PHY 104PHY 104

Tuesday, January 29, 2008Tuesday, January 29, 2008

PLANETARY MOTION PLANETARY MOTION

and and

GRAVITYGRAVITY

Review QuestionsReview Questions

1.1. View of Earth from the Sea of TranquilityView of Earth from the Sea of Tranquility

2.2. Why is the moon phase locked to EarthWhy is the moon phase locked to Earth

3.3. What is meant by the Line of Nodes?What is meant by the Line of Nodes?

4.4. How do we find a star by its coordinates?How do we find a star by its coordinates?

5.5. What is the difference between Umbra What is the difference between Umbra and Penumbraand Penumbra

6.6. What is the meaning of “Sidereal”?What is the meaning of “Sidereal”?

1. View of Earth from the Sea of Tranquility1. View of Earth from the Sea of Tranquility

2. Why is the moon phase locked to Earth?2. Why is the moon phase locked to Earth?

Near Side Far SideNear Side Far Side

3. What is meant by the Line of Nodes?3. What is meant by the Line of Nodes?

Intersection of Plane of Moon’s Orbit around Earth and Plane of Earth’s Orbit around Sun

4. How do we find a star by its coordinates?4. How do we find a star by its coordinates?

Divide up into 8 groups (~9 people per Divide up into 8 groups (~9 people per group)group)

Have someone from your group come get Have someone from your group come get a celestial sphere.a celestial sphere.

Use the celestial sphere to find the Use the celestial sphere to find the following stars.following stars.

Find the Celestial Equator, Move around Find the Celestial Equator, Move around to the correct Right Ascension, then move to the correct Right Ascension, then move up or down to the correct Declinationup or down to the correct Declination

Stars to LocateStars to Locate Aldebaran: Alpha TauriAldebaran: Alpha Tauri

RA: 4h 35.920m Dec: 16° 30.550‘RA: 4h 35.920m Dec: 16° 30.550‘ Giedi: Alpha CapricorniGiedi: Alpha Capricorni

RA: 20h 18.055m Dec: −12° 32.683‘RA: 20h 18.055m Dec: −12° 32.683‘ Markab: Alpha PegasiMarkab: Alpha Pegasi

RA: 23h 4.762m Dec: 15° 12.317‘RA: 23h 4.762m Dec: 15° 12.317‘ Tarf: Beta CancriTarf: Beta Cancri

RA: 8h 16.515m Dec: 9° 11.133‘RA: 8h 16.515m Dec: 9° 11.133‘ Spica: Alpha VirginisSpica: Alpha Virginis

RA: 13h 25.193m Dec: −11° 9.683'RA: 13h 25.193m Dec: −11° 9.683'

5. What is the difference between Umbra 5. What is the difference between Umbra and Penumbraand Penumbra

6. What is the meaning of “Sidereal”?6. What is the meaning of “Sidereal”?

Sidereal = “with reference to the stars”Sidereal = “with reference to the stars” Sidereal Day: Time for earth to rotate on its axis Sidereal Day: Time for earth to rotate on its axis

with respect to the stars. 23 hr 56 min.with respect to the stars. 23 hr 56 min. Solar Day: Time for earth to rotate on its axis Solar Day: Time for earth to rotate on its axis

with respect to the sun. 24 hourswith respect to the sun. 24 hours Sidereal Month: Time for moon to orbit the earth Sidereal Month: Time for moon to orbit the earth

with respect to the stars. 27 dayswith respect to the stars. 27 days Lunar Month: Time for moon to orbit the earth Lunar Month: Time for moon to orbit the earth

with respect to the sun, complete phases. 29 with respect to the sun, complete phases. 29 daysdays

Observed motion of the HeavensObserved motion of the Heavens

Stars – orbit the earth dailyStars – orbit the earth dailySun – moves through stars once per yearSun – moves through stars once per yearMoon – moves through stars once per Moon – moves through stars once per

monthmonthPlanets – look like stars, but move relative Planets – look like stars, but move relative

to the other stars.to the other stars.

Early Concepts of Heavenly MotionEarly Concepts of Heavenly Motion

Earth at CenterEarth at Center Stars rotate daily to Stars rotate daily to

the westthe west Sun rotates with the Sun rotates with the

stars, but moves stars, but moves slowly to the east slowly to the east relative to the starsrelative to the stars

Moon rotates with Moon rotates with stars, but moves to stars, but moves to the east relative to the the east relative to the starsstars

Planetary MotionPlanetary Motion

Planets generally move in a path like the sun Planets generally move in a path like the sun around the ecliptic.around the ecliptic.

Planets exhibit “retrograde” Motion – reverse Planets exhibit “retrograde” Motion – reverse course temporarily.course temporarily.

Ptolemaic SystemPtolemaic System

Deferent: Circular Deferent: Circular path around the Earthpath around the Earth

Epicycle: Circular Epicycle: Circular path followed by path followed by planet around planet around Deferent.Deferent.

When planet is on When planet is on inner portion of inner portion of Epicycle it Epicycle it experiences experiences retrograde motion.retrograde motion.

Copernican SystemCopernican System

Sun CenteredSun Centered Planets move in Planets move in

circular orbits around circular orbits around the sunthe sun

Earth is a planetEarth is a planet Retrograde motion Retrograde motion

due to Earth passing due to Earth passing other planet on its other planet on its orbit.orbit.

Inner and Outer Planetary MotionInner and Outer Planetary Motion

Johannes KeplerJohannes Kepler

Used Tycho Brahe’s Used Tycho Brahe’s observationsobservations

Devised 3 Laws of Planetary Devised 3 Laws of Planetary MotionMotion Planets orbit in Ellipses with Planets orbit in Ellipses with

sun at one focussun at one focus Planets sweep out equal areas Planets sweep out equal areas

in equal times. Planets travel faster when closer to in equal times. Planets travel faster when closer to the sun.the sun.

(Sidereal Period in years)(Sidereal Period in years)22=(semimajor axis in AU)=(semimajor axis in AU)33

Galileo Galilei (1564-1642)Galileo Galilei (1564-1642)

Developed Developed Astronomical Astronomical TelescopeTelescope

Discoveries in 1610Discoveries in 1610 Moons of JupiterMoons of Jupiter Craters on MoonCraters on Moon Rings of SaturnRings of Saturn Phases of VenusPhases of Venus

Isaac Newton (1642-1727)Isaac Newton (1642-1727)

Laws of MotionLaws of MotionObject at rest stays at rest, object in motion Object at rest stays at rest, object in motion

moves in a straight line at constant speed moves in a straight line at constant speed unless acted upon by a forceunless acted upon by a force

Force = Mass times AccelerationForce = Mass times AccelerationFor every action (force) there is an equal and For every action (force) there is an equal and

opposite reaction.opposite reaction.Universal Law of GravitationUniversal Law of Gravitation

Same force that causes an apple to fall Same force that causes an apple to fall causes the planets to orbit the sun.causes the planets to orbit the sun.

SummarySummary