Measuring distances in astronomy is very challenging because we can not travel the distance we want to measure. On Earth we primarily measure distance either by laying down a ruler between two points or by traveling between two points and measuring the time it takes. If we know our velocity then we can calculate the distance by distance = velocity x time. We don’t even have to travel, instead we can send electromagnetic radiation which we know travels at the speed of light or 300,000 km/s and just measure the time it takes the radiation to go the distance (and usually back).

In astronomy two other basic approaches are used to determine distance. The first is triangulation or parallax in astronomy speak. In this method one measures the angle of an object from one location and then moves to a different location and measures the angle again.  This creates a triangle and allows one to calculate the distance of the object.  Since the Earth moves 2AU every 6 months this is the natural way to get two measurements from two different locations. However, the farther away the object the smaller the change in angle which limits this approach. 

The second method used in astronomy to measure distance is to measure the apparent brightness of an object and compare it to the objects known luminosity called absolute magnitude in astronomy speak. Since we know brightness decreases as distance squared this allows us to measure the distance. The only problem with this approach is having a way to determine the luminosity of objects. Luckily there are pulsating variables, the HR diagram and supernova which all give us ways to estimate the luminosity of things without knowing distances.  If the apparent magnitude, m, and absolute magnitude, M, of an object are known then the logarithm of the distance, d, can be determined from 

 m – M = -5 + 5 log₁₀ d

Laboratory Tools

We will make use of four simulators in this lab all produced at the University of Nebraska-Lincoln. The four simulators are:

• The Parallax Explorer –  The left panel shows the Map, you can move the observer (the red X) along the road. The top right panel shows the Observer’s View, which depends on the observers position as determined by the red X.  The bottom right panel has the Controls.  Here you can take a measurement, clear your measurement set the error and show a ruler. You can only make changes for Preset A.  For Presets B and C you can not change the error or see the boat on the Map.   
• Spectroscopic Parallax Simulator –  The top left panel shows the Absorption Line Intensities  for different temperature stars. The red line can be dragged change a stars temperature and spectral class. The panel below this, Simulated Spectrum, shows how the spectrum of that star would look.  The bottom panel on the left, Distance Modulus Calculation, determines the distance to the star based its apparent magnitude and location in the HR diagram.   The distance is the number in blue.  The top right panel shows the HR Diagram. while the lower right panel shows the Star’s Attributes. Here you can change its apparent brightness and luminosity class.
• HR Diagram Star Cluster Fitting Explorer – The left panel shows the HR Diagram. The y-axis on the left side (red) shows the absolute magnitude M; the right side (blue) shows the apparent magnitude, m.   Click-dragging on the plot will allow you to move the stars up or down.  The upper right panel, Cluster Selection, allows you to choose the star cluster plotted in the HR Diagram.  The middle right panel, Diagram Options, just allows you to add a horizontal bar which is useful for reading off what the apparent magnitude is that corresponds to an absolute magnitude. The bottom right panel, Distance Modulus Calculator, will calculate the distance for a given apparent and absolute magnitudes.
• Supernova Light Curve Fitting Explorer – The top panel Light Curve Plot shows a model supernova light curve in red and allows you to select actual supernova data from a dropdown menu. You can also click on a horizontal bar to more clearly see how the apparent and absolute magnitudes compare. The bottom panel is a Distance Module Calculator, enter an apparent magnitude, m, and an absolute magnitude, M, and it will display the distance after the log.

Assignment

Starting with the parallax explorer first move the observer around and notice how the Observer’s view changes.  Then take two measurements far apart, show the ruler and measure the distance to where the lines cross. Now clear the measurements and set the error to 3.0. The boat is in the diamond region outlined by the two cones. Take a third measurement in between your first two and measure the distance range within all three cones.  Now switch to Preset B, take to measurements and determine the range of distances. Note there is no boat shown in this case.  Finally use Preset C. Take two measurements, you are only able to move the observer to 2 preset points. What is the distance range in this case? Include a table like the one below in your report

Preset	Number	Error	Distance
A	2	0.0
A	2	3.0
A	3	3.0
B	2	3.0
C	2	5.0

Now turn to the Spectroscopic Parallax Explorer.  The default should start with a star that  has a temperature of 5840K and an apparent magnitude of 1.0.  The luminosity class should be V. Record the distance.  Make changes to those quantities as shown in the table below and record the distances.

Temperature	Apparent Magnitude	Luminosity Class	Distance
5840	1	V
5840	6	V
5840	11	V
5840	1	II
3630	1	V
3630	1	III
35500	1	V
35500	1	I

Now turn to the HR Diagram Star Fitting Explorer. Here we will try to fit various star clusters to the main sequence. Some are much easier to fit than others you may want to start from the bottom of the list and work your way up. From the fit we can read off an apparent and absolute magnitude, you can show the horizontal bar to get two values. Then enter them in the Distance Module Calculator panel to get the distance. Record your values in a table like this

Cluster	Apparent Magnitude (m)	Absolute Magnitude (M)	Distance
Pleiades
Hyades
NGC 188
+ more

Finally let’s take a look at the Supernova Light Curve Fitting Explorer.  Here we can try and match data from supernova to a typical light curve, starting from the last choice may be easier. Note you can move the points in both the x and y directions. Use the horizontal bar to read off the apparent and absolute magnitudes and then calculate the distance. Record your values in a table like this.

Supernova	Apparent Magnitude (m)	Absolute Magnitude (M)	Distance
1999ee
1990N
+ more

Questions

1. At what temperatures does the luminosity class have a strong effect on the distance determined and when does it have a small effect?
2. Which method finds the smallest distances? Which method finds the largest distances?
3. Which method do you think is the most precise?