1. Physics 55 Friday, September 16, 2005 1.Celestial navigation, phases of planets and moons, retrograde motion 2.Will then turn to Kepler’s empirical laws of motion. 3.Newton’s laws of motion, connections to conservation laws. 4.The universal law of gravitation. 5.Application of gravity to the discovery of dark matter. 6.Tides, tidal forces, and the Roche limit.

2. Announcements 1.Professor Ronen Plesser will teach in my place this Friday. It will be a regular lecture, I am postponing his guest lecture on string theory until later in the course. 2.New assignment available on Wednesday. 3.Important dates: –Quiz 3 on Friday, Sept 30, –Midterm exam on Friday, October 7.Note: Fall break begins the evening of Oct. 7. –Final exam on Thursday, Dec. 15, 2-5 pm.

3. Path of Sun in Local Sky If dec of object > 0, will rise north of east, set north of west. If dec of object = 0, will rise exactly in east, set exactly in west. If dec of object < 0, will rise south of east, set south of west. Picture on left helps to explain why summer months are warmer than winter months: Sun stays longer in the sky.

4. Fall Equinox Comments: 1.This Wed, September 21, Sun will have RA ~12 h, dec ~0 o. Sun’s dec will remain negative until about March 21. 2.Since Sun lies on celestial equator this day, path of Sun during day traces out the celestial equator in your local. 3.Until spring equinox, Sun will now rise south of due east, set south of due west. How much to the south is hard to calculate, beyond the level of this course. 4.Sun will start spending shorter amount of time in sky, hence shorter days, cooler weather. 5.Sidereal time about equal to solar time on the day of the fall equinox since spring equinox will be on your meridian at about midnight, which is place of 0 RA.

5. PRS Question The city of Mumbai (formerly Bombay) in India has latitude 19 o N. On how many days of the year is the Sun at zenith at midday in Mumbai? 1.Zero. 2.One. 3.Two. 4.More than two. 5.I don’t know how to solve this.

6. Local Sky at Equator No circumpolar stars All stars eventually visible

7. Local Sky Near Durham

8. Celestial Navigation at Night: Latitude from Star’s Meridian Crossing Vega has dec=38 o 44’. If you measure altitude at meridian crossing of 78 o 44’S, latitude = 50 o N. What does one 1 o error mean in terms of distance?

9. Celestial Navigation During Day: Latitude from Sun’s Meridian Crossing We measure altitude of Sun’s meridian crossing to be 70 o N on spring equinox March 21 when Sun’s dec is 0 o. So latitude is 20 o S and we are in the southern hemisphere. Generally, you need a table or computer to know Sun’s dec on any given day.

10. Longitude From Universal Time Clock Need to compare location of star in sky now with time when star appears in same location in sky at some other known longitude such as Greenwich, England. Difference in time in hours times 360 o /24 hr = 15 o /hr gives you your longitude in degrees from Greenwich. Use Universal Time (UT) clock which records mean solar time with noon coinciding with noon in Greenwich, England. UT also known as “Zulu time” and “universal coordinated time”. Recommended book: “Longitude” by Dava Sobel.

11. Celestial Navigation Problem During a boat trip, you make the following observations: 1.It is the day of the summer solstice, June 21. 2.The Sun is on your meridian at altitude 66½ o in the North 3.Your universal time (UT) clock reads 06:00. What is your longitude and latitude? About where are you?

12. Question About Seasons Most important point: most planets have nearly circular orbits (why?!) so seasons are not due to variation in distance of Earth to Sun but because of tilt of planet’s axis. See 20-min online video “A Private Universe” at http://www.learner.org/resources/series28.html Think: How do lengths of day and night, and lengths of seasons, and properties of celestial sphere depend on the tilt of the Earth’s axis? If tilt were zero degrees, would there still be seasons? If tilt were 90 degrees, describe how days, seasons, celestial sphere would differ from present day situation? What about a tilt of 113 degrees from normal to the ecliptic?

13. Tilt of Axis Causes Earth’s Seasons SkyGazer: select menu Explore, then submenu Seasons of the Earth. Do Astronomy Place tutorial on Seasons.

14. Moons, Planets Always Half Illuminated

15. Phases of Moon and Planets

16. PRS Question Which planet(s) undergoes full (fully illuminated) and new (dark) phases like our Moon? 1.Venus 2.Mars 3.Venus and Mars 4.Neither

17. Retrograde Motion of Planets Think: If Earth somehow orbited more slowly than Mars around Sun, would retrograde motion still occur? Would an astronaut on Mars see Earth undergoing retrograde motion against the background of stars?