MIT Massachusetts Institute of Technology

Measuring Distances in the Milky Way

Roger Hajjar
Department of Physics & Astronomy
Notre Dame University
Louaize, Lebanon


The main aim of this lesson is to show students that distances may be determined without a meter stick—a concept fundamental to such measurements in astronomy. It introduces students to the main concepts behind the first rung of what astronomers call the distance ladder. The four main learning objectives are the following: 1) Explore, in practice, a means of measuring distances without what we most often consider the “direct” means: a meter stick; 2) Understand the limits of a method through the exploration of uncertainties; 3) Understand in the particular method used, the relationship between baseline and the accuracy of the measurement; and 4) Understand the astronomical applications and implications of the method and its limits. Students should be able to use trigonometry and know the relation between trigonometric functions and the triangle. A knowledge of derivatives is also needed to obtain the expression for the uncertainty on the distance measured. Students will need cardboard cut into disks. The number of disks is essentially equal to half the students in the class. Two straight drink straws and one pin per disk. Students will also need a protractor. The lesson should not take more than 50 minutes to complete if the students have the mathematical ability mentioned above. This lesson is complimentary to the BLOSSOMS lesson, "The Parallax Activity." The two lessons could be used sequentially  -  this one being more advanced  -  or they could be used separately.

After completing his graduate studies in Montreal, Canada, Roger Hajjar returned to Lebanon, his country of birth, with the dream of reviving astronomy in the land of his forefathers. He is now one of 4 astronomers at NDU, and 9 in Lebanon. He launched the NDU Astronomy Club with students in 1998 and is a founding member of the Lebanese Astronomy Group.

This is a Wikipedia discussion of the Cosmic Distance Ladder, the first step of which is examined in this BLOSSOMS lesson.

This is a Wikipedia entry on the Parallax, a displacement or difference in the apparent position of an object viewed along two different lines of sight

This is a discussion on the European Space agency website about Gaia, the ambitious mission to chart a three-dimensional map of our Galaxy and the Milky Way.

This is an educational page on the website of the European Space Agency with a wealth of educational resources about space mission, Gaia.

This is a Wikipedia entry on the satellite Hipparcos, the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial objects on the sky

This is an educational page on the website of the European Space Agency about the space mission, Hipparcos.


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This Lesson is in the following clusters: Astronomy, Geometry, Pythagorean Theorem