# The Parallax Activity: Measuring the Distances to Nearby Stars

David V. Black
Walden School of Liberal Arts
Provo, Utah

Determining the position of a star or other object in three-dimensional space is an important concept in astronomy. Finding stellar longitude (called right ascension) and latitude (declination) is easy enough, but it is much harder to find the radial distance to those objects. This lesson teaches how the distances to nearby stars are measured using the parallax effect: as the Earth orbits our sun, the positions of the nearest stars seem to wiggle back and forth compared to more distant stars. Knowing this parallax angle and the distance from the Earth to the sun, we can use the tangent function to measure the distance to a star. In this lesson, students will learn how parallax is measured and will practice using trigonometry to measure the height of local landmarks. They will then conduct an activity measuring the distances to “planets” and their parallax angles to simulated stars, then calculate the stars’ distances. Each team of students will need a simple quadrant built from a one-meter ruler, a protractor, a piece of string, and a weight such as a rubber stopper. They will also need calculators or trig tables to do the final calculations. This lesson will take approximately 90 minutes to complete.

David Black has taught computer technology and science classes for over twenty years in California and Utah. His students collaborate with scientists and engineers to create meaningful educational content, including 3D animations of lunar features for the NASA Lunar Science Institute and Martian dust storms for the Mars Exploration Student Data Team program; audio podcasts on astrobiology for the “365 Days of Astronomy” website; and videos for the SOFIA AAA program. Their blogsite, http://spacedoutclass.com, shares projects and lesson plans in astronomy and earth science for classes around the world.

David Black’s Blog: The Spaced Out Classroom:
http://spacedoutclass.com/2012/12/07/the-parallax-method/
Location for the full lesson plan and project description, as well as how the Media Design and Astronomy students at Walden School of Liberal Arts helped to film the project.

NASA’s Imagine the Universe “Ask an Astronomer”:
A good overview of methods for finding the distances to stars.

Windows to the Universe:
http://www.windows2universe.org/kids_space/star_dist.html
Brief description of the parallax and Cepheid variable methods.

Michael Richmond’s Physics 301 Lecture Notes:
http://spiff.rit.edu/classes/phys301/lectures/parallax/parallax.html
A more detailed description of parallax and an overview of the upcoming Gaia satellite, a successor to Hipparcos, which is scheduled to launch in 2013.

Prof. Richard Pogge’s Astronomy 162 Lecture Notes:
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit1/distances.html
Good overview of parallax and how to do calculations.

Gaia Homepage:
http://www.esa.int/Our_Activities/Space_Science/Gaia_overview
Follow up to the ESA Hipparcos satellite. It will launch this year and will measure the 3D position of one billion stars. 200 million will have their parallax measured to an accuracy 10 times higher than Hipparcos, or ten microarcseconds.

Universe at a Glance:
http://universeataglance.blogspot.com/2011/04/measuring-stellar-distances-for-stars.html
Excellent description of the methods used to find the distances to stars, including those beyond 1000 parsecs, including a bibliography for further information.

ABCs of Distance:
http://www.astro.ucla.edu/~wright/distance.htm
A good discussion of all of the techniques for finding the distances to stars and galaxies.

Space Telescope Science Institute:
PDF file created by Gail Schaefer at the Space Telescope Science Institute with images and an overview of the distance ladder and how the distances to stars and galaxies are measured.

Kodak’s Website on the Endurance Expedition:
http://www.kodak.com/US/en/corp/features/endurance/
Animated and interactive website on Frank Hurley’s amazing photographs of the expedition.

NOVA Online: Shackleton’s Voyage of Endurance:
http://www.pbs.org/wgbh/nova/shackleton/
NOVA retraces the Endurance expedition, including the final land crossing of South Georgia Island.

“Surveying – A Life Without Limits”: