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Sam Houston State University *

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1404

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Astronomy

Date

Oct 30, 2023

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pdf

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name: NI WNQNY 2 Ecipses & Transts small and distant it is from us, the transit of Mercury is difficult to observe. Venus transits only 4 times every 243 years but is easier to observe with a telescope. The last Venus transit occurred July 5-6, 2012 and won't happen again until the year 2117. In this lab you are going to investigate circumstances when the positioning of celestial bodies aligns and what we observe when that happens. You will also model (on a simplified level) observations made by astronomers over 100 years ago to calculate the distance of Earth from the Sun. Finally, you will begin to consider how astronomers might be able to use transit events in other solar system to determine information about the planets found there. LAB EXERCISE PART I: TOTAL ECLIPSES In the Retrograde Motion and Phases of Venus labs, we looked at the apparent diameters of Mars and Venus, and how they change as the planets move around the Sun. Let’s investigate this further. Your lab instructor has a number of Styrofoam spheres for you to investigate. Pick two that are noticeably different in size. Measure the diameter of each sphere and record it in the table below. Hold the larger sphere at arm’s length and measure the distance from the center of the sphere to your eye. Record this below. Now, while holding the larger sphere at arm’s length, position the smaller sphere such that it “appears” the same size to your eye. 1. Will the smaller sphere be Iocated r farther than the larger sphere? URS AW smoVlesh §pnive 1S Closer Measure the distance from the center of the smaller sphere to your eye and record it below. Diameter (d) Distance (D) Angular Diameter (3) Larger Sphere 1[.5W 2\ a2y, b Smaller Sphere qQ.6m W\ 7% ¥ \37,4 © 53 Scanned with CamScanner

NameN\C/$/\ N\$YYV\\\ ‘Lb Eclipses & Transits 2. How many times bigger is the larger sphere to the smaller one? L s e - 3. How many times farther is the larger sphere than the smaller one? 150 Hwes Bowxrer Use the following formula to calculate the angular diameter of each sphere: 8 = 206,265 Ly = : 2655 This yields an angular diameter in units of arcseconds (the angular diameter measurements you've observed in previous labs have used this angular unit). MAKE SURE THAT THE UNITS FOR DIAMETER AND DISTANCE ARE THE SAME! Angular diameter of larger sphere: 1.6 é\: ZO(Q,’L(OS "Z'z J=91,2%2.590L Angular diameter of smaller sphere: S’.Z()(alwg ?—6/ W\ $-\1$ \31.964 4. How do the two angular diameters compare? e diamerey 6 YR Symoney Spreve iS OWBSY Lunice Mg Yhon Ang | Y Yty SM\ It turns out that the same effect occurs with the Sun and Moon. When viewed in the sky, the Moon appears to be as big in the sky as the Sun. 54 Scanned with CamScanner

Name.‘“\%(.\ M\N\QW L® ~ Eclipses & Transits 5. We know the distances to the Sun and Moon. If the Sun is 400 times as far away from Earth as the Moon, yet appears the same size in the sky, how much bigger must it be than the Moon? U000 hwws \avraey Because the Moon and Sun have the same apparent diameter, when circumstances are just right, if the Moon passes directly in front of the Sun, it blocks our view of it and causes a total solar eclipse. 6. What if the Moon were a little farther away? How would that change what we see? R0 (Wgon WO dN Y oppeon +g ot JaY < an (WS, N (By the way, this is what is known as an annular solar eclipse.) 7. What if, instead, the Moon remained at its original distance, but were a little smaller? How would what we observe compare with the previous question? e Maon WoLIE kg WWEAE-aLr- +nan Hwoes W\/‘\O\)S\ g In the case of the Moon, we know that annular solar eclipses occur due to the varying distance of the Moon from Earth, and not due its diameter changing over time. 55 Scanned with CamScanner

name: INTCAA Mg Iy Uer PART I1: PLANETARY TRANSITS As Mercury and Venus orbit within Earth’s orbit, they periodically pass directly between Earth and the Sun, at a point called inferior conjunction (refer to the Planetary Configurations section in the Appendix for more details.) We can use observations of these transits to determine the distance from Earth to the Sun. Eclipses & Transits With the Sun as a backdrop, observers at different locations on Earth will see a transit occur across different portions of the Sun. By measuring the angular shift of the transiting planet when viewed from one location versus another, astronomers can use basic trigonometry to calculate the distance from Earth to the transiting planet. We will investigate the distance to Venus in the following example. ’ ’ Earth Not to Scale Figure 1: The transit of Venus is o'bserved to cross different parts of the Sun depending from where on Earth you observe. Looking at Figure 1, you can see that the angular separation (indicated by the Greek letter 6) of the two transiting paths L 4 depends on the distance between the two different i observation points on Earth (known as the baseline). If we H can measure this value, along with the baseline distance (B), "' then we can measure the distance (D) between Earth and fo] & =FA Venus. The trigonometric equation that applies to this situation is the tangent: i I (9) .82 AN3L5°D i Earth Figure 2: The distance to Venus from Earth can be calculated using basic trigonometry. 56 Scanned with CamScanner

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