polaris” (the tail star of the Little Dipper). Five thousand years ago the North Star was Thuban, and in 14,000 it will be Vega.

Phases of the Moon

Names of lunar phases, left to right:

Waning Crescent, Third Quarter, Waning Gibbous, Full, Waxing Gibbous, First Quarter, Waxing Crescent

The amount of the moon’s face that is “lit up” increases daily from New Moon to Waxing Crescent to Full, then decreases daily from Full Moon to Waning Crescent to New Moon.

“Shadow of the Earth” does not cause the phases of the moon

Earth and moon, both showing the “First Quarter” phase, seen from space.

Cause of Phases of the Moon:Changing angle between the earth and sun

The only region of the moon that you can observe from earth is the hemisphere of the moon that is on the inside of the moon’s orbit.

At new moon, you look in the same direction to see both the sun and moon. At new moon the far side of the moon is in total daylight!

At full moon, you look on opposite sides of the sky to see the sun and the moon. At full moon, the far side of the moon is in total darkness!

At the quarter moons, the earth, moon, and sun make a right-angle triangle.

When does the moon rise and set?(make it simple - assume 12 hours from rise to set)

Sunrise = 6am, Sunset = 6pm

The moon rises about 50 minutes later from one day to the next.

New moon must rise and set with the sun (6am and 6pm), respectively.

Full moon must rise when the sun is setting (6pm), and must set at sunrise the following day (6am).

First quarter is mid-way between new and full, so it must rise at noon (i.e. 6 hours later than the new moon rises) and set at midnight (i.e., 12 hours after it rose).

Third quarter is mid-way between full and new, so it must rise at midnight (i.e., 3 hours later than the full moon rises), and set at noon (i.e., 12 hours after it rose).

On the diagram, you can see anything that is 180o from you (the extent of your horizon)

Choose a spot on the earth to stand, then ride along with the earth as it rotates counter-clockwise

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Solar and Lunar Eclipses

Total solar eclipse time sequence

Total lunar eclipse time sequence

“Angular” Size

Physically, the sun and moon have very different sizes (diameter of sun = 1.39x106 km, diameter of moon = 3,476 km) but they appear to be about the same size in the sky

The angular size of an astronomical object (in units of radians) is given by:

A = D/d

where D is the diameter of the object and d is the distance to the object.

Very important: the units of D and d must be identical!!

The farther an object is from us, the smaller it will appear in the sky

Images of the planet Mars

Angular diameter of the sun (as seen from the earth)

diameter of the sun = 1.39x106 km = Dsun

average distance to the sun = 1 AU = 1.5x108 km = dsun

angular diameter = Asun = Dsun/dsun = 1.39x106 km/1.5x108 km = 9.27x10-3 radian

Radians are usually much too large a unit of measurement for astronomical angles. Most angles are measured in degrees, arcminutes, or arcseconds.

1 radian = 180 / degrees = 57.3 degrees

1 degree = 60 arcminutes = 3600 arcseconds

1 arcminute = 60 arcseconds

Asun = 9.27x10-3 radian = 9.27x10-3 radian x 57.3 degrees/radian = 0.53 degree

Asun = 0.53 degree = 0.53 degree x 60 arcminutes/degree = 32 arcminutes

Total vs. Annular Solar Eclipse

Total solar eclipse Annular (“ring”) solar eclipse

For a total solar eclipse to occur, angular size of the moon must be equal to or greater than the angular size of the sun.

You will explore conditions for an annular eclipse on HW #1

Why don’t we get a solar eclipse with every new moon and a lunar eclipse with every full moon?

Moon’s orbit is inclined at 5o to Earth’s orbit. It is only when the moon is precisely in the same plane as the earth’s orbit that eclipses can occur.

How to tell a planet from a star without a telescope

Five planets are visible without a telescope. They look like points of light (like stars), with one important difference.

“Planets” comes from the Greek word “planetes” meaning “wanderers”.

Planets move with respect to the (fixed) stars

Locations of Venus and Jupiter over the course of 6 nights. All photos taken when the star “Spica” was in the same location in the sky. Notice how Venus has moved much farther than Jupiter over this period of time!

The primary motion of the planets is from WEST to EAST

Sometimes the planets reverse their motion and travel from EAST to WEST, a phenomenon

known as “retrograde motion”

Example: Retrograde Motion of Mars

From Jan. 4, 1995 to March 25, 1995, Mars is moved “backward” in the sky (east to west)

On astronomical maps, east is on the LEFT and west is on the RIGHT. Why????

WestEast

From what perspective are you viewing this picture?

West

East

Astronomers look UP at the sky!

Actual image of Mars undergoing “retrograde motion”

Do you notice anything different about Mars when it is undergoing retrograde motion? (Assume all the individual exposures were the same length of time.) Retrograde motion is on the TOP part of the “loop” in the sky.

It’s all about perspective!

• We see the planets move with respect to the fixed stars

• Space is really 3-d (planets are much closer than the stars), but space looks 2-d (when you look at a picture of the sky you don’t have a sense of depth that tells you the planets are closer than the stars)

• The planetary motion you see is due to combination of: (1) earth’s motion about the sun and (2) the planet’s motion about the sun

• Retrograde motion happens when an inner planet (e.g., the earth) catches up to and “laps” an outer planet (e.g., Mars)

• All planets orbit in the same direction about the sun continuously, they only appear to go “backward”

Retrograde Motion of Mars

• Happens about once every 2 years

• Only occurs when Mars and Earth are near their distance of closest approach (called “opposition” because Mars and the Sun are on opposite sides of the sky, as seen from earth)

• Is currently going on! Mars will be at opposition next Friday (Jan. 29)

• For every 1 orbit of the Earth around the sun, Mars makes about 2 orbits around the sun

http://www.youtube.com/watch?v=72FrZz_zJFU

Does the earth really orbit the sun?What proof do we have?

Once again, it’s all a matter of perspective!

As the earth orbits the sun, nearby stars appear to shift their location in

the sky compared to extremely distant (“background”) stars.

The farther is a star, the smaller is its parallax.

If p is measured in arcseconds, the distance to the star is

d = 1/p

where d is in units of “parsecs”

1 parsec = 1 pc = 3.26 ly

The closest star to us (other than the sun) has a parallax of p = 0.7687 arcsec = 2.1x10-4 degree.

This is much too small to see without a telescope!!

Minute Paper

A few sentences on one of the following:

* something you found particularly interesting today

* something you found particularly confusing today

* questions on things from today that you would like to know more about

Be sure to PRINT your name legibly