Transcript Integrative Studies 410 Our Place in the Universe

Measurements & Units
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
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 ~1010 (10 billion) ly in diameter
• A parsec (pc) is a slightly larger unit of length
– 1 pc = 3.3 ly
The Universe is structured on
different length scales
Stars
nebulae
molecular clouds
star clusters
THE UNIVERSE
clusters
and
superclusters
galaxies
like the
Milky Way
quasars
Sun
planets
terrestrial
jovian
Solar System
black holes
pulsars
moons
comets
meteors
asteroids
dust
voids
Big  ----------------------------- small
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
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
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
Performing Experiments
• Experiments must be repeatable – requires careful
control over variables
• Possible outcomes of an experiment:
– The experiment may support the theory
• We then continue to make predictions and test them
– The experiment may falsify the theory
• We need a new theory that describes both the original data and
the results of the new experiment
• Since we cannot do every possible experiment, a
theory can never be proven true; it can only be
proven false
Making Measurements
• Errors
– Random
– Systematic
• With every measurement, it is essential to provide an
estimate of the uncertainty – the likely range of errors
• Example:
– Using a ruler marked in mm, we round to the nearest marking –
at most off by half a division, or 0.5 mm
– Cite a measurement of 15 mm as 15  0.5 mm to indicate that
the real value of the length is likely to be anywhere between
14.5 mm and 15.5 mm
– If a theory predicts a value of 15. 2 mm, then a reading of
15  0.5 mm is in agreement with the theory but a reading of
15  0.1 mm is probably not
Activity – Analyzing the Results
• Why aren’t all the results the same?
• How do we compare results?
• What kind of errors occurred?
• Is our error small or big?
• Is our result precise, accurate or what?
• So, do our results agree?
Why aren’t all the results the same?
• Useful questions to ask, if results don’t agree:
– Which object did you measure?
– What units where you using?
– What is your estimated error?
How do we compare results?
• Don’t compare apples with oranges!
• Need to use the same units
• 1 inch = 2.54 cm
• To get inches from centimeters, divide by 2.54
• To get centimeters from inches, multiply by 2.54
What kind of errors occurred?
• There are systematic and random errors
• To beat down random errors, measure the same
thing many times, and the errors will even out, i.e.
the overall error will be smaller
• The systematic error can be reduced by doing a
better experiment, or understanding your
instruments better (miscalibrations etc.)
• Human error is not an acceptable error source in
science! It just means you are a bad experimenter.
Is our error small or big?
• It depends!
• If you have a small error and the measured length
is also small, you might have a huge error!
• Use percentages:
– Percent error = (estimated error)/(result) x 100%
– Example: 51.3 cm ± 0.2 cm gives
– Percent error = (0.2 cm)/(51.3cm) x 100 % = 0.4 %
(This is a pretty small error)
Is our result precise or accurate or what?
•
•
•
•
Two different concepts: precision and accuracy!
High precision means small error
High accuracy means close to an accepted value
Examples:
****
high precision, high accuracy
****
high precision, low accuracy
*
* *
*
*
*
*
accepted value
*
low precision, high accuracy
low precision, low accuracy
So, do our results agree?
• Results agree, if they are within the error
margins of each other
• Examples:
|
O
| |
O
|
values very different, but errors large: agreement!
|
O | |
O
|
values closer, but errors smaller: no agreement!