Transcript for NASA Connect - Geometry of Exploration: Water Below the Surface of Mars

[ Music ]

[Garrett Wong] Hi.

I'm Garrett Wong.

I play the part of Ensign
Harry Kim on Star Trek Voyager.

On my show, Voyager and its crew
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.

In this episode of NASA Connect,
NASA scientists will show you how

to 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 belt
as hosts Jennifer Poli

and Dan Hughes navigate
you at warp speed

through another episode
of NASA Connect.

[ Music ]

[Jennifer] Hi.

Welcome to NASA Connect, the show
that connects you to the world

of math, science,
technology, and NASA.

I'm Jennifer Poli.

[Dan] And I'm Dan Hughes.

We're here at the Virginia
Air and space Center,

located in Hampton, Virginia.

[Jennifer] 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
from when space flight began.

And behind us, there's an exact
replica of the Viking spacecraft

that landed on Mars in 1976.

I was just a kid then.

[Dan] 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?

[Jennifer] Or is it a curve?

In 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'll 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.

[Dan] Plus, we'll explore
the age old question,

is there 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 Cainwright,
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.

[Dan] And to stimulate your
brain, every time Norbert appears

with a cue card, that your
cue to think about answers

to questions he gives you.

Got it?

[Jennifer] So, are you ready?

Let's get this story angle
on the world of geometry.

[Voices] Who was Pythagoras, and
what did he contribute to geometry?

Explain how geometry is
used in your everyday life.

[Jennifer] The word geometry
comes from two Greek words.

Geo, which means the earth, and
metron, which means to measure.

Today, geometry is more
the study of shapes

that 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.

[Dan] One of the greatest
mathematicians was an ancient Greek

and Pythagoras.

He discovered some of the most
important mathematical concepts

that came to be called geometry.

[Jennifer] One observation
he made was that gravity....

is vertical.

Or, 90 degrees to the horizon.

From this observation,
Pythagoras discovered

that the 90 degrees angles

from four right-sided
triangles make up a square.

Watch this.

If I have one right angle and it
plays three other right angles

around it, like this, I
eventually wind up with...

ta da. 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 multiplied 90 degrees
times four, you're right.

This square has 360 degrees.

What other shape has 360 degrees?

[Dan] A circle.

You know, Pythagoras proved
that there are relationships

between different geometric shapes.

What relationships can you see
between other geometric shapes?

[Jennifer] Get this.

Pythagoras found out even more
laws about the right triangle.

If we look at the same square,
but just a little different,

we can see that half the area of
the square equals a right triangle.

Now, how can we use math

to calculate the remaining
angles of a right triangle?

Simple. Squares are 360 degrees.

We know this.

We divide it in half; this
triangle must equal 180 degrees.

Now we know this is
a right triangle.

This equals 90 degrees.

If we subtract that from
180, we get 90 degrees.

These two angles must
add up to 90 degrees.

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 this.

In order to calculate the remaining
angles of a right triangle,

you have to use math and geometry.

[Dan] Geometry is used
in everything we do,

from constructing roads and
buildings to play football or pool.

OK. Here's a big play.

It's you and me.

OK. I'll toss the big pass
to you, you go down and out.

Got it?

[Jennifer] OK.

[Dan] 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.

[Jennifer] Hey, way to go, Dan.

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 and geometry.

[Lynn] 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.

Remember that Pythagoras's
Theorem is A squared plus B squared

equals C squared.

Now who can tell me
what that means?


[Charmaine] The sum of squares
of the two other sides, A plus B,

equals the square of the longest
side, C, which is the hypotenuse.

[Lynn] Good answer.

Now, we're going to
mark the right triangle

that we have in this paper.

And the shorter sides, also
called the legs, are A and B.

And the longest side
is C. Remember,

we called that the hypotenuse.

Now what Pythagoras did was
draw a square on the side

of A. Remember a square
is a number times itself.

A times B. And he drew a square
on the side of B. B times B.

And he drew a square on
the side of C. C times C.

And what we're going to do is
we're going to cut A squared off

of the side and then we are going
to cut B squared and make them fit

into C squared to prove
that Pythagoras was right.

First take your straight edge and
we're going to draw some parts of B

so we can cut it and it will fit.

Come along the side of C, come
straight down through B squared

until you touch the edge.

Now connect the lower corner of B
to the bottom edge of A squared.

This will form a perpendicular

Now take your scissors and
cut out A squared in one piece

and B squared in the pieces
that you have cut it into.

Then we'll fit it all
on to C squared to prove

that Pythagoras was right.

Have all of you put
your pieces together?

[Voices] Yes.

[Lynn] Then I guess
Pythagoras was right.

[Jennifer] And you know Pythagoras
also believed or postulated

that the shortest distance between
two points is a straight line.

[Dan] How come if you threw a
ball from point A to point B,

then I it curves or arcs?

[Jennifer] Well, Dan,
that's really very simple.

Ever heard of something
called gravity?

[Dan] In 1600, Johannes
Kepler, a famous astronomer,

proved that the planets
orbit 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.

[Speaker] What information
did scientists first discover

about Mars?

[Jennifer] Humans have known about
Mars since before recorded history.

In 1609, a man by the name
of Galileo first viewed Mars

with 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?

[Speaker] Besides
using the telescope,

how do scientists collect
information on Mars?

[Jennifer] Let me tell you.

NASA's Mariner 4 was
the first spacecraft

to take close-up pictures
of the red planet.

As it flew past Mars in 1965, it
showed a heavily cratered surface.

Six years later, in 1971,
Mariner 9 arrived at Mars

and became the first
artificial object ever

to orbit another planet.

Mariner 9 saw the Vallas Marineris,
a canyon that stretches 4500 km,

or 2800 miles, 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 surface.

[ Music ]

[Speaker] How did NASA
scientists use geometry

to navigate spacecraft
from Earth to Mars?

Explain the golden accomplishments
of NASA's ranking mission.

[Dan] All right, guys.

I want you to meet
Dr. Israel Taybach.

He was one of the engineers
who worked on Project Viking,

NASA's mission to Mars,
which landed two spacecraft

on the surface in 1976.

[Jennifer] Dr. Taybach, since
we've been talking about geometry,

could you tell me how geometry was
used to get the Viking to Mars?

[Dr. Taybach] Oh yes.

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

[unclear], which is an
ellipse which takes us

from the Earth's orbit
out to Mars orbit.

And we meet Mars when
it gets there.

[Jennifer] So if you shot directly
at Mars, it wouldn't get there.

[Dr. Taybach] No, it would go
to the sun and heat up too much.

[Jennifer] And that's the most
efficient way to get there.

[Dr. Taybach] Yes, it is.

[Jennifer] Less money,
less time....

[Dr. Taybach] Smaller booster.

[Jennifer] So Dr. Taybach,
let us get this straight.

Circles, ellipses, angles, geometry
really helps with the navigation

of a spacecraft to
Mars like the Viking.

[Dr. Taybach] All very essential.

[Jennifer] Here's an
experiment you can try at home,

with a responsible adult, that
will show you how curves and angles

of set 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 degree,

gravity will curve the path
down, away from the dart board.

And you miss.

But if you can aim a little
higher than 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

as the other variable,
then you are right.

The combination of speed and an
increased angle determines whether

or not I hit Mars, I
mean the dart board.

[Dan] What did the
Viking mission accomplice?

[Dr. Taybach] 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 Mars.

And we got some samples
from the surface,

and found that the
samples were all oxides.

Mostly iron.

And that's why Mars is so red.


[Dan] How long did
this mission last?

[Dr. Taybach] Well, they
guaranteed it for 90 days,

but it lasted for six years.

[Dan] Well, it looks like
Mars is a pretty cool place.

[Dr. Taybach] Yes, it really is.

[Jennifer] Don't Taybach,
thank you so much.

[Dr. Taybach].

You're welcome.

[Jennifer] We really appreciate you
helping us understand how you used

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 blast off.

[Voices] Hi.

We're from Bridge Street Middle
School in Wheeling, West Virginia.

NASA Connect asked us to
show you the student activity

for this program.

When you think of the earth
or Mars orbiting the planet,

you might think that the orbit
is in the shape of a circle.

It's really in the shape of a
squashed circle or an ellipse.

The German mathematician

and astronomer Johannes Kepler
discovered this a long time ago.

In this activity, we'll use
measurement and observation

to understand the meaning of
the eccentricity of the ellipse.

You will calculate the
distance between Earth and Mars,

determine the length
of their orbits,

and learn about their
orbital rates as compared

to their distances
in the assignment.

But before we get started, here
are the materials you will need.

A computer with a spreadsheet
program or calculators.

Centimeter graph paper, push prints
for each group, a string 25 cm long

for each group, cardboard, and
one metric ruler for each group.

Kepler stated that the orbit of
Mars or any planet is ellipse

with the sun at one focus.

The other focus is
an imaginary point.

There is 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 sun to each planet.

Astronomers often use the average
or mean distance from the sun

as instead of the
minimum or maximum.

Enter the data from the chart
into your 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 list, the eccentricity

of each planet's orbit.

Eccentricity gives an
indication of the roundness

or squashiness of each ellipse.

To understand what
this number means,

here's an experiment
to do with your team.

In a piece of centimeter
graph paper, draw two lines:

one near the middle vertically,

and one near the middle

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 cardboard.

Then place two push pins
along the horizontal line,

each 1 cm from the center point.

These pins represent the foci.

At this point, the
foci 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 centimeters the length

of the ellipse along
its major axis.

Record the distance between
the two foci and the length

of the major axis in a chart.

Then divide the distance
between the foci and the length

of the major axis and record
the quotient on the chart.

Now repeat these steps using the
following distances between foci:

3 cm, 4 cm, 5 cm,
choose your own distance.

After you have recorded the
distances between the foci

and the length of the major axes
in the data chart, use a calculator

to divide the use 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.

[Jennifer] 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 foci affect
the shape of the ellipse?

What is the relationship between
the value of the eccentricity

and the roundness or
squashiness 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 the 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 Mars.

What if Earth and Mars
were on opposite sides

of the sun, like this?

These activities and
more are located

in the educator's lesson
guide, which can be downloaded

from our NASA Connect web site.

[ Music ]

[Voices] Why do we explore Mars?

What tools and techniques
does NASA use to explore Mars?

[Jennifer] Why are
we exploring Mars?

Hey, that's a great question.

Let's go to NASA's Jet
Propulsion Laboratory at Pasadena,

California to learn more

about America's commitment
to Mars exploration.

[Speaker] 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 bacterial 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.

[Speaker] So where has
all the water gone?

Has it just floated off into space?

[Speaker] 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 understand

the history of water on Mars,
which is important in determining

if there is or ever was
last on that planet.

[ Music ]

[Voices] Why do scientists suspect
that there was once water on Mars?

What is the Mars Microprobe,

and how will it navigate
below the surface of Mars?

What is the relationship between
geometry and the Mars Microprobe?

[Jennifer] OK, guys.

I'm here with Dr. Robert
Mitcheltree, 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. Mitcheltree, what on
earth are we doing up here?

[Dr. Mitcheltree] 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 removed that water,

there would still be a distinctive
shape to the pattern it makes.

And it's those kind of patterns
that we see on the surface of Mars.

But none of them have
any water in them.

And we wonder, where
did the water go?

[Jennifer] So where do
scientists think the water went?

[Dr. Mitcheltree] Some of
them think it seeped beneath

the surface.

And that's the purpose of Mars
Microprobe: to go to Mars and look

for water beneath the surface.

[Jennifer] Is that the Microprobe?

[Dr. Mitcheltree] Well, this is
just a model of the Microprobe.

The actual Microprobe
is much larger,

about the size of a basketball.

But it has this same shape.

And it's this shape that's
actually like a right triangle,

that is used 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,

decelerating from 17,000 miles
an hour to 400 miles per hour

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.

[Jennifer] So once the
Microprobe penetrates the surface,

how does it find water
or look for water?

[Dr. Mitcheltree] Well, this really
small fist shaped instrument has a

small drill in it.

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 gassing of the dirt.

And that's how it looks for water.

[Jennifer] OK, big deal.

So what if it finds water on Mars?

[Dr. Mitcheltree] Water is the key

to understanding several
interesting aspects about Mars.

We don't go there just to
understand if there's water there.

It's what affect 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 life ever
existed there or still does.

[Jennifer] Well, that's definitely
something to think about.

Thanks, Dr. Mitcheltree.

[Dr. Mitcheltree] My pleasure.

[Jennifer] I appreciate it.

Hey, you. If you're interested
in topics like life on Mars

and other Mars explorations,

just check out the web site
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 Cainwright.

[Dr. Cainwright] 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

Let's check in with the students
to learn about their quest.

[Voices] The Mars millennium
Project challenges teens

across the nation to
design a community

for a hundred 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 quest can be broken
down into five simple steps.

Step one, reflection.

Our teachers explained
to us our mission.

We divided ourselves into four
groups: mission commanders,

environmental specialists,
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 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 helps 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 presentation

with our partner school using
videoconferencing 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 web site.

Also, we will post our
electronic survey for others to try

and to make their own comparisons.

[Dr. Cainwright] Jennifer, if
any of our viewers would like

to learn more about the
Mars millennium Project,

they should visit the NASA
Connect web site for a link

to the Millennium web site.

And now, as a final incentive,
registered submissions

to the Mars Millennium
Project received by June 1,

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?

[Jennifer] Thanks, Shelley, for all
that cool cyberspace information.

We'll definitely use it.

[Dan] Well, that's
about it for today.

[Jennifer] Now, before we go,
we've got lots of people to thank.

Especially the middle school
students and teachers,

the NASA researchers...

[Dan] NASA Langley Research Center.

[Jennifer] NASA Ames
research Center.

[Dan] NASA's Jet Propulsion

[Jennifer] Dr. Israel Taybach.

[Dan] And Dr. Shelley Cainwright.

[Jennifer] If you would
like a videotaped copy

of this NASA Connect show, and
the educator's guide lesson plan,

contact CORE: the
NASA Central Operation

of Resources for Educators.

All this information
and more is located

on the NASA Connect web site.

For the NASA Connect
series, I'm Jennifer Poli.

[Dan] And I'm Dan Hughes.

And we'll see you next time.

[Jennifer] On NASA Connect.


[Dan] Bye.

[ Music ]