Navigating in Space, how do they do it?

How does a space probe like Voyager 2 which was launched in 1977 visit the
four outer planets and travel over 17 billion kilometers over a space of 40
years with almost next there nothing in the way of fuel.

Apollo astronauts used three navigation systems to determine the proper flight paths to the Moon and back to Earth. These systems were used jointly or separately. Together they formed the Primary Guidance and Navigation System.

By the time Voyager 2 had reached Neptune it had swung by Jupiter, Saturn and
Uranus traveled 7 billion kilometers and was still within 100 kilometers of its target and all
with mid-1970s technology. In the movies spacecraft just seemed to fly where they
want and get there in no time at all but in our version of reality it's somewhat
more complicated and takes much, much longer to get around.

Can you imagine Spock saying to Kirk "we've just passed Pluto almost home only
nine years to go" just in case you missed the relevance of that it took nine years
for the new Horizons probe to get from Earth to Pluto, a distance of about five
billion kilometers and that was one of our fastest spacecraft. It might seem
like an impossible task but when you know how space and physics works it
becomes a set of procedures, science fact instead of science fiction and key to
all of this is knowing how gravity works and how it affects not only you and me
but also everything in the universe.

Apollo Guidance System.

The German mathematician Johannes Kepler first
worked out the laws of planetary motion 400 years ago, Isaac Newton then used
these as a basis for Newton's laws of motion and the creation of Classical
Mechanics. The means by which we can predict the movement of everything in
the solar system and beyond including planets, comets asteroids and
spacecraft with incredible accuracy. Newton's first law states that an object
at rest or traveling a straight line will stay that way unless a force acts
upon it.

A rock for example on the ground won't move by itself unless something
else picks it up or pushes it along. If that same rock were in space and moving
in a straight line it will not change its speed or direction of travel unless
an external force acts upon it. In space there is always a force acting
on a moving body and that force is gravity be it from the Sun, a planet or
even another rock. Anything with mass exerts a gravitational force, the larger
the mass the larger the force.

The other component to a moving object is its
speed. Newton's second law states that an object's speed will change when a force
is applied to it this is also reversible so a force is generated when its speed
changes. This is also the reason why an asteroid traveling at 17 km/s and
hitting the earth can be so devastating, it can release a huge amount of kinetic
energy with the sudden change in its velocity.

Apollo Earth Orbital Map
This map was used in conjunction with the optical and computer systems of the Apollo spacecraft for the astronauts to navigate Earth's orbit.

If you fire a projectile on earth, parallel to the ground it will eventually fall under the influence of
gravity back to the ground. If you fire your projectile fast enough and it
maintains that speed it's still traveling in a straight line
however, Earth's gravity continuously pulls on it and when the curvature of
its trajectory matches that of the earth it's now said to be in orbit around the
earth. In other words the force of a projectile trying to go in a straight
line is matched by that of gravity pulling it back to earth. This is how
satellites and space stations stay in orbit but they are also affected by the
tiny amount of drag of a very thin atmosphere high above the earth. This
slows them down and as the force keeping them in their orbits becomes smaller, the
balance between this and gravity gradually tips towards gravity.

Apollo Star Chart
Apollo 11 astronauts used this star chart while training for their 1969 lunar landing mission. It shows the locations, names, and code numbers for a select group of stars. The astronauts would key those numbers into their Apollo Guidance Computer while taking readings with a sextant.

As it pulls them down further as they get lower the atmospheric drag becomes even
greater reducing the speed even more without a periodic boost in speed to
increase their orbit they will eventually come back to earth. If however
a spacecraft increases its speed the orbit will become larger and more
elliptical but it will always return to pass through the point where the speed
was originally boosted. If the speed of our craft is increased enough then it
will escape the pull Earth's gravity and enter an orbit around
the Sun.

Increase for speed more and it will increase the size of its orbit, if
we get the speed boost correctly timed with an approaching planet in what's
called an "opportunity" we can get the orbit of our spacecraft to intersect the
orbit of a planet and a method known as the Hohmann transfer approach which is
one of the most common ways to get from one moving body to another, although
there are now more efficient but much longer ways like the low thrust transfer
method and the interplanetary transport network method.

Apollo Docking Target
This target and another mounted on the Apollo 11 lunar module were used to align the Apollo 11 spacecraft during docking maneuvers.

Once there, our spacecraft can either enter into an orbit around the planet or
we can use the planets gravity to slingshot around it or use gravity assist as it's known and
increase the craft speed relative to the Sun. Gravity assist works by using a
planet's gravity to pull on our spacecraft as it flies close by and can
be used to increase or decrease a spacecraft speed and as such make its
orbit larger or smaller and change its direction of travel.

If our craft is flying in the direction of motion of that of the planets then it's will speed
up. If it flies in an opposing direction then it will decrease its speed,
depending upon how it approaches the planet its course can be changed
dramatically and can even leave traveling in the opposite direction.

But there is no such thing as a free lunch and in order to obey the law of
conservation of energy, what energy our craft gains the planet
must lose. When the voyagers used Jupiter to increase their speed to get to Saturn,
Jupiter's orbit around the Sun slow but only by about one foot per trillion
years.

Apollo Command Module, Interior (Cockpit)

We can use this gravity assist method to move from planet to planet
further and further away increasing our craft speed as we go until it reaches
escape velocity the point where we'll be travelling fast enough to escape the
pull of the sun and leave of a solar them just like Voyager 1 has already
done.

But the Sun's gravity will still pull on the craft and slow it down,
in fact the Sun's gravitational effect extends out about two and a half
light-years and it will take Voyager traveling at over 60,000 km/h 40,000
years to reach the point where the sun's gravity no longer dominates. Newton's
third law states for every action has an equal and opposite reaction.

Apollo Operations Checklist
This is the Command Module Operations checklist used by astronaut and Command Module Pilot, Michael Collins, on Apollo 11 in July 1969.

Basically the thrust from an engine pushing backwards, moves a craft forwards.
Some people think that the thrust of a rocket pushes against the ground or the
atmosphere and thus it's impossible for them to work in space. This is clearly
not the case as our rockets and thrusters don't stop working once they
are in space when there is nothing for them to push against.

We use this thrust to increase or decrease speed and as such change our spacecraft's orbit as
well as move it in its X from Y planes with thrusters to orientate its antenna
with earth or point its cameras towards a target. Once we know how gravity
affects our spacecraft and that we can use it to move from planet to planet the
next thing we need is an accurate model of the solar system this will show us
where the planets will be in relation not only to the Sun but also to each other
and other objects like comets and asteroids.

This model is created from the planetary ephemeris which is like a time table for all the major bodies in the solar system and gives their positions relative to the Sun for any given time
both in the past and the future. This data has been built up over centuries we
were the first ones being created by the Babylonians as far back as 1200 BC.

By using celestial mechanics it's possible to calculate ephemeris for several
centuries into the future. Because space missions last for years or even decades
like the Voyager ones it would be impossible to plan missions without
knowing where the planets would be in the years ahead.

However these ephemerides are not perfect due to the gravitational effect
of unknown asteroids and may be and as yet unknown Planet X far beyond Pluto
NASA has updated his ephemerides almost every year for the last 20 years as new
data has come to light. So knowing how our spacecraft will move in space and
the position of the planets well into the future this allows navigators to
plot a course for our spacecraft with incredible accuracy.

This can be seen with the Voyager missions they used planetary ephemeris to find a once in a
175 year alignment in the planets Jupiter, Saturn Uranus and Neptune. This
was discovered by Gary Flandro in 1964 whilst working at JPL and allowed the
planers to come up with the Grand Tour. This would allow one spacecraft to visit
all four planets by using gravity assist and cut their mission time from 40 years
to less than 10 if they launched in 1977.

The original Grand Tour was to include Pluto but due to funding limitations it was left out but Pluto was visited by the new Horizons probe in 2015. Voyager 2 was the first to set off in 1977
on other grand tour of the four outer planets
and eventually traveled out in the plane of a solar system. This same technique of
gravity assist has since been used on the Galileo, Cassini and the New Horizons
missions.

Voyager 1 launched three weeks after Voyager 2 on a quicker route to visit Jupiter and Saturn and do a flyby of Saturn's moon Titan. But this would then put it on an upward trajectory and out
of a plane of a solar system to interstellar space. On its way out it was
turned around so it's camera could face back to earth and
take one last set of photos.

These were the farthest images of the solar system
ever taken and one of them captured Earth's place in it. Covering just 0.12 pixels
in size in the middle of a lens flare the famous "Pale Blue Dot"
as Carl Sagan called it was taken 6.4 billion kilometres
away looking down at a 32 degree angle onto the solar system.

Now we have a plan we still need something to guide our spacecraft along its planned trajectory.
For this they use an inertial navigation system basically this is a highly
accurate system of gyroscopes, accelerometers and other sensors that
can detect movement of a craft in any direction in space. Using this
information the navigators can work out if the craft is on course.

However inertial navigation systems are mechanical devices and as such suffer
from what is known as integration drift tiny errors in the gyroscopes and sensors. This
is compounded over time because they calculate their position as they move
along from the last previously calculated position, so the longer they
go the more the errors build up. The error in a good system is less than 1.1
kilometers per hour so if a journey to Mars lasted eight months, which will be
5760 hours, then the error would be about 6300 km
by the time it reached Mars, far too much when
you have to enter an orbit with an accuracy of just a few kilometers.

To compensate for the integration drift, another fixed reference system is needed
and this is the Stars. Just as marine navigators used a sextant to work out
their position, spacecraft use optical sensors and cameras to determine their
position and reset the inertial navigation systems. On the Apollo
missions the crew used a space sextant to correct the drift on the onboard
navigation system.

On the Voyager probes they used a star tracker that could look
for a very bright guide star which in voyagers case was Canopus.
It also had a Sun sensor that could be used in conjunction with a radio signal
from Earth. Newer spacecraft have more sophisticated systems which use cameras
to look for known objects like planets and even comets and asteroids as well as
the target itself. Even with the best planned course things will vary along
the way. Other forces can also affect a craft deep in space.

The solar wind for example, the flow of charged particles from the Sun can over time gradually
change the course of a spacecraft and has to be corrected for and timing is
everything. Our spacecraft must arrive at particular points in space along the
journey within a very small window of time. Traveling at 30 km/s and
approaching a planet to use it's gravity to swing by and change course, if you are
out by more than a few minutes or so it could mean the difference between being
sucked into the planet by its gravity or undershooting the planned course. To
communicate and work out the distance and speed of a craft, NASA uses the Deep
Space Network.

Deep Space Network Operations Center at JPL, Pasadena (California) in 1993.

This is a network of radio telescopes spread around the world so
that at least one will be in contact with a spacecraft at all times. By
sending a radio signal to the craft and having it returned the signal and using
the Doppler effect and a highly accurate atomic clock the slight difference
between the two signals can be used to calculate its distance from earth to
living 3 meters and its speed to within 180 millimeters per hour.

70m antenna in Robledo de Chavela, Community of Madrid, Spain

Combining all this information we are now able to send space probes with incredible accuracy,
so much so that we can now land on a comet as we did with the Rosetta probe
and it's Philae lander and to take close-up pictures of Pluto within a
two-hour time window, 9 years after launch and 5 billion kilometers away and
when we only had one third of Pluto's orbit mapped. Five spacecraft have now
achieved escape velocity using these methods we've spoken about and are now
the farthest objects created by man.

Pioneer 10, 11 Voyagers 1 & 2 & New Horizons. It's incredible to think that all of this was done based on theories that were developed hundreds of years ago by observation only and the
desire to figure out how the heavens worked long before we even thought it
was possible to get into space let alone use gravity as our main engines.