Geometry of exploration: Water below the surface of Mars?

[Music] hi I'm Garrett Wong I play the part of ensen Harry Kim on Star Trek voyage on my show Voyager and its crew travel to distant stars planets and galaxies of course when NASA scientists navigate spacecraft through our solar system it's a little more complicated than just punching coordinates into a computer on this episode of NASA connect NASA scientists will show you how they use math like geometry to launch spacecraft to Mars and how geometric shapes contribute to the exploration of the red planet so fasten your seat belts as hosts Jennifer pulley and Van Hughes navigate you at warp speed feed through another exciting episode of NASA [Music] connect hi 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 we're here at the Virginia Air and Space Center located in Hampton Virginia get a load of all the cool exhibits they have here there's an Apollo spacecraft that took astronauts to the Moon they have models of many Rockets since space flight began and behind us this is an exact replica of the Viking spacecraft that landed on Mars in 1976 I was just a kid then so how did NASA get from the Earth to the fourth planet from the sun now obviously there are no roads or signs in space is the path a straight line or is it a curve on today's NASA connect we'll learn how engineers and scientists use a branch of mathematics called geometry to navigate a spacecraft to Mars we'll also learn about the role that circles angles and ellipses play in the exploration of Mars we talk with researchers at NASA's jet propulsion laboratory in Pasadena California and NASA Langley in Hampton Virginia who are all working on that very thing we'll explore past present and future missions to Mars and see how geometry is used to get us there plus we'll explore the age-old question is their life on Mars later in the show we'll be joined by students from Bridge Street Middle School in Wheeling West Virginia NASA connect asked them to conduct a geometry activity using ellipses and circles they'll share their data with you so you can repeat the activity and obtain your own results plus we'll go on location with NASA's educational technology program manager Dr Shelley canr who is with some students in Virginia Beach Virginia these students are using the internet to conduct a web Quest on the future colonization of Mars we'll also learn how intelligent spacecraft are being developed to explore Mars in the Mars Millennium Project stay tuned to learn more about this awesome project and to stimulate your brain every time Norbert appears with a Q card that's your cue to think about answers to the questions he gives you got it so are you ready let's go get the story angle on the world of [Music] geometry who was Pythagoras and what did he contribute to Geometry explain how geometry is used in your everyday life the word geometry comes from two Greek words Geo which means the Earth Earth and Metron which means to measure today geometry is more the study of shapes than it is the study of the earth basically geometry is the branch of mathematics that deals with the position the size and the shape of figures one of the greatest mathematicians was an ancient Greek named Pythagoras he discovered some of the most important mathematical Concepts that came to be called geometry one observation he made was that gravity is vertical or 90° to the Horizon from this observation Pythagoras discovered that the 90° angles from four right-sided triangles make up a square watch this if I have one right angle and I place three other right angles around it like this I eventually wind up with taada a square that's pretty neat let's do the math knowing what Pythagoras discovered about the right angle can you calculate how many degrees are in this square if you multiply 90° * 4 you're right this square has 360 de what other shape has 360° a circle you know Pythagoras proved that there are relationships between different geometric shapes what relationships can you see between other geometric shapes get this Pythagoras found out even more laws about the right triangle if we look at the same square but just a little differently we can see that half the area of this square equals a right triangle now how can we use math to calculate the remaining angles of a right triangle simple squares are 360° we know this if we divide it in half this triangle must equal 180° now we know this is a right triangle this equals 90° if we subtract that from 18 0 we get 90° these two angles must add up to 90° this is true for every right triangle it's true for this right triangle it's true for this right triangle and it's even true for right triangles that look like [Music] this in order to calculate the remaining in angles of a right triangle you have to use math and geometry geometry is used in everything we do from constructing roads and buildings to playing football or [Applause] pool okay here's a big play it's uh you and uh me okay I'll toss the big pass to you you go down and out got it got it now let's see if I toss the ball directly to Jennifer and don't anticipate where she'll be I'll miss her completely however if I know she's cutting right and I throw the ball at the correct angle I should get the ball to her hey my perfect pass just created a right triangle geometry is everywhere hey way to go van without geometry it would be impossible to organize precise patterns and play a simple game of football my friend Lynn Chapel is an eighth grade math teacher at Huntington Middle School in Newport News Virginia let's see what information she has about Pythagoras in Geometry the most important discovery that Pythagoras made was the relationship between the longest side of a right triangle and the two shorter sides the longest side of the right triangle is called the hypotenuse now remember the Pythagoras's Theorem is a S Plus b^2 = c^2 now who could tell me what that means Charmaine the sum of the squares of the two shorter sides a + b equals the square of the longest side C which is the hypotenuse good answer now we're going to Mark the right triangle that we have on this paper and the shorter sides also called the legs are A and B and the longest side is C and remember we call that the hypotenuse now what Pythagoras did was draw a square on the side of a remember that a square is a number times itself a * a and he drew a square on the side of b b * B and he drew a square on the side of c c * C what we're going to do is we're going to cut a squar off of the side and then we're going to cut B squ and make them fit into C squ to prove that Pythagoras was right first take your straight edge and we're going to draw some parts of B so that we can cut it and it will fit coming along the side of C come straight down through b squ till you touch the edge now connect the lower corner of B to the bottom edge of a squared this will form a perpendicular line now take your scissors and cut out a squ in one piece p and B squared in the pieces that you've cut it into and then we'll fit it all on to C squ to prove the Pythagoras was right well if all of you fit your pieces together yes then I guess Pythagoras was right and you know Pythagoras also believed or postulated that the shortest distance between two points is a straight line well how come if you throw a ball from point A to point B then it curves or arcs well van that's rather very simple ever heard of something called gravity yeah heard of gravity in 1600 Johannes Kepler a famous astronomer proved that the planets orbited the sun in an ellipse that's another geometric shape if you take a circle and squash it a bit you get an ellipse like our football example if we want to navigate from Earth to Mars we have to take into account where Mars will be within its elliptical orbit what information the scientist first first discover about Mars humans have known of Mars since before recorded history in 1609 a man by the name of Galileo first viewed Mars through his newly invented telescope although his telescope was no better than a modern toy it revealed enough to prove that Mars was a large sphere a world shaped like the Earth could this other world be inhabited besid using the telescope how else the scientists collect information on Mars let me tell you NASA's Mariner 4 was the first spacecraft to take closeup pictures of the red planet as it flew past Mars in 1965 it showed a heavily crated surface 6 years later in 1971 Mariner 9 arrived at Mars and became the first artificial object ever to orbit another planet Mariner 9 saw the valis marinaras a canyon that stretches 4,500 km or 2800 mil across the face of Mars it is so long that if it were on Earth it would stretch all the way from Los Angeles California to New York New York all these discoveries by Mariner were seen from above the surface of Mars what we really needed was A View From The Martian [Music] surface how do NASA scientists use geometry to navigate spacecraft from Earth to Mar explain the goals and accomplishments of NASA's Viking mission all right guys I want you to meet Dr Israel tabac he was one of the engineers who worked on Project Viking NASA's Mission to Mars which landed two spacecraft on its surface in 1976 Dr Tac since we've been talking about geometry can you tell me how geometry was used to get the Viking to Mars oh yeah it's really relatively simple you know most orbits around the Sun are fairly circular so if we start from Earth for example and want to go to Mars we use what's called a home transfer which is an ellipse which takes us from the Earth's orbit out to the Mars orbit and we meet Mars when it gets there so if you shot directly at Mars it wouldn't get there no it go to the Sun and heat up too much and that's the most efficient way to get there yes it is less money less time smaller booster so Dr tabac let us get this straight circles ellipses angles geometry really helps with the navigation of spacecraft to Mars like the Viking all very essential here's an experiment you can try at home with a responsible adult that will show you how curves and angles affect the path of a projectile have you ever tried to aim a dart at a dart board pretend the dart is a rocket and the dart board is Mars now there are two variables that affect the results of this activity if you throw the dart in a straight line at an angle of 0° grab gravity will curve the path downward away from the dart board and you miss but if you aim a little higher for the dart board or at an increased angle you should hit the target so if the angle is one of the variables that affects this experiment what do you think the second variable is if you guessed speed or how fast I throw the dart is the other variable then you right the combination of speed and an increased angle determines whether or not I hit Mars I mean the dart board what did the Viking mission accomplish well the Viking Mission really consisted of four spacecraft two orbiters and two Landers Viking was the first spacecraft to land on the surface of ours and we got some samples from the surface and found that the samples were all oxides mostly of iron and that's why Mars is so red rust now how long did this Mission last well we guaranteed it for 90 days but it lasted for six years well it looks like Mars is a pretty cool place yeah it really is Dr tabek thank you so much you're welcome we really appreciate you helping us understand how you use geometry to navigate to Mars speaking of navigation NASA connect took a trip to Bridge Street Middle School in Wheeling West Virginia to see how students there are using geometry to understand the orbits of planets ready for blastoff hi we're from brid Street Middle School ining West Virginia NASA connect ask us to show you the Student Activity for this program when you think of the Earth or Mars orbiting a planet you might think that the orbit is in the shape of a circle it's really in the shape of a squash Circle or an ellipse the German mathematician and astronomer Johannes Kepler discovered this fact a long time ago in this activity you'll use measurement and observation to understand the meaning of the eccentricity of an ellipse you'll calculate the distance between Earth and Mars determine the lengths of their orbits and learn about their orbital r as compared to their distances from the Sun but before we get started here are the materials you'll need a computer with a spreadsheet program or calculators cenm graph paper two push pins for each group grou a string 25 cm long for each group cardboard and one metric ruler for each group Kepler stated that the orbit of mars or of any planet is an ellipse with the Sun at one Focus the other focus is an imaginary Point there's nothing there during part of its orbit around the sun Mars is closer to the Sun than it is at other times this relationship can be seen in solar system data charts that show the maximum and minimum distances from the the sun to each planet astronomers often use the average or mean distance from the Sun instead of the minimum or maximum enter the data from the chart into a spreadsheet program or use a calculator and for each planet find the mean distance from the Sun now make a sketch of the orbits of the Earth and Mars around the Sun another column of data on the planet chart lists the eccentricity of each planet's orbit eccentricity gives an indication of the roundness or squashes of each ellipse to understand what this number means here's an experiment to do with your team on a piece of centim graph paper draw two lines one near the middle vertically and one near the middle horizontally the lines intersect at the center point measure and cut a piece of string about 25 cm long tie a knot near the ends of the string to form a loop place the graph paper on a piece of of cardboard then place two push pins along the horizontal line each 1 cm from the center point these pins represent the fosi at this point the fosi are 2 cm apart Loop the string around the push pins then use a pencil to keep the string tight and draw an ellipse measure in cenm the length of the ellipse along its major axis record the distance between the two foty and the length of the the major axis on a chart then divide the distance between the FI by the length of the major axis and record the equ on the chart now repeat these steps using the following distances between fosi 3 cm 4 cm 5 cm choose your own distance after you have recorded the distances between fosi and the length of the major axis on the data chart use a calculator to divide the distance by the major axis length the quotient will give you the eccentricity for the ellipses remember the value of the eccentricity should be a decimal with a value of less than one on the chart make sketches of the ellipses you've created analyze your data guys this would be a great time to stop the video and consider the following questions how does the distance between the fosi affect the shape of the ellipse what is the relationship between the value of the excentric and the roundness or squashed of the ellipse although the orbits of both Earth and Mars are ellipses these orbits are close enough to being circles that we can estimate the distance from the Earth to Mars let's assume both planets are on the same side of the sun consider the mean distance from the Sun to each planet as the radius of a circle use the mean distance you calculated from the Sun to Earth and the Sun to Mars to determine the estimated direct distance between the Earth and and Mars what if Earth and Mars were on opposite sides of the sun like this these activities and more are located in the educator lesson guide which can be downloaded from our NASA connect website why are we exploring Mars what tools and techniques does NASA use to explore Mars why are we exploring Mars hey that's a great question let's visit NASA's jet propulsion laboratory in Pasadena California to learn more about America's commitment to Mars exploration NASA is committed to exploring Mars in fact they will be sending a robot to Mars once every two years for the next decade Mars is very interesting because not only is it right next door but it's the planet with the most hospitable climate in the solar system so hospitable in fact that it may once have been the home to primitive bacteria like life these pictures show dried up River and Lake beds and so we know that liquid water flowed on the surface billions of years ago so where has all the water gone has it just floated off into space scientists think that a lot of the water may be chemically bound to the soil or underneath the surface in either liquid or ice form understanding where the water currently is can help us to understand the history of water on Mars which is important in determining if there is or ever was life on that planet why do scientists suspect that there was once water on Mars what is the Mars micro probe and how will it navigate below the surface of Mars what is the relationship between geometry and the Mars micro probe okay guys I'm here with Dr Robert Mitchell Tre who is working on current Explorations into the Martian landscape right now we're on top of NASA Langley's impact Dynamics facility back in the 1960s this is where they tested the lunar Landers pretty cool Dr Mitchell tree what on Earth are we doing up here well I like it up here you can look down on the surface of the Earth from up here like you can look out at the water and how it meanders across the land there and we know that even if you remov that water there would still be a distinctive shape to the pattern it makes and it's those kind of patterns we see on the surface of Mars but none of them have any water in them and we wonder where did the water go so where do scientists think the water went well some of them think it seeped beneath the surface and that's the purpose of Mars micro probe to go to Mars and look for water beneath the surface is that the micro probe well this is just a model of the micro probe the actual micro probe is much larger about the size of a basketball but it has this same shape and it's this shape it's actually like a right triangle that is used to to fly through the atmosphere of Mars as it approaches the planet it'll be tumbling and then when it hits the atmosphere no matter how it hits the atmosphere it'll reorient itself and fly nose forward and it'll continue to fly like that all the way down accelerating from 177,000 mph to 400 mph when it strikes the surface this outer shell breaks away and the inside penetrometer that fist shaped instrument pierces down through the soil and begins looking for water underneath the surface so once the micr probe penetrates the surface how does it find water or look for water well this really small fist shaped instrument has a small drill in it and when it's down in the dirt it digs with the drill pulling some dirt inside of it and it has even a laser in there also and it uses the laser to shine some energy on the dirt and it measures the out gasing of the dirt and that's how it looks for water okay big deal so what if it finds water on Mars water's the key key to understanding several interesting aspects about Mars we don't go there just to understand if there's water there it's what effect water has on other things the more interesting question is the question of life all life we know on Earth is tied some way to liquid water and if we can find water on Mars we're one step closer to understanding if what if life ever existed there or still does well that's definitely something to think about thanks Dr mitry my pleasure appreciate it hey you if you're interested in topics like life on Mars and other Mars Explorations just check out the website address on your screen speaking of the web let's go on location to Virginia Beach Virginia with NASA's educational technology program manager Dr Shelley canri I'm here at Bayside High School in Virginia Beach Virginia where students from Bayside Middle School along with their partner School Brandon Middle School have been involved in a quest as participants in the Mars Millennium Project a national Arts sciences and Technology education initiative let's check in with the students to learn about their Quest the Mars Millennium Project challenges teams across the nation to design a community for 100 people arriving on Mars in the year 2030 we have used this challenge to create an online activity to work on one aspect of building a Mars Community the development of a public relations campaign to gather public support for the Mars mission our request can be broken down into five simple Steps step one reflection our teachers explain to us our mission we divided ourselves into four groups Mission commanders Environmental Specialist natural resource engineers and astronomy Specialists each group had specific questions to research and think about step two imagine we took the knowledge gained from our research to write a survey and then brainstormed how to use technology to conduct an electronic poll and to tabulate the results in the process we gained experience in the use of software for word processing and spreadsheets step three discover the results of our electronic survey were analyzed this information helped us see what were key issues to the public so we might address them in our advertising campaign step four create we have now entered the design phase of our Quest where we are creating ads and sharing our presentations with our partner School using video conferencing technology step five share our final step will be to share with NASA and others our Mars advertising campaign in the form of a multimedia presentation that we will post on the NASA connect website also we will post our electronic survey for others to try and to make their own comparisons but Jennifer if any of our viewers would like to learn more about the mar Millennium Project they should visit the NASA connect website for a link to the Millennium website and now as a final incentive registered submissions to the Mars Millennium Project received by June 1st 2000 will be placed on a microchip for transfer to Mars on a future NASA Mission now how's that for connecting thousands of young people through technology and then using technology to take their plans for the future to another planet thanks Shell for all that cool space information we'll definitely use it well that's about it for today now before we go we've got lots of people to thank especially the middle school students and teachers the NASA researchers NASA Langley Research Center NASA ases research center NASA's jet propulsion laboratory Dr Israel tabek and Dr Shelley kenr 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 information and more is located on the NASA connect website for the NASA connect series I'm Jennifer pulley and I'm Van Hughes and we'll see you next time on NASA connect bye bye bye oh good thing I have on a hard hat ellipses and angles really Aid in the navigation of spacecraft to Mars like the Viking to how can we get more information on the Mars micro Pro well I recommend the kids go to the Mars micro wed shot a circle a circle you know Pythagoras proved that there it's old meat now [Music] bill