Physics 101 Astronomy

• Quick review of Chapters 1 and 2, followed by the first exam.

• You will only need to write your name (lastname firstname) on the exam

• Pencils are available – ask for one.• Turn in exam sheet and SCANTRON

and sign your name on signature sheet.• Exit through the door in front-right.

Ch. 1 Review

What can we see in the visible sky?

• Humans can see about 6000 stars in the night sky (with good vision and a very dark clear night).

• Some of these form patterns called asterisms.

• These have been grouped into constellations (there are 88 of these in the current system).

The Constellation Orion, as seen in the sky and as imagined.

The Constellation Orion is actually three dimensional, but appears to us as a group of points on the “celestial sphere”

The Celestial Sphere appears to rotate around us at night. But you know that it is the Earth that is rotating.

To observers who think the earth is stationary, The celestial sphere appears to be rotating.

The Northern Sky, in a time exposure, shows the apparent motion of the northern part

of the celestial sphere around the Pole star, Polaris.

Declination and Right Ascension are used to indicate positions on the celestial sphere. They correspond to

latitude and longitude on the surface of the Earth.

The celestial sphere is oriented with respect

to the earth, with poles and an equator.

On the celestial sphere we use Declination like we use Latitude on the Earth.

On the celestial sphere we use Right Ascension like we use Longitude on the Earth, but

measured in hours, minutes, and seconds.

To an observer on the ground, directions are defined in this figure.

Seen from far above the North Pole, the Earth appears to be rotating counterclockwise (CCW).

Sun

If the Sun is directly above point A, then it is local noon there, and in 24 hours it will again be noon at that location on the Earth.

The Earth is also in orbit around the Sun,

taking 365.25 days to revolve once around.

This orbital motion is also CCW if viewed from above the north pole.

In 24 hours, which is called the solar day, the Earth must rotate more than 360 degrees!

Solar vs. Sidereal Day

• The solar day is 24 hours long, by definition, but Earth actually rotates through an angle of 360.986o in order to be aligned with the Sun. This is due to the orbital motion of the Earth, which means that the Earth has to rotate an additional 360o/365 or 0.986o per solar day.

Solar vs. Sidereal Day

• The sidereal day is, by definition, the times it takes the Earth to rotate around and come back into alignment with the stars. This is a rotation of exactly 360o and this takes 3.9 minutes less than 24 hours.

• 1 sidereal day = 0.9973 solar days.

The Zodiac is the set of constellations that the Sun appears to go through during the course of one year.

The Ecliptic is the path of the Sun on the celestial sphere, which is tilted with respect to the celestial equator,

due to the tilt of the Earth’s axis with respect to our orbit.

The axis of the Earth is not perpendicular to the plane of the orbit of the Earth around the Sun.

The Earth is tilted by 23.5o.

Precession of a top

• We can demonstrate a type of motion called “precession” by recalling the motion of a toy top (a wobbling motion).

• A bicycle wheel can be used to demonstrate precession.

• The Earth precesses because it is not a perfect sphere.

Precession of the Earth

Precession of the Earth takes 26,000 years.

The North Celestial Pole

moves around a circle on the

celestial sphere over long

periods of time.

Sequenceof photosof the Moon shows the Phasesof the Moon

Lunar Phases

Lunar Eclipse

Lunar Eclipse

Solar Eclipse

Solar Eclipse Types

Penumbra and Umbra

See detail on next slide.

Shadow of Moon seenfrom Mir space station

Animation of Moon eclipsing the Sun, as seen from the ground as the umbra passes over you.

Animation of the view from the dark side of the Moon, looking down on the Earth during a solar eclipse.

Eclipse Geometry is favorable approximately twice a year when the orbits of Moon and Earth line up as shown.

Eclipse Tracks (also see NASA Eclipse page, Mr. Eclipse and Eclipser)

Ch. 2 Review

Science is the key to understanding

• Science: a body of knowledge and a process of learning about nature (called the scientific method).

• Knowledge is acquired by observations and experiments.• Scientific method is a process for gaining more knowledge, that

can be tested and accepted by everyone. • Scientific theory is an explanation of observations or

experimental results that can be described quantitatively and tested.

• The theory must make testable predictions that can be verified by new observations or experiments, and can possibly be refuted.

• Theories can be modified and should be the simplest version that explains the observations (Occam’s razor).

• Observe, hypothesize, predict, test, modify, economize.

The Copernican Revolution

• The Copernican Revolution in our scientific understanding of the solar system is a prominent example of the scientific method.

• It replaced the older Greek theory of the solar system with a simpler model that described the motion of the planets.

Retrograde motion occurs over several weeks, and involves motion to the west, as compared to prograde (direct) motion, which is to the east(relative to the stars of the ”celestial sphere”).

Geocentric Model of planetary motion (Greek philosophy)

The Geocentric Model does explain retrograde motion, using concepts like deferent and epicycle.

These could be illustrated by swinging a ball on a cord as we

revolve a center of an epicycle around the Earth.

Ptolemy’s Model of planetary motion used deferents (big circles) and epicycles (little circles centered on a point that moves on the

deferent). This involved up to 80 circles to describe 7 objects!

Nicholas Copernicus and his Heliocentric model of the Solar System explained this in a simpler way with the Sun at the center.

The Heliocentric Model also explains the Retrograde Motion of the planets.

An illustration of retrograde motion, using Earth and Mars as the example.

Retrograde Motion of Mars as seen from Earth

Galileo Galilei and the Birth of Modern Astronomy

Galileo built a telescope in 1609 and looked at the sky. His observations confirmed the heliocentric model but did not answer all the questions nor provide detailed

mathematical models to calculate the orbits of the planets.

Four objects:

The Moon

The Sun

Jupiter

Venus

(and much more)

Galilean Moons of Jupiter

Small point of light could be seen near Jupiter. By observation during several weeks he deduced that these were moons and that

they revolved around Jupiter.

Perhaps this planet was like the Earth, with several moons of its own. It also seemed like

a miniature model of the heliocentric solar system.

In the Heliocentric model, Venus has gibbous phases. These are consistent with the observations in a telescope.

Venus Phases in the Geocentric model are always crescent,and obviously wrong as soon as you observe with a

telescope,since you will see gibbous phases at certain times.

After Copernicusand Galileo,

two major figureschanged the way

we come to understand the

Universe:

Kepler’s laws of planetary

motion

Newton’s laws of mechanics

Both described the positions and movement of the Sun, Moon, and 5 visible planets, as seen without a telescope.

The geocentric theory was too complicated (80 circles!). (Occam’s razor could be invoked to seek a simpler way.)

Once the telescope was used to observe Venus, the geocentric theory could not explain the phases of Venus.

The heliocentric theory of Copernicus explained many of Galileo’s observations, but also used circular orbits.

More accurate measurements did not agree with the simple theory of Copernicus (circles had to be replaced by ellipses in the newer theory of planetary motion).

Geocentric vs. heliocentric theories

More detailed observations were made by Tycho Brahe (commonly called Tycho, 1546 - 1601).

He made observations of a supernova in 1572 which convinced him that it was a distant star.

He received an island and built an observatory to measure planetary motion to high accuracy over a period of more than 20 years.

His observations were inherited by an assistant, Johannes Kepler, when Tycho died in 1601.

Further development of the heliocentric theory

Kepler used decades of Tycho’s observations in his mathematical calculations, to determine the shape of the planetary orbits, and the speed of the planets as they went around the Sun.

This massive effort resulted in three major statements about the characteristics of planetary orbits:

Kepler’s three laws of planetary motion.

Kepler’s first law: The orbital paths of the planets are elliptical, with the Sun at one focus.

Kepler’s second law: An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time.

Kepler’s third law: The square of the planet’s orbital period is proportional to the cube of its semimajor axis.

Kepler’s laws of planetary motion

For an ellipse,

r1 + r2 = 2a

The eccentricity is defined as:

e = c/a

A circle results when e = 0

Some Properties of Planetary Orbits

Kepler’s first law: The orbital paths of the planets are elliptical, with the Sun at one focus.

Kepler’s second law: An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time.

Kepler’s third law: The square of the planet’s orbital period is proportional to the cube of its semimajor axis.

Kepler’s laws of planetary motion

Kepler’s Second Law: The two shaded areas have equal areas and are swept out in equal periods of time (10 days in this example).

So planets move faster when they are close to the Sun.

Kepler’s first law: The orbital paths of the planets are elliptical, with the Sun at one focus.

Kepler’s second law: An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time.

Kepler’s third law: The square of the planet’s orbital period is proportional to the cube of its semimajor axis.

Kepler’s laws of planetary motion

The Astronomical Unit is about 150,000,000 km

Kepler’s Third Law: P2 (in years) = a3 (in a.u.)Basically, it means that large orbits have long periods.

Isaac Newton developed a quantitative and explanatory theory of mechanics, explaining the motion of objects resulting from forces.

Newton’s Second Law: F = maThe acceleration of a mass is proportional

to the total force acting upon it, and inversely proportional to the mass of the object.

Newton’s Third Law: Action-reactionFor every force acting upon an object (action),

there is a force acting on another object (reaction) which has the same magnitude (size) but

points (acts) in the opposite direction.

Newton’s First Law: The law of inertia. An object will continue in it’s motion without change of velocity unless

it is acted on by a net external force.

Newton also developed the universal law of gravity.

Gravitational force varies with the distance between the objects.

It depends on the product of the two masses, i.e.,

m1 x m2

and on the inverse of the square of the distance between the masses

(assuming they are small

compared with the distance).

1/r2

The Sun’s gravity causes planets to move on a path called an orbit. These orbits obey Kepler’s Laws.

Newton’s Laws explain Kepler’s Laws

• Newton’s Laws account for all three of Kepler’s Laws. • The orbits of the planets are ellipses, but it is also possible to

have orbits which are parabolas or hyperbolas. (conic sections)• Edmond Halley predicted a comet would return in 1758 and every

76 years after that. (seen in 1910, 1986, and will return in 2061) Halley’s comet has an elliptical orbit extending out past Neptune.

• William Herschel discovered Uranus in 1781 by accident. • After 50 years it was seen to deviate from an elliptical orbit, and a

calculation led to the discovery of Neptune in 1846. • To be precise, elliptical orbits would only occur if there were only

the Sun and one planet. There are 8 planets and other objects which cause deviations from the perfect elliptical orbit.