Download Getting there: how do you fly to Saturn (without a huge cost)? From

Getting there: how do you fly to Saturn
(without a huge cost)?
From the website:
http://www.jpl.nasa.gov/cassini/Mission/traj.html
"Time is designed so that motion looks simple."
John Wheeler
Pretend you're one of the science investigators, a private eye that's found an important
clue to the mystery of the universe. You've decided to go do some detective work at
Saturn, and have gathered the latest and greatest in James Bond secret service gear.
Now you must find a way to get to your destination, Saturn, to solve the mystery. Well,
a nice fusion or warp drive would do the trick -- but these technologies just haven't
come up yet. Right now they're just special effects on TV. So you must scheme
carefully, and "steal" some precious energy wherever you can find it. You discover a
secret technique to hop aboard a planet's gravitational field, like stowing away on an
ocean vessel. Knowledge and hard work will get you where you need to go, and you
decide to call your clever scheme "gravity assist."
A generation of television viewers the world over has been awed by the power of the
forces unleashed during a rocket launch. Cassini trajectory designers, however, know
that modern rocketry has its limits. For instance, in order to go straight to Saturn, a
spacecraft must be flung into deep space with a speed of about 10 kilometers (6
miles) per second! The Titan IV booster with a Centaur upper stage is quite capable
of flinging the Cassini spacecraft away from Earth into space, but only with a speed of
about 4 kilometers (2.5 miles) per second. How, then, can we get to Saturn? The
answer lies in the use of your gravity assist scheme. Basically, the idea is to use the
gravity of other planets to do the dirty work of accelerating the spacecraft so that it can
finally reach Saturn. During the planetary swingby there is an exchange of energy
between the planet and spacecraft, enabling the spacecraft to increase its velocity
(speed and direction) relative to the Sun.
Did you know...? The Cassini spacecraft is about
the size and weight of an empty 30 passenger
school bus. It weighs roughly 5650 kg (6 tons),
over half of which is rocket fuel.
Before the concept of gravity assists was proposed in
the early 1960s, planetary spacecraft were realistically
limited to visiting Venus, Mars, and Jupiter. The other
planets simply could not be reached by reasonably
sized spacecraft without taking decades to get there.
Using gravity assists, missions to all the planets are
possible. The only energy required is that needed to get to the first planet; all
subsequent planets are more or less "free."
Gravitational assist is such a powerful technique that even to longtime practitioners of
the art and science of trajectory design it sometime seems like magic.
The Voyager missions provided perhaps the most impressive illustration of the
technique. These missions took advantage of a planetary alignment which occurs only
once every 175 years to slingshot two spacecraft from planet to planet over 12 years.
Straight talk about gravity
The force of gravity, as every school child knows, is what keeps us attached to the
Earth. Isaac Newton discovered that the reason the Earth exerts gravitational force is
because it has mass. (Newton arrived at this conclusion, as the story goes, after an
apple hit him on the head.) Anything which has mass exerts gravitational force. The
more massive the object, the greater the gravitational force it exerts.
Space travel is based on the idea that the adage "what goes up must come down" is not
always true. If we give an object (a spacecraft, for instance) a high enough speed, it
goes into orbit around the Earth; faster still, and it leaves Earth orbit. The speed at
which an object leaves Earth's orbit is called, naturally
enough, the escape speed.
When a spacecraft leaves Earth's orbit, it goes into its
own orbit around the Sun. The transition is a gradual
one, governed by the fact that the gravitational force
exerted by an object (e.g. Earth) decreases as the
distance from it increases. As the Sun is the most
massive object in the solar system, when we get far
enough away from Earth the Sun's gravitational force
dominates by far. A spacecraft moving away from Earth
behaves more and more like it is orbiting the Sun and
less and less like it is orbiting the Earth. Eventually, it
gets far enough away from the Earth that the influence of Earth's gravity is practically
unnoticeable.
The process is reversed during a flyby of a planet. Initially, the spacecraft is far from the
planet, in orbit around the Sun. As it gets closer to the planet, the planet's gravitational
force gets stronger, overpowering the Sun's influence in the vicinity of the planet. Since
the spacecraft's speed is greater than escape speed, the spacecraft continues right on
by the planet, instead of going into orbit around it.
However, the planet's gravity bends the spacecraft's trajectory as it flies by. This
means the spacecraft leaves the flyby in a direction different from the one it came from,
and when it leaves the planet behind for the void of deep space, its orbit around the
Sun is no longer the same as it was before the flyby.
The closer the flyby and the more massive the planet,
the more the trajectory is bent. Any increase or
decrease in the spacecraft's speed results from an
energy exchange between the planet and the
spacecraft. That is, if the spacecraft speeds up in its
orbit around the Sun, the planet must actually slow
down, and vice versa. However, because the planet is
so much more massive than the spacecraft, it only has
to slow down a tiny bit (too small to notice or measure)
to give the spacecraft a whopping acceleration.
The difficulty of explaining this energy exchange led to this amusing anecdote which
occurred at a press conference on the Galileo mission to Jupiter several years ago. After
hearing a lengthy explanation of how the Galileo spacecraft would use Earth flybys to
speed it up in order to fling it out to Jupiter, a concerned reporter asked if the resulting
slowdown in the Earth's orbit around the Sun would do harm to the environment. The
reply was an emphatic denial, coupled with a more detailed explanation of why the
slowdown was insignificantly small. Then, a long-forgotten voice offered a waggish
suggestion: in order to restore Earth to its pre-Galileo speed, we would just have to
launch another spacecraft and make it fly by Earth on the opposite side!
Cassini's main trajectory: gravity assists galore!
Cassini's "primary" trajectory is designed to get a 5650 kilogram (about 12,450 pounds,
or a small school bus!) spacecraft to Saturn in about six years and nine months. The
Cassini spacecraft is initially actually launched inward, not outward, and is aimed
toward Venus rather than Saturn. After examining literally thousands of different
possible paths, the mission designers came up with an outstanding trajectory, consisting
of two Venus flybys, a flyby of Earth and one of Jupiter. Only after these four "gravity
assists" is the spacecraft finally able to reach Saturn. It has "stolen" speed from the
other planets by using their gravitational fields.
Did you know...? When the Voyager spacecraft flew by Jupiter, it gained 16
kilometers (10 miles) per second of speed at a cost of slowing down Jupiter by 1
foot every trillion years!
The Cassini primary mission is scheduled for launch in October 1997 using the Titan
IV/Centaur, with an Upgraded Solid Rocket Motor (SRMU). The Venus-Venus-EarthJupiter Gravity Assist (VVEJGA) trajectory compensates for the necessary energy to
reach Saturn, requiring a deterministic or Deep Space Maneuver (DSM).
This maneuver will be executed after the first Venus flyby (April 1998) to lower
perihelion (the closest point with respect to the Sun) and place the spacecraft on the
proper course to encounter Venus for a second time in June 1999.
Planetary encounters (Venus twice, Earth, Jupiter, then Saturn) in the Cassini primary
trajectory (Image only available electronically)
After the Earth flyby in August 1999, the Cassini spacecraft will be on its way to the
outer planets, flying by Jupiter in December 2000. The fortuitous geometry of the
trajectory provides a unique opportunity of a double gravity-assist, from the second
Venus flyby to Earth within 56 days, reducing the total flight time to Saturn to 6.7 years.
The primary trajectory takes advantage of the fact that Jupiter, which is the heaviest
planet in the Solar System (and therefore, the best to use for gravity assists), is in the
right spot with respect to Saturn (in other words, on the same side of the Sun and so
forth) for us to use it as our last slingshot. Waiting any longer would prevent us from
using Jupiter's gravity, since it wouldn't be lined up right with Saturn, and we'd need to
use a lesser trajectory (at the very least, it would take longer to get there).
Six years may seem like a long time to get to Saturn (which may not seem so far away,
since you can usually point to it at night, even in smoggy Los Angeles), but remember
that Saturn is ten times as far away from the Sun as the Earth is, about 1,430,000,000
kilometers (900,000,000 miles) -- so Cassini's journey is enormous. From the
spacecraft's point of view, the trip is equivalent to that of an ant that has to crawl
around the Earth 60 times! And without gravity assists or a much larger launch rocket,
we just couldn't get there at all.