the show you're about to watch concerns
the space shuttle mission unlike any
other you've ever seen the tethered
satellite mission while the mission was
successful in proving an idea that had
only been a theory we had some hardware
problems and the tether did not extend
as far as we wanted it to go as often
happens in research we learn from things
when they go wrong here we learned
enough to prove that this truly unique
concept really does work
in this program we do calculations based
on the length we expected the tether to
extend not how far it actually extended
so keep this in mind and enjoy the show
-
an ordinary summer's day at the lake the
Sun the water good fun and physics
physics you might not think so but yes
take this water skier for example
there's a lot of basic physics involved
in skiing there's the force of gravity
the pull of the rope the resistance of
the water the skier balances these
forces and a few more to keep a stable
center of mass gliding across the water
but the physics is so basic he doesn't
even have to think about it
he just skis and if he doesn't get it
right the first time he tries again
until he does but in space
we usually get only one shot at a task
so before we do anything we analyze it
to get the physics right the first time
that's important because what you think
should happen in space isn't necessarily
what will happen let's say we want to
speed up the orbiter to rendezvous with
a spacecraft just ahead do we fire the
orbiters jets to go faster no if we
follow intuition and fire the jets to
speed up will actually be propelled into
a higher orbit that will end up slowing
us down so up here in space we can't
always depend on what we think will
happen we have to know what will happen
and that takes a good understanding of
physics
physics whether we use it to rendezvous
with satellites in space or describe
waterskiing on the earth has unlimited
applications and today we have a really
unique one to show you welcome aboard
the space shuttle Atlantis where we're
about to launch a new type of spacecraft
it's called the tethered satellite
that's because the entire time it's
deployed it remains tethered to the
orbiter by a two millimeter diameter
strand of insulated copper this is one
of the most complex missions ever
attempted by a space shuttle crew what's
amazing is that most of the physics that
we use to fly the tethered satellite is
the same physics that you study in high
school it includes concepts like gravity
angular momentum and center of mass in
the next few minutes we're going to see
how these concepts relate to the orbiter
the satellite and the tether we begin
the experiment by deploying the tethered
satellite we do this from the top of a
12 metre boom to protect sensitive parts
of the orbiter small invisible nitrogen
jets are used to get the satellite and
tether in motion once they are far
enough away from the orbiter we can turn
the Jets off and the satellite and
tether will continue to deploy
what makes the satellites continue to go
up after all you can't push on the road
well that's where the physics comes in
we take advantage of a force that causes
the tether to continue extending on its
own away from the earth it's a force
that gets stronger as the tether gets
longer when what is this force well its
gravity gravity but how can gravity make
things go up well which one of those
things that doesn't make sense that's in
you understand the physics so let's look
at the physics of gravity all objects
are cooled by Earth's gravity even
objects in space but the further away
from the earthly objects are the less
the earth gravity pulls on them Sir
Isaac Newton described the force due to
gravity as an inverse square law that
means that an object two times as far
away from the center of the earth at
another object with the same mass fields
only a quarter of the gravitational pull
it's a mouthful but next to the tether
gravity is the most important influence
on our tethered satellite let's find out
why we'll calculate using Newton's to
measure the
when the 500 kilogram satellite is in
the cargo bay six thousand seven hundred
kilometers from the center of the earth
it has a certain amount of force on it
if we extend its 10 kilometers upwards
gravity pulls on it about 30 Newtons
less extending it's another ten
kilometers reduces gravity is gripped by
another 13 Newtons
for a total of 26 we said that gravity
is an inverse-square force and for our
purposes the distance involved is from
the center of the Earth's orbit and to
the satellite as it moved away from the
orbital but the distances the satellite
is moving away from the orbiter are much
smaller than the distance to the center
of the earth if you put a force on these
smaller distances we see that the change
in force is linearly proportional to the
change in distance
we call this difference in the force of
gravity with distance the gravity
gradient force Britons being the
mathematical term for difference
when the tether length doubles the
gravity gradient force doubles
now we have enough information to
understand why the tether reels out and
stays out so let's put it all together
the acceleration caused by the Earth's
gravity is greater for objects closer to
the Earth's center
this means the orbiter is trying to
accelerate towards the Earth faster than
the satellite this extra acceleration
causes the orbiter to want to fall away
from the satellite creating a stretching
force along the length of the tether and
that's the force that keeps the tether
taut and makes the tethered satellite go
up but how can gravity make something go
up doesn't that violate the law of
conservation of energy
could we be getting something for
nothing to understand how gravity can
make something go up we need to go a
little deeper into dynamics and look at
the concept of center of mass the center
of mass is the point in a system where
the system is evenly distributed and in
balance balance or equilibrium is
important because it means the system is
stable we're all in the same orbit
around the Earth Jeff the orbiter and
these two apples the center of mass
between two objects such as these apples
doesn't change just because they're in
orbit their center of mass is between
them here when I start them spinning
their center of mass continues to be in
the same place if I cut the string so
the apples are attached by the longer
string the center of mass is still in
the same place inside the orbiter which
means in the same orbit what does this
have to do with the orbiter and tethered
satellite when the tethered satellite is
in the orbiters cargo bay the center of
mass is inside the orbiter when we
deploy the satellite do you think the
orbit of the center of mass changes if
it did then we would be violating the
law of the conservation of energy
however like the apples the orbit of the
shuttle satellite system doesn't change
because no external force has been
applied to the system but the positions
of the orbiter and satellite do change
to keep this
systems center of mass in the same orbit
and continue its stable equilibrium
around the earth let's look at that
concept in action on the ground to make
a seesaw balance one person sits in the
middle if we add another person the one
in the middle has to move to keep the
center of mass in place
it's the same for our tethered system
when the satellite is extended like the
heavier person on the seesaw the orbiter
stays closer to the center of mass let's
see how much the one hundred thousand
kilogram orbiter moves away from the
center of mass when the five hundred
kilogram satellite is deployed 20
kilometers you could work this problem
out for yourselves because the orbiter
is more massive it moves only about a
hundred meters away from the center of
mass while the satellite moves away
almost 20 kilometers and the center of
mass of the system stays in its original
orbit because the orbiter moves so
little it almost seems like the
satellite alone is moving up but now we
know both objects are moving one up and
one down once you understand this
principle you can also see this
situation is symmetrical we could just
as easily have made the satellite go
down 20 kilometers in the orbiter go up
100 meters
here's another way of looking at it
think of a pulley system a heavyweight
moves a little to balance a light weight
that moves a lot the weights can move in
either direction the center of mass
stays constant but in space we don't
need a pulley a tether will do now let's
look at the forces that keep the tether
system stable along a vertical axis when
this toy is punched gravity makes it
return to a vertical position the
tethered system could also be perturbed
off the vertical axis without any
restoring force the system would rotate
like these tethered apples but the
tethered system stable equilibrium keeps
it aligned along a vertical axis what
causes the tethered system stable
equilibrium and space well once again
gravity is at work you see gravity pulls
on both ends of the system
the pull on the satellite at the upper
end of the tether makes the system want
to depart from the vertical while a pole
on the orbiter at the lower end makes
the system return do you remember the
gravity gradient the end closest to the
earth feels the greatest acceleration so
the system feels a net torque and the
tether returns to the vertical it
doesn't matter if the mass is at the end
of the system are equal or not the
gravity gradient is stabilizing the
system but gravity gradient is only part
of the story there's another force at
work remember we saw that there is an
approximate force of 26 Newtons
for the gravity gradient over a 20
kilometer tether
well when the tether is extended 20
kilometers our force measuring device
measures 40 Newtons not 26 Newtons
now where did this extra force come from
here is a clue it's the same force we
feel when we will an object around on a
string and the strain stretches the
faster the speed the harder the force
tries to fling the object away from the
center
as you have seen gravity helps keep the
Tetra vertical
and you can actually calculate this
expert force and it turns out it's about
half the gravity gradient force a
significant effect
therefore as it orbits the earth it is
actually rotating once per orbit about
its center of mass creating this extra
force that stretches the tether we can
see it in action another way if we have
one of our crews spin a bucket of water
around in a circle the water will stay
inside a bucket as long as the motion
continues stop the motion the force
disappears and the water obeys the law
of gravitational attraction like the
gravity gradient force it is also
proportional to the length of the tether
as long as the rate of rotation stays
constant
and speaking of constants we've always
assumed that the tether remains at a
constant length and this is not always
the case when we lengthened or shortened
the tether another physics principle
that you've heard of comes into play and
that angular momentum you see it here in
the motion of the skater angular
momentum is the product of an object's
rotational inertia and angular velocity
about a particular axis when the object
changes its mass distribution the
angular momentum stays the same but the
rotation rate changes we call this the
conservation of angular momentum and you
can see for yourself how this principle
works stand on a turntable with your
arms outstretched and weights in your
hands
have someone start you spinning now
bring your arms in you speed up that's
because the more the mass is
concentrated towards the center of mass
the faster the mass spins now let's see
how this part of physics relates to our
spaceship and the data satellite when
the tether is pulled in the rotating
mass of the system is concentrated into
a smaller area and the system tries to
speed up just like the skater when the
tether is let out the mass is
distributed in a bigger area and the
orbiter and tether system slow down just
like the students slow down
when she extended her arms in the
orbiter we see this from a slightly
different perspective because we are
part of the rotating system remember
during most of the mission for
scientific reasons the orbiter is moving
with the tail forward do you notice how
from our point of view the satellite
moves forward with respect to our
direction of motion and moves backward
with respect to our direction of motion
when it's let out and this is called the
Coriolis effect and it occurs in all
rotating systems as a consequence of the
conservation of angular momentum
it is the tendency of objects in
rotating systems to move in a curve as
opposed to a straight line
we'll try to throw a ball from someone
on one side of a merry-go-round
to someone on the other side of the
merry-go-round as we can see the ball is
thrown in a straight line but not from
this point of view here it appears the
balls trajectory is curving and this is
what makes the satellite move backward
or forward as we reel it out or in the
Coriolis effect is what makes hurricanes
spiral and other weather systems curved
we won't go into the mathematics here
except to say that the larger the tether
reel out or reeling rates the greater
the backward or forward motion of the
satellite from the vertical so let's
review the aspects of tether dynamics
that we've looked at so far gravity
center of mass and angular momentum all
of these concepts are studied in your
first-year physics course yet all of it
is used in a way like nothing you've
ever seen before and there are even more
uses of tether technology on orbit we
found we could use the tether to
generate electricity as the copper cord
tether flew through the Earth's magnetic
field
so the question left is what can we use
this to other technology for we could
use tethers to directly study parts of
the Earth's atmosphere that we can't
reach by any present-day technology
tethers could reduce the need for
chemical fuels in space boosting objects
to stay in orbit and assisting others to
deorbit and engineers could use the open
wind tunnel of the Earth's upper
atmosphere for testing the hypersonic
aerodynamics of reentry vehicles and
aerobraking technology
it's even possible that one day tether
driven electric cable cars will ferry
space travelers from earth to
geostationary orbit what uses of tether
technology can you think of the limits
are not of physics but of the human mind