Artist concept of NASA's Dawn spacecraft

Dear Dawnniversaries,

Dawn is celebrating the second anniversary of leaving its home planet by engaging in the same function it has performed most of its time in space: with the utmost patience, it is using its ion propulsion system to gradually modify its orbit around the Sun.

In its interplanetary travels, the spacecraft has thrust for a total of about 389 days, or 53% of the time (and about 0.000000008% of the time since the Big Bang). While for most spacecraft, firing a thruster to change course is a special event, it is Dawn’s wont. All this thrusting has cost the craft only 103 kilograms (228 pounds) of its supply of xenon propellant, which was 425 kilograms (937 pounds) on September 27, 2007.

The thrusting so far in the mission has achieved the equivalent of accelerating the probe by 2.62 kilometers per second (5870 miles per hour). As previous logs have described, because of the principles of motion for orbital flight, whether around the Sun or any other gravitating body, Dawn is not actually traveling this much faster than when it launched. But the effective change in speed remains a useful measure of the effect of any spacecraft’s propulsive work. Having accomplished only one-fifth of the thrust time planned for its entire mission, Dawn has already far exceeded the velocity change achieved by most spacecraft. (For a comparison with probes that enter orbit around Mars, refer to a previous log.)

Since launch, our readers who have remained on or near Earth have completed 2 revolutions around the Sun, covering about 1.88 billion kilometers (1.17 billion miles). Orbiting farther from the Sun, and moving at a more leisurely pace, Dawn has traveled 1.57 billion kilometers (980 million miles). As it climbs away from the Sun to match its orbit to that of Vesta, it will continue to slow down to Vesta’s speed. Since Dawn’s launch, Vesta has traveled only 1.18 billion kilometers (730 million miles).

Readers with nothing better to do have already discovered that much of the text in the 3 preceding paragraphs is taken verbatim from the log that commemorated Dawn’s first anniversary of being in space, with the principal changes being that the numbers are updated here. (In addition, most of the humor was removed to comply with a request from the Glum Legion of Ardent Dawnniversaries). This is not a result of any more otiosity than normally displayed by your correspondent; rather, comparing the beginning of this log with last year’s may be helpful for measuring the progress in the intervening time. Of course, most of the last 12 months was devoted to coasting, and the gravitational boost from Mars is not reflected in the effect of the ion thrusting, but the comparison may be illuminating for some readers. This also provides a handy preview of the beginning of the September 27, 2010 log. [Note to self: Perhaps there really is an option here for greater lassitude. Think about that after taking a nap.]

Another way to investigate the progress of the mission is to chart how Dawn’s orbit around the Sun has changed. This discussion will culminate with a few more numbers than we usually include, and readers who prefer not to indulge may skip this material, leaving that much more for the grateful Numerivores.

Orbits are ellipses (like flattened circles, or ovals in which the ends are of equal size). So as members of the solar system family follow their paths around the Sun, they sometimes move closer and sometimes move farther from it. For thinking about these distances, we may remind ourselves once again of the convenient unit of measure in the solar system, the astronomical unit (AU).

In addition to orbits being characterized by shape, or equivalently by the amount of flattening (that is, the deviation from being a perfect circle), and by size, they may be described in part by how they are oriented in space. Using the bias of terrestrial astronomers, the plane of Earth’s orbit around the Sun is a good reference. Other planets and interplanetary spacecraft travel in orbits that are tipped at some angle to that. Vesta and Ceres do not orbit the Sun in the same plane that Earth does, and Dawn must match its orbit to that of its targets. (The major planets orbit closer to the plane of Earth’s orbit, and no spacecraft has had to venture as far out of that plane to orbit another body as Dawn will.)

Now we can see how Dawn has been doing by considering the size and shape (together expressed by the minimum and maximum distances from the Sun) and the angle of its orbit on its anniversaries. (Experts readily recognize that there is more to describing an orbit than these parameters. Our policy is to link to the experts’ sites when their readership extends to 1 more elliptical galaxy than ours does.)

The table below shows what the orbit would be if the spacecraft terminated thrusting on its anniversaries; the orbits of its destinations, Vesta and Ceres, are included for comparison. Of course, when Dawn was on the launch pad on September 27, 2007, its orbit around the Sun was exactly Earth’s orbit. After launch, it had its own orbit.

Minimum distance from the Sun (AU) Maximum distance from the Sun (AU) Angle from Earth’s orbit
Dawn’s orbit on Sept. 27, 2007 (before launch) 0.98 1.02 0.0°
Dawn’s orbit on Sept. 27, 2007 (after launch) 1.00 1.62 0.6°
Dawn’s orbit on Sept. 27, 2008 1.21 1.68 1.4°
Dawn’s orbit on Sept. 27, 2009 1.42 1.87 6.2°
Vesta’s orbit 2.15 2.57 7.1°
Ceres’s orbit 2.54 2.99 10.6°

Readers may disregard the table or gaze into it for insight or inspiration for as long as they like. The point of it, however, is to illustrate both that Dawn has come a long way since the launch pad, and it has a long journey ahead before it begins its exploration of Vesta.

But the trek will be a little shorter than mission planners had anticipated until quite recently. As we have seen in a previous log, the plan for thrusting depends on how much electrical power will be available to the ion propulsion system, which converts electrical power into thrusting power. Greater electrical power translates into higher (but still exceptionally gentle) thrust.

Last year Dawn’s engineers, who remain on distant Earth, devised a method to calibrate the solar arrays, and the spacecraft dutifully carried it out. The resulting data, combined with an extensive refinement of the mathematical model that predicts solar array power, allowed the team to be confident in increasing the prediction of the future availability of power by up to 10%. Equipped with this crucial information, they could update the plan for thrusting.

Many other factors affect the design of the thrust profile as well. As one example, how effective the thrust is depends on how massive the spacecraft is. Although weightless, Dawn still has mass (the resistance to a change in its velocity), and the greater the mass, the lower the acceleration provided by the ion thruster. This phenomenon is no different from what readers experience frequently even in the gravity of their home planet. The heavier the load you carry, the more gradually you will accelerate, whether the effort is exerted by the muscles in your legs (or wings or tentacles, depending on your species) or the engine in your car (or spaceship). Dawn’s mass decreases as the mission progresses because the ion propulsion system expends xenon and the reaction control system expends hydrazine. By refining predictions for how much of these propellants will be onboard at all times for the rest of the mission, engineers could predict how long it will take Dawn to propel itself into the same orbit around the Sun as Vesta and then later into the same orbit as Ceres.

After an extended set of analyses late in 2008 and the first half of 2009, all the elements needed to update the thrust plan were in place. The seemingly modest improvement in solar array power is by far the dominant one. When all were combined, the result revealed that Dawn’s remarkable maneuvering capability over the course of the mission will be even better than engineers had been counting on. The probe will be able to reach Vesta about 6 weeks earlier than had previously been planned. Moreover, the newfound capability will enable the craft to travel from Vesta to Ceres more quickly, so the deadline for leaving the first world to reach the second on schedule in 2015 is about 6 weeks later.

Together, these changes allow the explorer to increase its planned 9-month stay at Vesta to 12 months. This is of extraordinary benefit to the project. Vesta promises to be a fascinating place to visit, and we know quite well from other solar system adventures that no matter how much data we collect, there is always still more to learn. Mission planners had been working hard to squeeze as much as possible into the precious time they expected Dawn could spend at Vesta, so being able to increase the duration of its residency there by a third makes a tremendous difference. As details continue to be formulated for all the activities necessary to operate at and study this alien world, the additional time will prove extremely valuable in allowing the team to accommodate the glitches that are inevitable in such a complex expedition and to uncover as much of Vesta’s intriguing story as possible.

Dawn is already following the new flight plan, targeting where Vesta will be in July 2011. It is not enough, though, just for them to be in (nearly) the same place at the same time. That would result in a flyby, but our probe will enter orbit around the protoplanet, accompanying it on its orbit around the Sun, just as satellites of Earth remain close by throughout the planet’s solar orbit. The craft will remain with Vesta until July 2012, when it will begin thrusting to Ceres. We have discussed before why flying by (providing only a glimpse of each body) is significantly less challenging than matching orbits (enabling more extensive explorations), a capability that would be essentially impossible without the ion propulsion system. A subsequent log will delve further into this issue, as it is a fundamental feature of this ambitious mission.

As Dawn begins its third year in space, now on its new and better course, much work remains before it can return the scientific bounty it seeks. We hope readers will continue to follow the progress of this bold adventure in the exciting years to come.

Dawn is 1.50 AU (225 million kilometers or 140 million miles) from Earth, or 555 times as far as the moon and 1.50 times as far as the Sun. Radio signals, traveling at the universal limit of the speed of light, take 25 minutes to make the round trip.

Dr. Marc D. Rayman
4:34 am PDT September 27, 2009

P.S. The astronomical unit has been mentioned in these logs frequently enough that we will include that convenient unit of measurement from now on in the famously unimaginative concluding paragraph. It might appear redundant to present the distance from Earth both in astronomical units and in terms of how many times as far as the Sun it is. Isn’t that simply 2 different ways to describe exactly the same quantity? Well, no it is not; they are different, although they are close. An astronomical unit is the average distance between Earth and the Sun and hence does not change. The actual distance varies slightly throughout the year, so Earth’s distance from the Sun at any given time may not be precisely the average value of 1.00000000 AU (149,597,871 kilometers or 92,955,629 miles). This would be more apparent if your correspondent did not round off the numbers as dramatically. The details on that closing text are that Dawn is 1.50456971 AU (225,080,425 kilometers or 139,858,224 miles) from Earth. At the same time, Earth is 1.00222102 AU (149,928,510 kilometers or 93,161,078 miles) from the Sun, very close to the average, but not exactly equal to it. So Dawn is 1.50123544 times as far from Earth as the Sun is, given the distance to the Sun now. When rounded off, the distance in astronomical units and the distance in terms of how far the Sun is both come out to 1.50, but we see they are not really equal. Other times of the year, when the actual distance to the Sun is farther from the average, the difference will be apparent. As long as these secrets of the final paragraph are being revealed, here are the rest: the distance relative to the moon is rounded to the nearest multiple of 5, and the travel time for radio signals to the nearest minute. But just for this special occasion: Dawn is 556.865373 times as far as the moon right now, and radio signals take 25 minutes 1.574966 seconds. Approximately. Best regards to the Numerivores.

› Learn more about the Dawn mission


  • Marc Rayman