Homework 1

Unit 2. Problems 13, 16, 18,

Unit 3. Problems 9. 18, 19, 20

For Honors: special assignment (talk with me after the lecture if

you have not done this)

Unit 8. Problem 20

Unit 10. Problem 17, 18

Reading: Units 1-11

For Honors:One should write 15 page research proposal that will

discuss either a mission, or an instrument that will make an advancement in our knowledge of

Astrophysics possible beyond the present day horizont.The intended project should include an

extensive (1) introduction that shows the present day ways to solve a particular problem, (2) a discussion of

the proposed solution, (3) the benefits that this solution will have in terms of advancing our knowledge, (4) bibliography with references to web resources and original research papers. The proposal is due two

weeks before the end of the classes.

The Celestial Sphere I

• Stars in the universe are located at various distances from Earth, but can be imagined as lying on a sphere, with the Earth at its center.

• This sphere appears to rotate around the Earth, giving the impression that stars rise and set.

• Since earliest times, humans have sought to understand the night sky

• A useful model of the sky is called the Celestial Sphere

• It is not real – it is simply a tool for understanding and prediction

The Celestial Sphere II

• Important Terms– Zenith: The point directly overhead on the celestial

sphere (CS)

– Nadir: The point opposite the zenith on the CS

– North or south celestial pole: The point around which the stars appear to rotate

– Celestial Equator: An extension of the Earth’s equator expanded out to the surface of the CS.

– Horizon: The lower edge of the visible CS

Constellations and Asterisms

• The human mind is very good at recognizing patterns – consequently we have found and named patterns of stars on the celestial sphere

• The names of these patterns have their origins in mythology from all over the globe

• Sometimes very hard to see!

• These patterns are called constellations– 88 internationally recognized

constellations, covering the entire sky

– Star names frequently include the name of the constellation in which they are located

• Some popular patterns are not constellations – these are called asterisms

– Big Dipper

– The Teapot

The Ecliptic

• The ecliptic ‘belt’ on the celestial sphere is tipped relative to the celestial equator due to the 23.5° inclination of the Earth’s rotational axis

• In June, the Sun appears north of the celestial equator

• In December, the Sun appears south of the celestial equator

• Twice a year, the sun appears on the celestial equator – these times are called the equinoxes

The Seasons I

• The Earth’s inclination is ultimately responsible for the change in seasons.– In June, the Northern

Hemisphere is tilted towards the Sun

– In December, the Northern Hemisphere is tilted away from the Sun

• Common Myths:– Summers are warmer because the Earth is

closer to the Sun than in Winter• Actually, the opposite is true!

– The tilt of the Earth’s axis brings the Northern Hemisphere closer to the Sun in Summer, and farther from the Sun in Winter

• True, but this accounts for only a minute fraction of the extra heating

The Seasons II

• This tilt has two important effects

– In Summer, the Sun spends more time above the horizon – days are longer, resulting in more heating

– In Summer, light from the Sun strikes the ground more directly, concentrating the Sun’s energy.

• Summers are therefore warmer than winters!

Precession I

• The Earth spins about its axis like a top, but the Sun’s gravity adds a little tug

• This tug results in the axis of the Earth rotating, or precessing, with a 26,000 year period

Precession II

• Thanks to precession, Polaris (the North Star) will not always be “The North Star!”

• 6000 years ago, the North Star was Thuban, a star in the constellation Draco

• In 12,000 years, the Earth’s axis will point toward Vega, a bright star in Lyra

What Time Is It?

• There are many ways to measure time on Earth– Sunrise to sunrise

• Problem – seasons change sunrise times!

– The time between successive crossings of the meridian by the Sun (Solar Day)

• Problem – inaccuracies due to clouds

Length of Daylight Hours

• The number of daylight hours a place has depends on that place’s latitude on the Earth

– Regions close to the northern pole get more daylight hours during the summer, and less in winter

– Within the Arctic Circle (higher than 66.5 degrees latitude), there are some summer days where the Sun never sets!

– Regions close to the equator get close to 12 hours of sunlight all year.

Time Zones

• The globe is divided into 24 time zones, designed such that local noon roughly corresponds to the time when the sun is highest in the sky

• If it is noon on the Prime Meridian in Greenwich, UK, it is midnight on the opposite side of the world. This midnight line is called the International Date Line

The Phases of the Moon

• As the Moon moves around the Earth over its 29.5 day cycle, one half of its surface is always lit by the sun

• From Earth, we see only portions of the illuminated surface, giving the appearance of phases of the Moon– Full Moon: The Earth is between

the Moon and the Sun, so we see all of the illuminated surface

– New Moon: The Moon is between the Earth and the Sun, so we see none of the illuminated surface

During the winter the temperature is lower because the Sun

• A. Stops moving

• B. has lower temperature

• C. is farther away from the Earth

• D. does not rise as high in the sky

Size of the Earth

• Eratosthenes (296-195 b.c.e.) wanted to know the size of the Earth

• He noted that the sun could be seen from the bottom of a well in Syene, so the Sun must be directly overhead

• Then he measured the angle the Sun made with the horizon in Alexandria (7 degrees)

• Calculated a diameter of 13,000 km, almost exactly correct!

Measuring Angular Diameter

• In Astronomy, we will frequently estimate the sizes of planets, etc.

• To do this, we measure the angle that the object makes in the sky.

• We say that an object subtends an angle (A) in the sky

• For example, the moon subtends 0.5 degrees.

• The Sun also subtends 0.5 degrees, which is why solar eclipses are so beautiful!

Measuring Linear Diameter

• If we measure the angle subtended by an object in the sky (A), and we know the distance to it (d), we can calculate its actual, linear diameter (L)!

The Motion of the Planets

• Because the planets’ orbits all lie in more or less the same plane, the paths of the planets through the sky all lie close to the ecliptic, appearing to move through the constellations of the zodiac

• Only Pluto seems to move far from the ecliptic

Retrograde Motion

• As the Earth catches up to the orbital position of another planet, that planet seems to move backwards through the sky.

• This is called retrograde motion

• Posed a frustrating problem to the ancients – if all planets moved in perfect circles, how could they move backwards, and why only occasionally?

Geocentric Models

• Models in which everything revolves around the Earth are called Geocentric models.

• From earliest Greek times, this kind of model was used to describe the heavens

• Planets and stars resided on their own spheres, each tipped slightly relative to each other. This reproduced the motion of the planets and Sun through the sky.

• Did not explain retrograde motion!

Epicycles

• Ptolemy (100-170 C.E.) improved the geocentric models by including epicycles– Planets were attached to small circles

(epicycles) that rotated.

– These epicycles were attached to a larger circle, centered on Earth

• This can be visualized as a planet attached to a Frisbee, attached to a bicycle wheel with the Earth at the center.

• Did a fair job of reproducing retrograde motion.

Heliocentric Models

• Nicolas Copernicus devised a heliocentric (Sun-centered) model in which everything, including the Earth, revolves around the Sun

• Retrograde motion is a natural result of these models!

• Copernicus was also able to measure the relative distances between the Sun and the planets

Mercury and Venus

• It was found that Mercury and Venus were closer to the Sun than the Earth, as they were never found very far from the Sun in the sky

• Mercury’s greatest elongation, or angular separation from the Sun, is never more than 28 degrees

• Venus’s greatest elongation is never more than 47 degrees

• Mercury is therefore closer to the Sun than Venus

Tycho Brahe (1546-1601 C.E.)

• Built instruments to measure the positions of planets very accurately (~1 arc minute)

• Found that comets moved outside of the Earth’s atmosphere

• Witnessed a supernova and concluded that it was much farther away than any celestial sphere

• As he could detect no parallax motion in the stars, he held that the planets go around the Sun, but the Sun, in turn, orbits around the Earth

Johannes Kepler (1571-1630

• Using Tycho Brahe’s data, discovered that planets do not move in circles around the Sun, rather, they follow ellipses with the Sun located at one of the two foci!