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Annual parallax and distance

By changing the star distance and observation baseline, we distinguish between the total angular displacement and parallax angle that appear at both ends of the orbit.

    E14 · Annual parallax and distanceReady
    You can also experiment with the numbers and controls below the scene.

    Earth Science, Astronomy, Space / Principles and Exploration

    Annual parallax and distance — principles and investigation

    Nearby stars appear slightly different in position against the distant background as Earth orbits the Sun. Compare the parallax angle by adjusting the star's distance, Earth's orbital position, and orbital radius. By distinguishing between the definition of parallax and the total change in position over a half-year period, we can understand the meaning of the distance unit parsec.

    How does it work?

    If p=0.1″, then 10 pc≈32.6 light years. The more distant a star is, the smaller the parallax is.

    Key relationship

    d(pc)=1/p(″) · Standard total angular displacement=2p

    Try this investigation

    1. Press the Observation A and B buttons alternately or move the position slider. Observe changes in the positions of nearby stars relative to a fixed background star.
    2. Run and record 10 pcs of the same star from A and B, respectively, at both ends of the orbit. The difference between offsets with opposite signs is the total angular displacement.
    3. Record the conditions in which only the distance is increased to 20 pc and the condition in which only the orbital radius is increased to 2 AU and compare the total angular displacement.

    Interpreting your results

    What is the relationship between the standard parallax p and the total angular displacement between the two observation points?

    p is a semi-angle corresponding to the orbital radius of 1 AU. The total angular displacement at both ends is 2p and d(pc)=1/p(″).

    Assumptions and limitations

    It is a small angle approximation assuming a circular orbit and a star oriented perpendicular to the orbital plane. p is always the standard parallax angle for 1 AU. At radius b AU, total displacement = 2bp, distance = b/(displacement/2). Background stars are fixed and intrinsic motion, atmospheric shaking, and measurement errors are omitted. The screen angle is an enlarged picture, not the actual angle.