1. Measurements & Units

2. Significant Figures There is an uncertainty with every measurement  reflect this in the number of digits used in quoted results Do not count trailing or leading zeros Examples: –12.3 (3 sig figs) –1.23 (3), 0.45 (2), 0.00234 (3), 1200 (2) –4.56 10 15 (3)

3. Estimates Scientists often use a “back of the envelope” calculation to get a sense for how big a number should be Recipe: round every number involved up to one sig fig and keep the exponent

4. Think inside the box! In essence, mathematics is a set of line by line instructions Use them diligently, and a lot of problems become mere exercises, i.e. tedious but straightforward

5. Fermi Questions Attributed to Enrico Fermi Try to get the order of magnitude of a quantity with very little data available Making a crude estimate is better than not doing anything

6. Example: Parcel of the Earth The land area of the earth is divided up into equal parcels for each person on earth. How much would you get? –Need area of earth –Area of land –# People on earth

7. Astronomical Measurements – the Metric System Units of length: –meter (m) 1 yd. 4 in. –kilometer (km) = 1000 m or about 0.6 mi. Units of mass: –kilogram (kg). 1 kg weighs about 2.2 lbs. (lb.=unit of weight) Units of time: –second, same as in the English system

8. Light Years and Parsecs A light year (ly) is the distance light travels in a year –About 10 16 m (~6 trillion miles) Speed of light is 3  10 8 m/sec or 186,000 mi/sec –A unit of distance, not time! –Observable universe is ~10 9 (10 billion) ly in diameter A parsec (pc) is a slightly larger unit of length –1 pc = 3.3 ly

9. The Universe is structured on different length scales THE UNIVERSE clusters and superclusters voids galaxies like the Milky Way quasars Stars nebulae molecular clouds star clusters Solar System black holes pulsars Sun planets moons comets meteors asteroids dust terrestrial jovian Big  -----------------------------  small

10. Different lengths scales  Different length units Human scale: meters (yards) –Human height: 1.8 m Geographical scale: kilometers (miles) –Distance to Cincinnati: 100 mi Solar system scale: Astronomical Unit –Distance Earth-Sun: 1 A.U. Intragalactic scale: lightyears (parsecs) –Next star: 4 lightyears Intergalactic scale: millions of lightyears (Megaparsecs) –Andromeda galaxy: 2.2 million lightyears = 0.67 Mpc Cosmological Scale: billions of ly (Gigaparsecs) – Edge of observable universe: about 15 billion ly

11. Different lengths scales  Different length measurements Human scale: yardstick Geographical scale: triangulation Solar system scale: Radar ranging Intragalactic scale: –Close stars: stellar parallax –Far: spectroscopic parallax Intergalactic scale: –Close: Variable stars –Far: Tully-Fisher relation Cosmological Scale: Hubble’s Law

12. Units Dimensions and units are different! To convert from one unit to another use conversion factors –2 miles = (2 mi)*(1) = (2 mi)(1600 m/1 mi) = 3200 m