PHY 104 Tuesday, January 29, 2008 PLANETARY MOTION andGRAVITY

Review Questions 1. View of Earth from the Sea of Tranquility 2. Why is the moon phase locked to Earth 3. What is meant by the Line of Nodes? 4. How do we find a star by its coordinates? 5. What is the difference between Umbra and Penumbra 6. What is the meaning of “Sidereal”?

1. View of Earth from the Sea of Tranquility

2. Why is the moon phase locked to Earth?

Near Side Far Side

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? Divide up into 8 groups (~9 people per group) Divide up into 8 groups (~9 people per group) Have someone from your group come get a celestial sphere. Have someone from your group come get a celestial sphere. Use the celestial sphere to find the following stars. Use the celestial sphere to find the following stars. Find the Celestial Equator, Move around to the correct Right Ascension, then move up or down to the correct Declination Find the Celestial Equator, Move around to the correct Right Ascension, then move up or down to the correct Declination

Stars to Locate Aldebaran: Alpha Tauri Aldebaran: Alpha Tauri RA: 4h m Dec: 16° ‘ RA: 4h m Dec: 16° ‘ Giedi: Alpha Capricorni Giedi: Alpha Capricorni RA: 20h m Dec: −12° ‘ Markab: Alpha Pegasi Markab: Alpha Pegasi RA: 23h 4.762m Dec: 15° ‘ RA: 23h 4.762m Dec: 15° ‘ Tarf: Beta Cancri Tarf: Beta Cancri RA: 8h m Dec: 9° ‘ Spica: Alpha Virginis Spica: Alpha Virginis RA: 13h m Dec: −11° 9.683'

5. What is the difference between Umbra and Penumbra

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 with respect to the stars. 23 hr 56 min. Sidereal Day: Time for earth to rotate on its axis with respect to the stars. 23 hr 56 min. Solar Day: Time for earth to rotate on its axis with respect to the sun. 24 hours Solar Day: Time for earth to rotate on its axis with respect to the sun. 24 hours Sidereal Month: Time for moon to orbit the earth with respect to the stars. 27 days Sidereal Month: Time for moon to orbit the earth with respect to the stars. 27 days Lunar Month: Time for moon to orbit the earth with respect to the sun, complete phases. 29 days Lunar Month: Time for moon to orbit the earth with respect to the sun, complete phases. 29 days

Observed motion of the Heavens Stars – orbit the earth daily Stars – orbit the earth daily Sun – moves through stars once per year Sun – moves through stars once per year Moon – moves through stars once per month Moon – moves through stars once per month Planets – look like stars, but move relative to the other stars. Planets – look like stars, but move relative to the other stars.

Early Concepts of Heavenly Motion Earth at Center Earth at Center Stars rotate daily to the west Stars rotate daily to the west Sun rotates with the stars, but moves slowly to the east relative to the stars Sun rotates with the stars, but moves slowly to the east relative to the stars Moon rotates with stars, but moves to the east relative to the stars Moon rotates with stars, but moves to the east relative to the stars

Planetary Motion Planets generally move in a path like the sun around the ecliptic. Planets generally move in a path like the sun around the ecliptic. Planets exhibit “retrograde” Motion – reverse course temporarily. Planets exhibit “retrograde” Motion – reverse course temporarily.

Ptolemaic System Deferent: Circular path around the Earth Deferent: Circular path around the Earth Epicycle: Circular path followed by planet around Deferent. Epicycle: Circular path followed by planet around Deferent. When planet is on inner portion of Epicycle it experiences retrograde motion. When planet is on inner portion of Epicycle it experiences retrograde motion.

Copernican System Sun Centered Sun Centered Planets move in circular orbits around the sun Planets move in circular orbits around the sun Earth is a planet Earth is a planet Retrograde motion due to Earth passing other planet on its orbit. Retrograde motion due to Earth passing other planet on its orbit.

Inner and Outer Planetary Motion

Johannes Kepler Used Tycho Brahe’s observations Used Tycho Brahe’s observations Devised 3 Laws of Planetary Motion Devised 3 Laws of Planetary Motion Planets orbit in Ellipses with sun at one focus Planets orbit in Ellipses with sun at one focus Planets sweep out equal areas in equal times. Planets travel faster when closer to the sun. Planets sweep out equal areas in equal times. Planets travel faster when closer to the sun. (Sidereal Period in years) 2 =(semimajor axis in AU) 3 (Sidereal Period in years) 2 =(semimajor axis in AU) 3

Galileo Galilei ( ) Developed Astronomical Telescope Developed Astronomical Telescope Discoveries in 1610 Discoveries in 1610 Moons of Jupiter Moons of Jupiter Craters on Moon Craters on Moon Rings of Saturn Rings of Saturn Phases of Venus Phases of Venus

Isaac Newton ( ) Laws of Motion Laws of Motion Object at rest stays at rest, object in motion moves in a straight line at constant speed unless acted upon by a force Object at rest stays at rest, object in motion moves in a straight line at constant speed unless acted upon by a force Force = Mass times Acceleration Force = Mass times Acceleration For every action (force) there is an equal and opposite reaction. For every action (force) there is an equal and opposite reaction. Universal Law of Gravitation Universal Law of Gravitation Same force that causes an apple to fall causes the planets to orbit the sun. Same force that causes an apple to fall causes the planets to orbit the sun.

Summary