ASTR 112 Lecture 3 - Dirk Grupe PDF

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Dirk Grupe...

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Astronomy 112-320 – Lecture 03 • Todays Lecture: How to read Graphs Physicists/Astronomers use graphs • Graph help us to understand our observations • They allow us to formulate rules, laws and theories • E.g. Hubbles law: distance vs velocity • This allows to predict when you measure a distance what the velocity will be and vice versa v = H0 x d v = velocity H0 = Hubble constant d = distance in Mpc Physicists/Astronomers use graphs • Example: you drive with your red Corvette with 30 m s-1 (equivalent to 108 km/h or 67 Mph) • Every second you measure the distance that you have passed. Physicists/Astronomers use graphs • You can have these measurements in a table • Do you really see what’s going on? • Graphs are a way for data visualization • Graphs show the relations between properties. Physicists/Astronomers use graphs What does the Graph tell us? • We see a relation between time and distance. • The slope in this graph defines the velocity = distance/time • So to get the slope we need to check how the distance changes over time What does the Graph tell us? • For a linear relation like ours for the slope is simple the velocity defined by: • Which for example in our case is x1 = 1 à y(x1) = 30 and x2 = 11 à y(x2) = 330 • So then the result is: • Which is nothing else then velocity slope= (y2 −y1) /(x2 −x1) slope=330−30 11−1 = 300m 10s =30m/s Graphs help us to understand the relations between properties • ‘real’ world example UV spectral slope vs. Optical to Xray spectral slope in AGN: • The bluer a source the weaker it becomes in X-rays Another example: Keplers Third Law • Consequences: –Distant planets take longer to orbit the Sun. –Distant planets travel at slower speeds. –This is what made Kepler name this law the Harmony of the Worlds ( ) ( ) 2 3 years AU PA = Problem: In Astronomy we deal with large numbers! • Astronomical object often display huge dynamical ranges • Example: Light curve of a Gamma-Ray Burst: Solution: log-log Plots • We have already seen that logarithms are extremely useful to deal with large numbers • The same is true for plots where we now plot one or two properties on a logarithmic scale Another example for graphs: The Hertzsprung – Russell –Diagram for stars...