Measurements%20

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 1015 (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 1016 m (6 trillion miles)
• Speed of light is 3 ? 108 m/sec or 186,000 mi/sec
• A unit of distance, not time!
• Observable universe is 109 (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
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 Hubbles 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