Astronomy Rough Notes - Scaling

BRING: Handouts Calculators Globe, tennis ball, stand for ball Cardboard suns, BBs Meter sticks

HANDOUTS: Scaling Example (included in notes below) Scaling Exercise (Answers to Scaling Exercise – now posted here) Scaling Practice (Answers to Scaling Practice - now posted

Recall units and SI prefixes from last time.

HOW CAN I IMAGINE THE SIZE OF THE UNIVERSE? I. Take virtual trips. II. Use large units like a light year. III. Use big numbers like 2.2 X 1018 m. IV. Use scale models.

I. VIRTUAL TRIPS 1. Powers of Ten video from last time (on reserve in MCTC library) 2. On the web http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html 3. Cosmic Voyage video (on reserve in MCTC library) - excellent

II. USE LARGE UNITS Speed of light = 186 000 mi/s = 300 000 km/s = 7 ½ times around Earth in one second!! =FAST

Light-second Distance light travels in one second (Speed of light = 186 000 mi/s) So 1 light-second = 186 000 mi Example – Earth to Moon ~ 1.3 light-seconds Traveling at the speed of light would take you 1.3 seconds to reach the Moon (~10 hours by rocket at 25 000 mi/h)

Light-year (symbol ly) Distance light travels in one year

Example – Sun to Proxima Centauri ~ 4.2 ly Light from the Sun takes ~4.2 years to reach the NEXT nearest star III. Large numbers - SCIENTIFIC NOTATION (Expressing big numbers) 102 means 10 X 10 = 100 And 1 1 1 104     0.0001 104 10101010 10000

108 is 100 000 000 (Use spaces not commas)

10-7 is 0.000 000 01 (Use a 0 in front of the decimal)

6.3 X 102 means 6.3 X 100 which is 630. For a short cut, start with 6.3 and move the decimal two places right giving 630.

Convert 2.81 X 104 to a standard number. Start with 2.81 Move the decimal four places right. 28 100.

4.903 X 10-3 means 4.903 X 0.001 which is 0.004903. For a short cut, start with 4.903 and move the decimal three places left, ie, 0.004903

Convert 8.2 X 10-5 to a standard number. Start with 8.2 Move the decimal five places to the left. 0.000 082

Practice problems for powers of ten and scientific notation:

Check the web for more practice. Here are two of many sites: http://janus.astro.umd.edu/astro/scinote/ or at http://chemistry2.csudh.edu/lecture_help.scinot.html

CALCULATOR using EXP or EE key Your calculator may display differently. Ex: 5.28 X 106 Enter on calculator: 5.28 EXP (or EE) 6 Displays 5.28 06 (You must remember that the 06 is the power of ten) Now press =. Displays 5280000. Ex: 2.3 X 1015 Enter on calculator: 2.3 EXP (or EE) 15 Various displays depending on calculator…. Now press =. Might display 2.3 15 (Remember that this is some calculators way of saying 2.3 X 1015 ) Ex: How many miles are in a light year? Light travels at 186 000 mi/s Start multiplying…

CONVERTING BETWEEN m, cm, mm Converting cm to mm (1 cm = 10 mm) Note: when converting from larger to smaller unit, the number of them gets bigger! With a smaller unit, you need more of them. Convert 4.3 cm to mm Larger unit to smaller unit Need larger number. (10 times more) 4.3 cm is 43 mm More examples in class

IV. SCALE MODELS Scaling example 1 – Room Given: Room height is 3.2 m and you want to scale it down by a factor of 15 Procedure: Divide the true height by the scale factor (15 times smaller) 3.2 m / 15 = 0.21 m Build model: You would now build your scale model room 0.21 m or 21 cm high

Scaling example 2 – Earth-Moon system

Use a SCALE FACTOR of 4 X 107 on the celestial objects listed below. Celestial Object Actual Size or Scaled Size or If Needed, Scaled Common Object Distance Distance Size or Distance (in m) (in km, cm, mm) Moon diameter 3.5 X 106m 0.088 m 8.8 cm Tennis ball Earth diameter 1.3 X 107m 0.33 m Earth globe Earth to moon 3.8 X 108m 9.5 m Length of class room Mpls To Stillwater 48 000 m 0.0012 m 1.2 mm Thickness of pen tip Thickness of book 0.02 m 5 X 10-10 m Too small (careful)

GROUP EXERCISE Scaling Exercise (see above link under handouts)

WIND UP Larger scale factors. Which focus questions.

HOMEWORK Reread Ch 1. Reread Appendix A on SI system and Scientific Notation. Work the scientific notation exercises (see above link) and check your answers. Work the Scaling Practice handout above. (Check on-line for answers in a few days.) Read Ch 2. Skim Ch 3 and 4. Write out your answers to the appropriate focus questions (the ones we have covered so far).

Revised 18 Jan 2007