Geometry of Exploration: Eyes Over Mars (2000)

[Music] hey Bill n the Science Guy here when you dream about going places where does your mind take you somewhere on Earth or to the Stars if you spend time looking at the stars you'll notice one that's a bit red it's actually not a star at all it's the planet Mars it's the next place humans are going to explore of course none of this exploration could be done without Science and Mathematics on this episode of NASA connect NASA researchers will show you how the principles of geometry are used to survey and map our planet Earth and the planet Mars so hang tight as Vance Jennifer and the NASA science gu survey Earth and Mars on this episode of NASA [Music] connect [Music] hey guys welcome to NASA connect the show that connects you to the world of math science technology and NASA I'm Jennifer pulley and I'm Van Hughes today we're here at the Virginia Living Museum in Newport News Virginia and right now we're standing on a su dial which is basically a plate marked with hour lines and a Gomen a Gomen is a rais projection that casts a shadow from the Sun Jennifer why don't you come be the Gomen according to your Shadow it's time to start the show well van this isn't a bad way to tell time but you know I think I'd rather use my Watch you know throughout history the sun and stars govern people's days years and even their lives using Sun dials and observing Shadows was one way ancient people told time get this you can even measure height and distance with shadows cast from the Sun in fact you can even measure the circumference of an entire planet like Earth or Mars with something as simple as a shadow and geometry on today's NASA connect we will examine how NASA researchers use the principles of geometry to survey the world around us and the worlds Beyond us we'll focus our telescope to see how geometry and satellites are used to measure map and Survey other planets like Mars which by the way can be seen quite well in this planetarium anyway we'll visit some students from George Washington University who are studying and surveying the Martian landscape at Nasa Langley Research Center in Hampton Virginia and we'll visit a researcher from NASA's jet propulsion laboratory in Pasadena California who will show us how geometry is used by NASA's Mars Global surveyor later on in the show students from Central Middle School and Charlotte Courthouse Virginia will join us they've got an awesome experiment you'll want to try plus NASA's educational technology program manager Dr Shelley canright will introduce us to some students from Davis Middle School in Hampton Virginia these students are using the internet to create their own Mars surveyor we'll learn more about this web based activity later in the show hey as we go through the show our friend Norbert will visit you too every time he appears with a Q card that's your cue to think about the answers to the questions he gives you got it plus we'll go to NASA ases research center in Moffet field California there we'll get all the latest information on the search for Life on Mars and learn all about green slime so hang tight as NASA connect takes you on a global surveyor mission to our planet Earth and to planet Mars what is surveying how do survey use geometry surveying is a measurement of angles and distances elevation and direction this especially useful for locating property boundaries construction layout and map making okay Terry can you tell me how surveyors use this equipment and geometry to survey land yes let's look at this Transit it contains a telescope rope a compass and a protractor and it's used to measure horizontal and vertical angles you can measure angles in the field with this and measure those same angles back at your desk with a protractor this instrument is used to lay out objects like football fields baseball fields soccer fields uh today let's demonstrate how we use this by laying out this football field all right first we pick a starting point and set the transit over to point we call this point Corner number one then we measure 300 ft to the next corner and call it Corner number four we mark this corner with a corner marker with zero on the scale we look through the telescope and line up Corner number four we know that the angle between the sides of a rectangle is 90° so we turn the telescope towards Corner number two until we can read 90° on the transit Circle or scale now we measure the width of the football field 150 ft and Mark Corner number two next we move the transit over Corner number two with zero on the scale we look through the telescope at corner number one marker we turn the telescope towards Corner number three until we can read 90° on the scale we measure 300 ft and Mark Corner number three we now have all of the corners marked applying one of the basic rules of geometry we know that the sum of the interior angles of a four-sided polygon is 360° so our last angle must measure 90° for a correct layout the rule for checking to angles of any object is that the sum of the interior angles of a closed polygon is equal to the number of sides minus 2 * 180° you know Jennifer the Art and Science of surveying have been used for over 3,400 years to map and measure our world today scientists at Nasa are preparing to measure and map the planets of our solar system H who knows maybe one day one of you will help survey Mars did you know that George Washington was a surveyor before he became president did you know Louis and Clark use transits on the exploration mission to understand angles and circumference let's look at something we can all relate to Pizza take the slice of pizza can you tell just by looking at it how many slices were in the original pizza and how big around it was sure you can all it takes is a little geometry a pizza usually has eight identical slices but not always so let's measure the angle width of the slice that's the part you put in your mouth first excuse me sir what is this protractor read uh the protractor reads an angle with of 45° right so what is the measurement of all the other angles touching the center they have to be equal or the same measurement 45° right now most pizzas are circular and circles measure 360° if you divide 360° by 45° The Original Pizza had eight slices now let's figure the circumference of this pizza most pizzas are measured in inches so using the pizza with eight slices if the length of the crust Arc is 5 1/2 in how round is your pizza if there are eight slices and the crust Arc measures 5.5 in long then 8 * 5.5 in = 44 in the pizza has a circumference of 44 in great try this one what if the angle width of your pizza slice measures 30° and the crust Arc is 2 1/2 in how many slices would there be in the original pizza and what is the circumference I've got it 360° / 30° = 12 slices 12 slices time 2.5 in equals a circumference of 30 in so sir would you rather eat a 12 slice pizza or an eight slice pizza H I'll choose the eight slices I couldn't possibly eat 12 did you know that over 2,000 years ago a Greek librarian used geometry to determine their circumference of the [Music] Earth I AR ston need find the circumference of the earth what are the angle relationships between parallel lines and a transversal the concept of the Earth being a large sphere was not unknown to the ancient Greeks and everyday observation such as The Disappearance of ships below the Horizon indicated that the Earth might be spherical or round but how large was it the person who figured it out was a librarian named Aristophanes who lived in Alexandria Egypt about 300 BC while looking through a scroll one day he read that at noon on the longest day of the year a vertical column cast no shadow in Cen a city south of Alexandria Aristophanes knew that this did not happen in Alexandria he thought to himself how was it possible to have shadows in Alexandria and not in cine at the same time of day Aristophanes figured out that the sun must be directly overhead in cin but not in Alexandria aha here was proof Pro that the earth's surface is curved using a little geometry aristan set out to determine the circumference of the earth and find out just how big it is just like our pizza example if our friend Aristophanes could determine the central angle at the center of the earth and the length of the edge or Arc then he could figure out the circumference of the earth now finding the length of the edge or Arc was fairly simple math a stanes asked a friend to walk from Alexandria to cine to measure the distance between the two cities his friend estimated the distance to be around 800 km or about 500 mil finding the central angle however would take some geometry first Aristophanes assumed correctly I might add that the sun's rays are parallel since the sun is so far away check this out in this diagram we can see that there is no Shadow at cine while there is a shadow in Alexandria the line that is formed by the Noman or vertical column at Alexandria and the center of the earth Cuts or intersects the two parallel lines formed from the sun's Rays a line that intersects two parallel lines is called a transversal the two angles formed from the transversal line and the parallel lines are called alternate interior angles and according to geometric rule they are equal let's prove it take a piece of paper of any width and draw a diagonal line on it label the angles A and B just like this now cut the paper along the diagonal so you have two triangles compare angles A and B by placing one angle on top of the other hey what do you notice the angles are equal no matter what size paper you started with right when two parallel lines are intersected by a transversal the alternate interior angles are equal huh aristes was quite a geometer from his measurements aristes calculated the sun's Rays made an angle of 7 1/ 12° at Alexandria now since this angle was formed by two parallel lines and a transversal the central angle of the earth must also be 7 1/ 12° by knowing these two things the central angle and the distance from Alexandria to cine Aristophanes calculated the circumference of the earth 360° / 7 1/ 12° equals 48 slices of the Earth are you still with me okay hang tight we're almost there now if you remember that the estimated distance between Alexandria and cine is 800 km and you multiply that Distance by the number of slices in the earth 48 what is the circumference of the earth well if you estimate estimated that distance to be 38,000 km you're absolutely right aristophanes's estimate was really close to the Earth's circumference which is 4,74 KM his percentage error was about 5% and was probably due to an error in the distance between the two cities 5% huh that's pretty good considering Aristophanes used only his feet his eyes his imagination and of course his knowledge of geometry there are other ways that we survey the Earth which Aristophanes never dreamed of NASA scientists use airplanes and satellites but what if we wanted to survey other planets like Mars NASA scientists are doing that right now but first let's head to Central Middle School in Charlotte Courthouse Virginia there students are following in the footsteps of Aristophanes hi we're from Central Middle School in Charlotte courthous Virginia NASA connect asked us to show you how to do the Student Activity for this show in this lesson you will work in small groups to take accurate measurements of Shadows using geometry to determine the size of an angle here are the materials you'll need for each group a straight stick approximately 91 cm long a meter stick or tape measure a piece of string approximately 91 cm and a rocker weight a scientific calculator index card Compass copies of the student data chart for each student let's begin divide the class in research groups of three to five members set your measurement station by first placing the gnomen perpendicular to the ground for your measurement to be accurate it is critical that the N is vertical to check the vertical position tie the the rock or weight to the string and dangle it above the ground in front of the Gman next measure the height of the Gman place an index card under the station to Mark where the shadow ends take measurements every 2 minutes beginning at least 10 minutes before local noon which is the time that the sun is highest in the sky this will most likely not be noon as indicated on your time measuring device students should note that when the sun is highest in the sky the shadow length is the shortest since the edge of the Shadow is fuzzy and the shadow is moving from east to west in northern hemisphere be careful in deciding where to place your mark record your data on data chart one now back in your classroom locate the latitude and longitude of your school location and record it on data chart number one identify your best Shadow length this is the best Shadow length at local noon time next calculate the tangent by dividing the length of the Shadow by the height of the Gomen locate this number or the nearest rounded number on the tangent table the measure of the tangent can also be found by dividing the length of a shadow by the height of an object on the scientific calculator record t tent on student data chart make a scale drawing of your Gman and Shadow complete the triangle and measure the tangent with a protractor to verify your calculations what's next Jennifer let's analyze the data by reviewing the results of this activity and by responding to the following questions did the weather conditions affect the results of this activity if so how as the shadow lengthens over time how will the angle be affected if each group uses a gnen with the different length how will that affect the results of this activity for more activities like this check out our website at edu lc. nasa.gov SLC connect NASA connect would like to give a special thanks to the mentor from the aiaa chapter at Howard University in Washington DC we appreciate all your help with the Student Activity okay let's review we've seen how the sun's position satellites and geometry Help Us survey the Earth but what if we wanted to survey Mars well we don't live on Mars so how do scientists and NASA survey the red planet I thought you'd never ask let's visit NASA's jet propulsion laboratory in Pasadena California and find out [Music] what is the Mars glob of s and where is it how does the Mars Global surveyor use geometry to survey the Martian landscape the Mars Global surveyor is a spacecraft that is in orbit around Mars its purpose is to take pictures of Mars to measure the temperature of the surface and the atmosphere of Mars and to bounce laser signals off the surface of Mars to precisely determine the shape of Mars you might think of Mars as simply being a sphere by looking at pictures of it but to scientists it it has lots of bumps and ridges for example the poles of Mars are so cold that the atmosphere actually condenses out to form dry ice at the PO and as much as 25% of the atmosphere condenses out into to the dry I at the pole so there's quite a large change in the in the atmosphere also Mars is known for having a large bulge on the side of it the largest uh volcano in the solar system known as Olympus Mons and so one of the functions of the Mars Global surveyor was to measure the shape of Mars to carefully determine how big is this bulge because it it has a huge effect on on the orbits of spacecraft it is it's such a large bulge on the side the way that we use um geometry to convert the L pulses into the shape of Mars what we have to do is carefully time how long it takes for the pulses to reach Mars and bounce back to the spacecraft and then we combine that with the shape of the orbit which we determine by looking at how the radio signal changes as the spacecraft goes around Mars what is Arrow breing how does geometry influence Arrow braing arrow braing is when when we use drag from the atmosphere to gradually shrink the orbit down so what we had to do is use the drag from the atmosphere to gradually slow the orbit down so that it would shrink from this highly elliptical 45-hour orbit down to a very circular 2hour orbit around Mars This is geometry in action how would you like to try your hand at designing your own Mars Global surveyor before introducing you to our featured edtech activity in middle school I want to give you a quick tour of Norbit's lab you already know norber he's that funny character that provides us with the CU cards and other learning activities and AIDS to help us understand the math science and technology Concepts presented in each of the NASA connect programs his lab is your interactive link to activities and resources on the web so you'll get the most out of NASA connect just click on the rooms to enter areas like career corner where you'll meet some of our guests and members of our television team there's a steady room with terms and definitions related to the show and a page with links to other cool sites and this is where you'll get to the online activity especially created in partnership with NASA's learning Technologies team to introduce us to the web activity for this show let's pop in on a teacher and her students at Davis Middle School in Hampton Virginia thanks jelly my name is Vivian Carr and I'm a math and science teacher here at Davis Middle School my students love coming to the computer lab they use it for reinforcement and enrichment of many skills in most of the content areas now I'd like to introduce you to Ruby Bruno Ruby tell us how do you use technology technology is a tool that we use in several ways for communication with others through email for conducting research using the internet for writing papers and preparing electronic presentations of our work and for participating in problem solving online projects such as which is NASA connect to reinforce what we are learning in class in the online component for this show we're learning what goes into the design of a spacecraft used for planetary observation to do this we learn about different instruments used for observing planetary surfaces from space one of these is a camera we get to pick out what we think are the right batteries to use as well as the size of the solar panels required to run the spacecraft we'll also have to consider the cost and weight of the vehicle as we try to put together the best possible planetary Observer we can whip all the variables given to us in the activity well Jennifer the students here at Davis Middle School leave you and our viewers with the challenge to assemble and test their very owned Mars surveyor in a costeffective way that produces the best results viewers can find that challenge in Norbit's lab on the NASA connect website see you on the web let's head to NASA Langley Research Center in Hampton Virginia meet up with some George Washington University graduate students they are using pictures from the Mars Global surveyor and geometry to survey [Music] Mars how Shadows measured on Mars how is geometry used to determine the height of land formation on Mars hey guys I want you to meet Corey Hernandez and Brooke Anderson they're graduate students at George Washington University guys what are you studying over there well with simple geometry and shadows we're able to determine the elevation on Mars surface such as a mountain Olympus Mons that's three times the size of Mount Evers or Valley Val marinaras which is the size of the United States wow those are some pretty large land formations so let me get this right what you're telling me is that geometry is used to determine the elevation of land formations on Mars yes and we set up an example here for you to demonstrate this if this is a mountain on the surface of Mars This is a protractor to to measure the angle of the sun this is a magic ruler to measure the length of a shadow if this flashlight represents the sun we know that like here on Earth the sun is directly overhead at 90° at High Noon okay and as the day goes on it goes down to 0° at Sunset so Cory what you're telling me is this model here creates a right triangle the bottom leg can be represented by the length of the Shadow which we can get from taking a picture with the Mars Global surveyor now the sun makes an angle between the hypotenuse and the bottom leg so let's pretend it's midafternoon on Mars the sun would be at about an angle of 45 de mm which Brook how long is our shadow it gives us about 17 cm oh wow so you got your angle there yes so using our formula remembering the tangent of 45° is equal to 1 which we can find from our scientific calculators or our tangent tables we can find the height of our Mountain to be 17 cm so to double check our answer we can see that the height of a mountain is 17 cm that's about what you calculated that's pretty cool Cory well I looked at Mars through the telescope and it is definitely red but could green slime have once existed on the red planet that's one of the many reasons NASA a research center in Moffet field California is studying Mars so now let's join researcher Chris McKay with the latest on green shine I'm interested in Mars and in particular life on Mars we know that early in Mars history had had water lots of water we can see the rivers and lakes that were formed by that water the question is when it had water did it have life to understand how life might have survived on a cold Planet like Mars and where to look for it we go to places on Earth where life is surviving in very cold dry conditions mars-like conditions this is a rock from the Antarctic the dry valleys of Antarctica most mars-like place on Earth in this rock there's life but it's hidden inside The Rock just below the surface there's a layer of green and these are algae and Lykan and they're growing inside the rock because the rock provides them a source of moisture while at the same time allowing enough light to come through by studying life forms in these environments we learn about the strategies that life can use in a cold dry place and we might apply those strategies to the search for Life on Mars and maybe we'll find evidence that there was life there when Mars was not too much colder than the dry valleys of Antarctica well looks like the sun has shifted and that's about all we have time for today but before we go Jennifer and I would love to hear from you with your comments and ideas so why don't you drop us a line at Nasa connect NASA LC ms400 Hampton Virginia 23681 or if you're on the web email us at connected. lc. nasa.gov we'd like to thank everyone who helped us today the Virginia Living Museum George Washington University our NASA researchers from NASA Langley Research Center NASA as Research Center and NASA's jet propulsion laboratory Dr Shelley canright and especially the students and teachers from our Middle School thanks guys if you would like a videotape copy of this NASA connect show and the Educators guide lesson plans contact core the NASA Central operation of resources for educators all this information and more is located on the NASA connect website for the NASA connect series I'm Jennifer pulley and I'm Van Hughes see you next time take the slice of pizza we got it what is serving one of the functions of the Mars Global surveyor was to watch it fall off how geometry used to measure today we'll use this of dump what are the angles the sun would be would be would be at about an angle of 45 degrees how shatters sh okay so tell me what you're studying over there welcome to NASA connect sorry it's my fault welcome to NASA connect sorry and I'm Van Hughes today we're here at the all right I think I see who wao