Lab6-Distance-Ladder

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Louisiana State University *

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1109

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Astronomy

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Apr 3, 2024

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Name: _________________________ Lab 6 – The Distance Ladder Introduction Distance is one of the most difficult things to measure in astronomy. You cannot see distance. You never know if you are looking at a low luminosity star nearby or a high luminosity star far away. In both cases, the star can appear to be equally bright. To deal with this, astronomers have developed a hierarchy of techniques for measuring greater and greater distances, called the Distance Ladder. In this lab, we will ex plore the Stellar Parallax, Cepheid Variable Stars, and Hubble’s Law. Parallax Parallax is a geometrical effect that can be used to obtain a direct measurement of the distance to an object. With current technology, parallax can only be used to measure distances out to about 500 parsecs, which is about 1.5 × 10 16 kilometers. This might seem like a great distance, but it is only about 7% of the way to the center of our Milky Way galaxy.
What is parallax? Questions: 1. Predict what your finger would appear to do relative to the background if you were to put it about 3 – 4 inches from your face and close one eye at a time while watching it. 2. Now go ahead and do this. Was your prediction correct? Comment. Notice how much your pencil appears to shift with respect to the distant objects. This is called parallax: the apparent shift of a foreground object with respect to background objects due only to a change in the observer's position. 3. How the apparent motion of your finger would change if you moved your finger twice as far from your face? 4. Now do this. Was your prediction correct? Comment. 5. If you had amazing go-go-gadget stretchy arms, can you imagine a limit to how far you could move your finger and still see it appear to move? If so, how far away do you think that would be? (To get an idea of this distance, have someone far away from you hold up their finger.) 6. What is it about our eyes that allows us to see this apparent motion?
The distance between the two observing positions is called the baseline. In the above exercise, the baseline is the distance between your eyes. Stellar Parallax In order to observe stellar parallax at all, astronomers must utilize the longest baseline that is available, namely the diameter of the earth's orbit: The stellar parallax angle, p, is defined by astronomers to be one-half the maximum change in position of the star relative to the background in one year, and so is the angle subtended by one Astronomical Unit (1 A.U. = average Earth-Sun distance) at the distance of the star. Because parallaxes are typically one arc-second or smaller, it is useful to calculate how large a distance this corresponds to. Since the distance to the stars is so very large, we can take the Earth-Sun line and replace it by the arc of the large circle of radius r centered at the star. (See dashed circle in Figure 5.) The circumference of this circle is 2πr. The length of the arc (1 A.U.) is in the same ratio to the circumference of the circle as the angle p is to 360 degrees. Expressed mathematically, this is 1 ?𝑈 2𝜋? = ? 360° Solving for r this may be expressed as ? = 360° 2𝜋? × ?𝑈 Replacing 360 degrees by 1,296,000" (since there are 60" in 1' and 60' in 1o, there are 60 x 60 x 360 = 1,296,000" in 360 degrees) and dividing by 2π, we obtain ? = 206265" ? ?𝑈 If the parallax angle is equal to 1" of arc, the distance is thus 206,265 A.U. This distance = 206,265 A.U. is given a new name, 1 parsec, meaning the distance corresponding to a parallax of 1 second of arc, using a baseline of 1 A.U. When distance is expressed in parsecs (abbreviated pc) and parallax angle is expressed in seconds of arc, the previous equation becomes simply ?(𝑖? ??) = 1 ?(𝑖? ??????? ?? 𝑎??)
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