“Cloudy Night” Lab: Heliocentric Parallax
Name: _________________________________
Section: _________________________________
Lab Partner(s): ______________________________________
One way to determine the distances to the stars is with the heliocentric parallax
method. As the Earth orbits the sun, our position in space changes by 2
astronomical units (AU). If we observe a nearby star 6 months apart, the star's
angular position will appear to shift relative to more distant background stars. If
we know how large an AU is, we can determine the actual distance to the shifting
stars. This lab will demonstrate this technique.
To calculate the distance, we need to know the angular shift. However, in order
for the equation to be as simple as possible, we define the parallactic angle (p) to
be one-half of the angle shown above. The equation used to calculate
distances is:
1
d = ----p
The d must be in units of parsecs; each parsec is equal to 206265 AU. The p must be in
arcseconds. There are 60 arcminutes per degree, and 60 arcseconds per arcminute.
Preliminary Questions
1. What is the distance in parsecs of a star with a parallax of one arcsecond? __________
2. What is the distance in AU of a star with a parallax of one arcsecond? __________
3. A larger parallax indicates a larger / smaller distance. (circle one)
Instructions
The computer can simulate a number of different fields (areas on the sky). For this lab, it
will randomly select three fields for your use. For each field, you can blink back and forth
between 2 virtual photo taken six months apart. As you blink between the photos, you’ll
notice several stars shift. These are the stars for which you will be measuring the parallax
and calculating the distances. We’ll be using a grid overlaid on the photos to measure the
shift, and the grid is not measured in degrees. Each grid unit is one tenth of an arcsecond;
this information will be used to convert the measured values into arcseconds.
1. Write down the number of the field.
2. Blink to identify the shifting stars.
3. Turn on the overlay grid, and measure the positions of the three stars on one photo.
 The X direction is the horizontal direction; the Y is vertical
 The 0,0 point is in the upper left corner
 X increases to the right and Y increases to the bottom
 Estimate the position to the nearest 0.1 grid unit
4. Record these in the X1 and Y1 columns
5. Blink to the other photo, and record the positions in the X2 and Y2 columns
6. Repeat for two more fields
Field Number
Star
X1
(grid units)
Y1
(grid units)
X2
(grid units)
Y2
(grid units)
A
B
C
A
B
C
A
B
C
Now, we need to change you measurements into a parallactic angle, and then we’ll
calculate some distances! Please show all work.
1. Calculate the amount that each star has moved horizontally (in grid units) and fill in
the X2-X1 column
2. Calculate the amount that each star has moved vertically (in grid units) and fill in the
Y2-Y1 column
3. Calculate the total distance (S) the star has moved (in grid units) by using the
Pythagorean theorem
4. To convert this shift into the parallax, convert S into arcseconds. Then divide by two.
5. Use the information provided in the introduction to calculate the distance to each star.
Field Number Star
X2-X1
Y2-Y1
S
Parallax
Distance
(grid units) (grid units) (grid units) (arcseconds) (parsecs)
A
B
C
A
B
C
A
B
C
The following space is provided for you to do your work in:
Questions
1. The smallest shift you can reliably measure on the screen is about 0.2 grid units. This
corresponds to the precision of positions measured with the best Earth-based optical
telescopes. If you cannot measure an angle smaller than this, what is the largest distance
at which a star can be and still have its parallax measured?
2. If Earth orbited the Sun at the distance of Jupiter, the diameter of its orbit would be
about five times greater than its actual value. Would this larger orbit affect the size of the
parallactic angle measured for a given star? How?
3. If Earth were orbiting at Jupiter’s distance, we would be able to measure parallaxes for
more stars / fewer stars / the same number of stars. (circle one)
Explain why you chose that answer. If you chose more or fewer stars, explain how many
more or fewer.
Reference:
http://www.missioncollege.org/depts/astro/Astrolab/parallax.pdf