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 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 10 (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 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

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 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 * * * * low precision, high accuracy * * * * low precision, low accuracy accepted value

So, do our results agree? Results agree, if they are within the error margins of each other Examples: | O | values very different, but errors large: agreement! | O | values closer, but errors smaller: no agreement!