Date modified: Mon 2023-09-18 . 09:01 AM
Date created: Sat 2023-10-07 . 09:02 PM
# Celestial navigation - Part 2 North Star and the Southern Cross. You may have seen long exposure images of the night sky like this: ![[1 teaching/summer program 2023/week 2/---files/Celestial_navigation 2023-05-16 11.58.44.excalidraw.svg]] %%[[1 teaching/summer program 2023/week 2/---files/Celestial_navigation 2023-05-16 11.58.44.excalidraw|🖋 Edit in Excalidraw]], and the [[summer program 2023/week 1/---files/Celestial_navigation 2023-05-16 11.58.44.excalidraw.dark.svg|dark exported image]]%% ![[---images/---assets/---icons/question-icon.svg]] What do you notice? What is causing the trail of circular arcs of light? ![[---images/---assets/---icons/question-icon.svg]] What does it mean to see a star in this image that is not moving in a circle, what does it mean? In the northern hemisphere, this star that does not appear to move does exist, and it is the **North Star** or **Polaris**. It is in the direction that is parallel to Earth's rotational axis from the north pole, sometimes we call this the celestial north pole. ![[1 teaching/summer program 2023/week 2/---files/Celestial_navigation 2023-05-16 12.50.12.excalidraw.svg]] %%[[1 teaching/summer program 2023/week 2/---files/Celestial_navigation 2023-05-16 12.50.12.excalidraw|🖋 Edit in Excalidraw]], and the [[summer program 2023/week 1/---files/Celestial_navigation 2023-05-16 12.50.12.excalidraw.dark.svg|dark exported image]]%% ![[---images/---assets/---icons/question-icon.svg]] By this diagram, can we see the North Star if we are in the Southern hemisphere? Suppose that we are in the Northern hemisphere, and suppose that we can identify which star it is the North Star, then we can in fact deduce our latitude ![[---images/---assets/---icons/exclaim-icon.svg]]! (In addition to knowing which way is north). Since the North Star is so far away from Earth, the light we see from it are all roughly parallel (to Earth's rotational axis). Using a string and plumb bob, we can measure the angle of elevation of the North star from the horizon. ![[1 teaching/summer program 2023/week 2/---files/Celestial_navigation_2 2023-05-16 13.10.35.excalidraw.svg]] %%[[1 teaching/summer program 2023/week 2/---files/Celestial_navigation_2 2023-05-16 13.10.35.excalidraw|🖋 Edit in Excalidraw]], and the [[summer program 2023/week 1/---files/Celestial_navigation_2 2023-05-16 13.10.35.excalidraw.dark.svg|dark exported image]]%% ![[---images/---assets/---icons/question-icon.svg]] If the angle of elevation you measure of the North Star from the horizon is $L$ degrees, what is your latitude? Hint: Complete the following diagram to help you -- The circle represents Earth and its rotational axis is indicated, and say you are at some location $P$. Draw in a couple more lines. What line of direction will you see the North Star from $P$? What line of direction do you see the horizon? Where is the angle is $L^\circ$? And what is your latitude? (Recall light from very far away are essentially parallel.) ![[1 teaching/summer program 2023/week 2/---files/Celestial_navigation_2 2023-05-16 13.20.04.excalidraw.svg]] %%[[1 teaching/summer program 2023/week 2/---files/Celestial_navigation_2 2023-05-16 13.20.04.excalidraw|🖋 Edit in Excalidraw]], and the [[summer program 2023/week 1/---files/Celestial_navigation_2 2023-05-16 13.20.04.excalidraw.dark.svg|dark exported image]]%% ![[---images/---assets/---icons/question-icon.svg]] Los Angeles is in the Northern hemisphere with latitude of about $34^\circ N$. If you are in Los Angeles and look northward in the night sky, what angle of elevation above the horizon would you expect to find the North Star? === ## How to find the North Star? Now that you know how the angle of elevation of the North Star tells you your angle of elevation, how do we find the North Star? Using the cup of the Big Dipper, one can follow where it is pointing, to the tail of the Litter Dipper, to which you find the North Star! ![[1 teaching/summer program 2023/week 2/---files/Celestial_navigation_2 2023-05-21 09.03.10.excalidraw.svg]] %%[[1 teaching/summer program 2023/week 2/---files/Celestial_navigation_2 2023-05-21 09.03.10.excalidraw|🖋 Edit in Excalidraw]], and the [[summer program 2023/week 1/---files/Celestial_navigation_2 2023-05-21 09.03.10.excalidraw.dark.svg|dark exported image]]%% ![[---images/---assets/---icons/question-icon.svg]] Suppose you see the following the night sky, and a tree directly in front of you (and at the same elevation as you) stands 20 ft tall and 50 ft away. Estimate your latitude. (Would your height matter?) ![[1 teaching/summer program 2023/week 2/---files/Celestial_navigation_2 2023-05-21 10.06.25.excalidraw.svg]] %%[[1 teaching/summer program 2023/week 2/---files/Celestial_navigation_2 2023-05-21 10.06.25.excalidraw|🖋 Edit in Excalidraw]], and the [[summer program 2023/week 1/---files/Celestial_navigation_2 2023-05-21 10.06.25.excalidraw.dark.svg|dark exported image]]%% On the state flag of Alaska, one would find the Big Dipper and the North Star, designed by then 14-years-old Benny Benson, an Alaskan native, whom often look to the night sky when growing up in an orphanage. [^benson] Another historical note. When Harriet Tubman led the former slaves to the free north, they would be taught how to read the night sky, identifying the Big Dipper and the North Star to find their way north. References of the stars were memorialized in many African-American folk songs, such as **Follow the Drinking Gourd.** [^tubman] === ## What about in the southern hemisphere? Unfortunately, there is no pole star currently in the southern celestial pole. However the pole position can be approximated by using the **Southern Cross** (Crucis) the the **Southern Pointers** (Centauri), consisting of $\alpha$ Centauri and $\beta$ Centauri (each a binary star system): Following the diagonal of the Southern Cross from $\gamma$ Crucis to $\alpha$ Crucis, and the **perpendicular bisector** of the Southern Pointers, they intersect at an (approximate) location of the Southern celestial pole: ![[1 teaching/summer program 2023/week 2/---files/Celestial_navigation_2 2023-05-21 11.37.12.excalidraw.svg]] %%[[1 teaching/summer program 2023/week 2/---files/Celestial_navigation_2 2023-05-21 11.37.12.excalidraw|🖋 Edit in Excalidraw]], and the [[summer program 2023/week 1/---files/Celestial_navigation_2 2023-05-21 11.37.12.excalidraw.dark.svg|dark exported image]]%% ![[---images/---assets/---icons/question-icon.svg]] Say on an imaginary coordinate system, we have the coordinates of the following stars: $\alpha$ Crucis: $(-12.5,16.9)$ $\gamma$ Crucis: $(-15.4,20.8)$ $\alpha$ Centauri: $(-22.3,9.2)$ $\beta$ Centauri: $(-20.8,12.5)$ Find the coordinates of the intersection that gives the approximate celestial south pole. The Southern Cross is prominently featured on **both** the Australian flag and New Zealand flag. Somewhere between $\alpha$ and $\beta$ Centauri, is **Proxima Centauri**, which is the closest star to our solar system, at 4.2465 light years. === [^benson]: More information from Alaska Historical Society, https://alaskahistoricalsociety.org/discover-alaska/kids-page/benny-benson-an-alaska-kid-who-made-history/ [^tubman]: From the National Park Services, https://www.nps.gov/articles/drinkinggourd.htm