Tracking
How do you keep track of an object that's been hurled away from Earth, to
fall for years through the solar system? How do you know where it is, and
how fast it's travelling?
We use the uplink and the downlink, working together, to solve these problems.
Cassini can only be tracked because it has a radio
transmitter
which sends signals to Earth. (This is true
with all other interplanetary spacecraft as well.) The transmitter aboard
Cassini is linked with its own radio receiver, so that they can be used
together for various tracking operations. And with the powerful transmitters
and sensitive receivers of the
Deep Space Network (DSN), Cassini has nowhere to hide!
An Unending Job
The process of tracking the spacecraft
is iterative. First the Cassini navigators
tell you where to find the spacecraft
(what angles to point the antenna, what radio frequencies to use.) Those nav
predictions are based on past tracking experience. You track the spacecraft
for several hours, gathering more tracking data, (that is, the position and
speed of the spacecraft). The navigators take this new information, and use
it to update their computer model of the spacecraft's trajectory. Then they
predict how to find the spacecraft for the next tracking period, to get more
tracking data. The process never ends!
One tracking method is called ranging. Ranging determines the distance (range)
from Earth to the spacecraft and back, by placing specially coded radio signals
(called ranging pulses) on the uplink, and noting the exact time. When the
spacecraft receives them, it puts them on the downlink right away. When they
come back to Earth, the exact time is noted again. So: the ranging computer
knows what time it sent the pulses, and it knows what time they came back.
Since the speed of the radio signals is known (they travel at the
speed of
light), the round-trip distance
can then be computed. Well, there are a few other factors, too. How long did
it take for the ranging pulse to "turn around" inside the spacecraft's
electronics? We know that miniscule delay from testing before launch. How
long did it take the ranging pulse to travel through the cable from the
computer to the antenna before leaving Earth? That's found by testing and
calibrating the system. And how far did the Earth move while the ranging
pulses were travelling to the spacecraft? Well, that's known, too, from data
obtained from
astronomical observations. All these data are processed by highly
evolved computer programs within the ranging system.
Triangulation
Ranging is a very useful technique, and it can pinpoint the round-trip
distance to the spacecraft to within a single
meter. This permits Cassini
to be located by triangulation: If you
measure the range to Cassini from a DSN station in the northern hemisphere,
and you do the same from a station in the southern hemisphere (and you
have measured the distance between the two Earth stations, too) then
trigonometry says you can locate
the spacecraft. If measurement A is equal to B, the spacecraft is between the
stations. If A is longer than B, Cassini must be further south. You get
the picture.
By its nature, though, ranging can only measure the total round-trip distance.
Since the spacecraft is moving, the range from the Earth to the spacecraft
will be a little different from the range back to Earth. And if the
spacecraft's speed is changing, you have to figure that in, too. More pieces
of the puzzle must be found...
Another use of uplink and downlink, working together for tracking, takes
advantage of the Doppler effect to determine the speed at which the
spacecraft is moving toward or away from Earth. You know what
Doppler
effect is. If an object is
sending out waves, be they sound, radio, or light, you can sense its motion
by analyzing waves received. When a noisy truck passes you on the street,
you can notice a change in the sound. As it approaches, its sound seems to
have a higher pitch, a higher frequency; then, as it sweeps by you, you
can notice a sudden drop in the frequency of its sound. That's because the
driver shifted gears. No, just kidding, it's because of the Doppler effect!
Let's take a closer look at the Doppler effect, using the example of a
noisy truck. (There are plenty here in the greater Los Angeles area.)
In this cartoon, there's a truck standing still with its engine running.
While the truck is standing still, the sound waves are evenly spaced, and
they effect Ana and Joe in the same way. They both hear the same sound, that
is, the sound which the engine is making, and which the driver hears.
In this cartoon, the truck is moving forward. It's still putting out sound
waves as before, but now, every time a wave comes out, the truck has moved
forward a little. Since the speed of sound is constant (as long as the
atmospheric conditions are constant), the waves are closer together when
they reach Joe in front: they arrive more frequently. Joe's ears and brain
interpret this higher frequency of waves as a higher pitch sound; Joe hears
a higher note than the driver does.
But look at how the waves spread out as they arrive at Ana's location. They
get there less often, less frequently, and so Ana perceives a lower note
than the driver hears. Both Ana and Joe are noticing the Doppler effect
(named for nineteenth-century Austrian mathematician and physicist
Johan Christian Doppler who
first described it).
The Missing Ingredient
Now, Joe or Ana could make careful measurements of the exact frequency of the
sound they are receiving, and, based on what frequency of sound the engine is
actually generating, they could figure out the truck's speed! But there's a
trick: How do you know exactly what frequency the engine is really generating?
The driver might be changing the engine speed! Let's take a closer look at
the problem.
Radio waves,
although they travel much faster than sound does, exhibit the same Doppler
effect when the source is moving with respect to the observer. Police
officers can measure your speed as you drive, by making use of the Doppler
effect. They have a radar device, which has a radio transmitter to beam a
signal toward your car. Your moving car reflects it back to the device's
receiver. The device's computer knows the transmitter's exact frequency, and
it measures the frequency of the reflected signal that it receives. The
device compares the two. (Since it uses its transmitter frequency as a
reference, it doesn't have to know anything about the automobile.) The
difference between the transmitted frequency and the reflected frequency can
only be due to Doppler effect, caused by your moving car. So the device
calculates your speed and displays it for the officer.
The officer would give Cassini a ticket because of its very high speed, up
to 40 kilometers a second in the inner solar system. Trouble is, though,
no radar device is powerful enough or sensitive enough to bounce its signal
off a tiny, distant, speeding spacecraft. There are other ways, however...
Ultra
We can command Cassini to use a special
"ultra-stable oscillator" (called the USO)
on board as a reference for generating its downlink frequency. That would be
like telling the truck driver to keep the engine at a constant and exact
speed... "Hey, run your engine at exactly 2001 rpm, and don't let it change
for a long time." This way, when we receive Cassini's downlink signal, any
difference between the ultra-stable thing's known frequency, and the
measured downlink frequency, is mostly from Doppler effect. And from there
you can calculate Cassini's speed. Well, first of all you have to realize
that the Earth is moving too. Once you subtract the predicted effects of
Earth's motions, what's left, for the most part, is Cassini's speed toward
or away from Earth! Simple, huh?
Ultra-ultra
But there's a way to get even better precision. Cassini's USO is nice, but its
frequency isn't really as stable or as exactly known as the navigators would
like it to be. Down in the basement of each DSN tracking complex in the
desert, is a room carefully kept at a constant temperature all year long, and
it is the wine cellar! No, just kidding. In that room, there is a frequency
reference called a
hydrogen maser . It produces a radio frequency that is very, very
constant (that's what "stable" means here). It's MUCH more stable than the USO.
The signal from the
hydrogen maser is amplified in the tracking station's
transmitter, and sent up to Cassini. When Cassini has been commanded NOT to
use its USO, here's what it does: it uses the uplink frequency that it
receives, to compute its downlink frequency. Then Cassini's transmitter
sends that frequency as its downlink. That way, all the uncertainty is
removed, and the Doppler effect can be measured so precisely that you can tell
Cassini's speed to within a few millimeters per second.
That scheme is called coherent mode,
because Cassini's downlink frequency is coherent with (based on) the uplink
frequency. When Cassini is using its USO, by the way, it's called
non-coherent mode, because the downlink is not coherent with the uplink.
(They're working on yet another frequency reference to put in that basement
room, called a trapped-ion standard. It's even more stable than the hydrogen
maser,
and it will be used for certain radio science experiments).
Pointing
The DSN's large dish-shaped antennas on Earth, literally radio telescopes,
must be pointed to within a small fraction of a degree of a spacecraft's
location to be able to receive its downlink. Once the downlink is acquired,
you can start the uplink, and do ranging and Doppler measurements. Cassini's
navigators publish predictions of where the spacecraft will appear to be in
the sky, based on their previous nav solutions, and that's where you point
the DSN antenna.
Which Way?
Originally, just after launch, though, the antenna pointing angles are used
as a form of input to the tracking process. You point the antenna to where
you think the spacecraft is, and see what you get. Move the antenna around
a little and see if you get a better signal. That's not too hard to do
because the spacecraft is close to Earth, and so its downlink is strong. When
you have the best signal, notice exactly what the pointing angles are;
that's important tracking data for the navigators. But later while in cruise
when Cassini is farther away, these antenna pointing angles are too rough a
measurement to be of any value for tracking. You depend on precision ranging
and Doppler to track the spacecraft.
