[meteorite-list] Dawn Journal - January 27, 2009

From: Ron Baalke <baalke_at_meteoritecentral.com>
Date: Thu, 29 Jan 2009 10:25:22 -0800 (PST)
Message-ID: <200901291825.KAA26879_at_zagami.jpl.nasa.gov>

http://dawn.jpl.nasa.gov/mission/journal_1_27_09.asp
 
Dawn Journal
Dr. Marc Rayman
January 27, 2009

Dear Dawncers,
 
Dawn continues on course for its pas de deux with Mars on February
17. The planet's gravity will gracefully assist the spacecraft on
its way to rendezvous with its intended celestial partners Vesta
and Ceres in the more distant asteroid belt. Even the
extraordinary capability of its ion propulsion system would not be
sufficient for Dawn to complete its celestial dance without the
help of Mars.
 
In the last log we saw that the mission
operations team was preparing to adjust the probe's flight path to
keep it on target for next month's flyby. Just getting to the
vicinity of Mars is not sufficient, as the passage by the planet
is only one short segment of a very long itinerary. Indeed,
choreographing Dawn's trajectory is a complex matter of finding
the most efficient route through the solar system to travel from
the moving platform on which it started (Earth) to encounter Mars
in just the right way to reach Vesta at the proper time to
complete its work there before it has to begin the trek to Ceres
to meet it on schedule, aided during most of the journey by the
ion propulsion system. Dawn must arrive at Mars on time, traveling
in the correct direction and at the necessary location, for the
gravitational slingshot to yield the desired effect. Flying the
spacecraft through that "window" at Mars is like threading a
celestial needle.
 
Early this month, engineers determined that the craft's
interplanetary route was so close to the one planned originally
that it was unnecessary to refine it. In part, this is a
reflection of how accurate the first (and now only) trajectory
correction maneuver (TCM1 "where do
normally undemonstrative engineers come up with these incredibly
cool names") was when it was executed on November 20. In addition
however, Dawn does not need to be aimed as accurately as a typical
spacecraft might for such a gravity assist. The ion propulsion
system will be used so extensively between Mars and Vesta to
continue modifying the probe's orbit around the Sun that it has
enough leverage to compensate for a significant range of
deviations from the mathematically optimal bending of its course
by Mars' gravity.
 
To understand the targeting at the red planet, at the request of
readers on planets of all colors throughout the constellations
Sagitta and Sagittarius, we shall extend the analogy of the
archery problem described in an earlier log.
We can follow both the spacecraft
and the arrow as each travels to its goal. Of course, while the
arrow's path ends when it produces a satisfying thunk at the
target, Dawn's target is a region of space near Mars that is much
more penetrable. There are other important differences between the
two problems, not the least of which is that Dawn has thrust with
its ion drive most of the way to Mars. (For the complete list of
caveats that apply to the analogy, contact the Dawn legal department.)
 
When Dawn was fired into space, aiming for the window near Mars
was analogous to shooting an arrow at a target 47 kilometers (29
miles) away. In the center of the target is a red circle 30
centimeters (almost 1 foot) in diameter, representing Mars. Of
course, we don't want our arrow to hit the red bull's-eye! Rather,
our goal is a spot about 2.2 centimeters (7/8 of an inch) outside
the circle, near the 11:00 position.
 
By the time of TCM1 2 months ago, Dawn had traveled 880 million
kilometers (550 million miles), corresponding to the arrow having
sailed 39 kilometers (24 miles) from our bow. After flying that
tremendous distance, our projectile was headed for the bull's-eye
itself, so we applied a tiny adjustment to put it on course for
the real aim point.
 
By January 15, when the mission operations team had scheduled TCM2,
Dawn had put more than another 110
million kilometers (70 million miles) behind it, so our arrow
would have streaked another 5 kilometers (3 miles) closer to its
target. Even with so far still to go, the aim is so good that no
further correction is needed.
 
Although controllers will continue to monitor Dawn's trajectory
and refine the predictions of its course, as long as the arrow
flies true, it will reach its target. With the latest estimate,
instead of hitting the mathematically optimal spot, it will strike
less than 2 millimeters (a little over 1/16 of an inch) farther
from the bull's-eye. It won't quite land at the 11:00 position,
but it will be less than a third of the way to the tick mark just
after the 11:00 marker, where the hour hand would be pointing at
about 11:04. This is comfortably within Dawn's allowance for accuracy.
 
These coordinates correspond to the spacecraft passing about 543
kilometers (337 miles) above the reddish surface of the planet
rather than the original plan of 500 kilometers (311 miles). While
that may seem like a large difference, the effect of a gravity
assist largely depends on the distance from the center of a
planet, not the surface. In that context, instead of passing about
3896 kilometers (2421 miles) from the center, Dawn will pass 3939
kilometers (2448 miles) from that reference location. (The arrow
strikes 17.4 centimeters, or less than 6 7/8 inches, from the
middle of the bull's-eye rather than 17.2 centimeters, or 6 3/4
inches.) The mission easily could accommodate much larger
deviations from the original plan.
 
And what does the difference mean for the overall journey to the
asteroid belt? Dawn's 4-month period of coasting between Mars and
the resumption of ion thrusting will be shortened by about 4 days.
As the spacecraft will thrust for most of the 2.5 years from Mars
to Vesta, powering up the ion drive a few days earlier is
virtually inconsequential.
 
Over the coming weeks, navigators will continue to gather data on
Dawn's route through space to refine their computations, and some
of the numbers above likely will change a little. It might be
tempting to think that if we had truly perfect knowledge of the
spacecraft's position and velocity at some time then we could
predict the encounter details correspondingly accurately. After
all, the gravitational forces from the Sun and Mars and even other
planets and asteroids, far though they are from Dawn, are very
well known indeed. It turns out, however, that there are other
forces acting on the spacecraft as well. They are like a soft but
variable breeze blowing on the arrow we have aimed at the distant
target, making the already challenging archery problem still harder.
 
Light, as insubstantial as it feels to our corporeal readers, has
momentum, so as the Sun shines on Dawn, it constantly modifies the
trajectory. (The force from the light is far greater than from the
solar wind, the stream of charged particles that our star blows
into space. The effects of the solar wind are too tiny to matter.)
The constant nudge from the Sun's light is small, but it needs to
be incorporated into the targeting, and that is difficult because
the size of the effect depends on the reflective properties of the
spacecraft. Light bouncing off a polished piece of metal provides
a different force from light absorbed by a dull black thermal
blanket. As the spacecraft changes its orientation, different
components are exposed to the light from the Sun, and the angles
at which they are illuminated change. Navigators are able to
account somewhat for the solar pressure, but the small uncertainty
in it contributes to the uncertainty in the encounter details.
 
Dawn itself is responsible for an even larger variability in its
own trajectory. As we have seen before, the spacecraft is equipped
with reaction wheels, which are part of the attitude control
system. (To achieve a certain mystique
about their work, engineers use the term "attitude" to describe
the orientation of the probe in the weightlessness of spaceflight;
the system also happens to have a very sanguine attitude about its
work.) By electrically spinning the wheels faster or slower, the
spacecraft can control its attitude (and sometimes even its
outlook). The reaction wheels are used to start and stop turns as
well as to hold the craft's attitude steady, right now, for
example, keeping the main antenna pointed to Earth. The solar
pressure not only alters the spacecraft's trajectory but it can
rotate the spacecraft as well, just as wind can both propel and
turn what it blows against. Attitude control automatically changes
the wheels' speeds to counteract this effect. The consequence,
however, is that the units gradually speed up as they hold their
own against the incessant solar pressure.
 
The wheels cannot increase their speeds indefinitely, and they
lose effectiveness when they reach their limit. To allow them to
slow down, attitude control calls upon its colleague the reaction
control system to fire small thrusters,
which use the rocket propellant hydrazine. The force essentially
reverses the influence of the solar pressure that has caused the
wheels to spin up, thus allowing them to spin down without the
spacecraft ever having to change its attitude. Indulging their
usually secretive poetical impulses, engineers refer to this
process as "desaturating the reaction wheels."
 
In addition to slowing the wheels, the thrust from the hydrazine
pushes the spacecraft, modifying its trajectory. During the
current phase of the mission, the thrusters are operated twice a
week to desaturate the reaction wheels, so engineers need to
quantify the ramifications of firing the reaction control
thrusters prior to the encounter with Mars. Here again, while the
phenomena are understood, there remains some level of uncertainty
in how accurately they can be predicted, given imperfect knowledge
of the actual effect of the solar pressure and details of how the
spacecraft will operate its 6 thrusters to reduce the speeds of
the 3 operating wheels.
 
The uncertainty in the change in the spacecraft's speed from the
desaturation of the reaction wheels is around 1 millimeter/second
(12 feet/hour). Except to our readers in the planetary nebula NGC
6543 (sometimes known as the Snail Nebula), this speed may seem
very slow, but consider a simplified example of how this affects
the calculation of exactly where Dawn will be as it sails past
Mars. Suppose the planetary encounter is 5 weeks away, and all
present and future trajectory parameters are known perfectly
except the result of the desaturation scheduled for 4 weeks before
the encounter. (This example disregards all the other
desaturations yet to occur, treating them as if they would be
known exactly.) The best prediction of the effect on the
spacecraft's trajectory of that desaturation still a week away is
included in the analysis to determine where Dawn will be when it
reaches Mars, but that prediction is off by just 1
millimeter/second. That speed, when maintained for the more than
2.4 million seconds in the 4 weeks between the desaturation and
the flyby of Mars, leads to a distance of more than 2.4 kilometers
(1.5 miles). So, if the actual effect of the desaturation is 1
millimeter/second different from what is included in the
computations, Dawn's actual position will wind up 2.4 kilometers
away from the calculated position. Of course, all other parameters
are not known perfectly, and there are more desaturations before
Mars, so the actual encounter conditions can change by much more
than in this illustration. Nevertheless, there has been great
effort to establish how unpredictable all the factors are, and
engineers are confident the trajectory is well within the required
window to achieve the needed assistance from Mars.
 
The powerful tug exerted by the planet will bend Dawn's path by
about 78 degrees. To picture that angle, suppose Mars is a dot at
the center of a clock, and Dawn flies toward it (or, more
accurately, toward the required window very nearby) from the 12.
If the planet had no gravity, the spacecraft would continue in a
straight path, exiting the face of the clock by the 6. Instead,
the probe takes a sharp turn at the center of the clock and heads
out between the 3 and the 4. (This is not the same clock used in
the discussion of solar conjunction in the previous log.
Be sure to check out the full selection of celestial timepieces
in your planet's Dawn gift shop.)
 
The deflection from Mars changes Dawn's orbit around the Sun (as
does thrusting with the ion propulsion system). To enter orbit
around Vesta, Dawn needs to match its orbit around the Sun to the
one that Vesta is in, and the Mars encounter is designed to help
accomplish that, bringing Dawn's plane into closer alignment with
Vesta's. (We saw in the previous log
that part of the journey requires changing the plane of Dawn's
solar orbit.) The gravity of Mars will alter Dawn's orbital plane
by about 5.2 degrees, a seemingly modest angle. Yet, if it were up
to the spacecraft to accomplish such a change on its own, it would
require a velocity change of more than 2.3 kilometers/second (5200
miles/hour).
 
Thanks to the design of the Mars encounter, there is another
benefit as well. In addition to tilting Dawn's orbit around the
Sun, Mars changes its shape, enlarging the elliptical orbit and
sending the probe farther from the Sun.
 
In considering the size of solar system orbits, it often is
convenient to measure lengths with the "astronomical unit",
which is simply the average distance
between the Sun and Earth. So 1 astronomical unit (AU) is 150
million kilometers (93 million miles), conveniently helping your
correspondent locate not only how far he lives from the Sun, but
also how far he works from it.
 
If Mars had no gravity and thus could not divert Dawn on its
travels, the craft's current elliptical orbit would take it as
close as about 1.23 AU to the Sun and as far as 1.69 AU away. (For
comparison, Mars orbits between about 1.38 AU and 1.67 AU.) As we
saw in a log last summer, Dawn is
temporarily heading in toward the Sun now. Without the effect of
Mars, and with no additional ion thrusting, our interplanetary
robot would reach that minimum distance in June 2009, and by early
May 2010 it would have swung out to the greatest distance, only to
begin falling back again as it followed its elliptical loop.
 
After the boost from Mars, if Dawn undertook no further thrusting,
it would come no closer than 1.37 AU to the Sun, reaching that
distance in April 2009. Then it would head out to 1.84 AU,
arriving there in April 2010. In this new orbit, Dawn still will
be a long way from Vesta (which never dips even quite to 2.1 AU
from the Sun) and still farther from Ceres (which travels out to
3.0 AU), yet it will be much closer than it would have been
without Mars' help.
 
Reshaping Dawn's orbit, quite a separate effect from reorienting
it, would require more than 1.1 kilometers/second (700
miles/hour). The combination of these two benefits is equivalent
to the planet imparting about 2.6 kilometers/second (1600
miles/hour) to the spacecraft.
 
Dawn's unique propulsion system allows it to change its own speed
by well more than this during its mission. Yet the famously gentle
ion thrust means it would take quite a while to achieve these
changes, and the mission itinerary, fit between the September 2007
launch and the February 2015 arrival at Ceres, does not afford
enough uncommitted time. There are other technical reasons as well
that making these changes only with its built-in capabilities
would be impractical. The encounter with Mars is a free way to get
significant help.
 
Is it really free? Well, in these difficult economic times, there
is a cost we are obligated to divulge in the interest of full
disclosure. The changes to Dawn's orbit come at the expense of
Mars' orbit. Just as when you throw a ball forward, you feel a
"reaction" force backward, in pushing the spacecraft one way, Mars
reacts by moving the other. Mars exerts a force on Dawn, but Dawn
exerts an opposite force on Mars. As the planet's mass is nearly
600 million million million times that of the spacecraft, the
effect on our probe is far larger than on the fourth planet from
the Sun. The cost of helping Dawn is that Mars will slow in its
orbit enough that after 1 year, its position will be off by about
the width of an atom. Adding up the growing deficit, it would take
180 million years for Mars to be out of position by 2.5
centimeters (1.0 inches). That is the cost, and, on behalf of Dawn
and all who share in the eager anticipation of the mysteries it
will reveal in the asteroid belt, we express our gratitude to Mars
for its upcoming sacrifice!
 
The control team's best estimate now is that Dawn's closest
encounter with Mars will occur at about 4:29 pm PST on February
17. In the next log, we will cover some of the spacecraft's
activities during its short visit, but we conclude this one with a
note about the plans. Many spacecraft have visited this intriguing
planet already, and it has been studied extensively from orbit and
from the surface for years and years. During its brief passage,
Dawn cannot learn much that is new. On the other hand, Mars is so
well characterized and familiar that it provides a useful
reference for calibrating Dawn's scientific instruments. As we
will see, the calibration plan precludes obtaining the highest
resolution images that might otherwise be attempted. Such a
strategy may seem surprising to all those who appreciate
spectacular pictures of Mars, but, of course, there are already
many many such images, and future missions will produce even more
that will continue to captivate and inspire us.

The instrument calibrations will be a nice bonus, but if Dawn
ended up flying by Mars and conducting no calibrations whatsoever,
as long as the trajectory targeting were correct, everyone on the
project would consider it a success, because the gravity assist is
all that is required for the mission to forge ahead to its goal of
unlocking exciting secrets deep in the asteroid belt. Dawn's focus
is on preparing for the unknowns of Vesta and Ceres rather than
the knowns of Mars.


Dawn is 4.6 million kilometers (2.9 million miles) from Mars. It
is 358 million kilometers (222 million miles) from Earth, or 900
times as far as the moon and 2.41 times as far as the Sun. Radio
signals, traveling at the universal limit of the speed of light,
take 40 minutes to make the round trip.
Received on Thu 29 Jan 2009 01:25:22 PM PST