Marc Rayman • May 06, 2014
Dawn Journal: Explaining Orbit Insertion
Dear Compedawnt Readers,
Less than a year from its rendezvous with dwarf planet Ceres, Dawn is continuing to make excellent progress on its ambitious interplanetary adventure. The only vessel from Earth ever to take up residence in the main asteroid belt between Mars and Jupiter, the spacecraft grows more distant from Earth and from the sun as it gradually closes in on Ceres. Dawn devotes the majority of its time to thrusting with its remarkable ion propulsion system, reshaping its heliocentric path so that by the time it nears Ceres, the explorer and the alien world will be in essentially the same orbit around the sun.
In December, we saw what Dawn will do during the “approach phase” to Ceres early in 2015, and in January, we reviewed the unique and graceful method of spiraling into orbit. We described in February the first orbit (with the incredibly cool name RC3) from which intensive scientific observations will be conducted, at an altitude of 8,400 miles (13,500 kilometers). But Dawn will take advantage of the extraordinary capability of ion propulsion to fly to three other orbital locations from which it will further scrutinize the mysterious world.
Let’s recall how the spacecraft will travel from one orbit to another. While some of these plans may sound like just neat ideas, they are much more than that; they have been proven with outstanding success. Dawn maneuvered extensively during its 14 months in orbit around Vesta. (One of the many discussions of that was in November 2011.) The seasoned space traveler and its veteran crew on distant Earth are looking forward to applying their expertise at Ceres.
As long-time readers of these logs know so well, the ion thrust is uniquely efficient but also extremely low. Ion propulsion provides acceleration with patience. Ultimately the patience pays off, enabling Dawn to accomplish feats far beyond what any other spacecraft has ever had the capability to do, including orbiting two extraterrestrial destinations. The gentle thrust, comparable to the weight of a single sheet of paper, means it takes many weeks to maneuver from one observational orbit to another. Of course, it is worthwhile to spend that much time, because each of the orbital phases is designed to provide an exciting trove of scientific data.
Those of you who have navigated around the solar system, as well as others who have contemplated the nature of orbits without having practical experience, recognize that the lower the orbital altitude, the faster the orbital motion. This important principle is a consequence of gravity’s strength increasing as the distance between the massive body and the orbiting object decreases. The speed has to be higher to balance the stronger gravitational pull. (For a reminder of some of the details, be sure to go here before you go out for your next orbital expedition.)
While Dawn slowly reduces its altitude under the faint pressure of its ion engine, it continues circling Ceres, orbiting in the behemoth’s gravitational grip. The effect of combining these motions is that the path from one altitude to another is a spiral. And as Dawn descends and zips around Ceres faster and faster, the spirals get tighter and tighter.
The first coils around Ceres will be long and slow. After completing its investigations in RC3, the probe will spiral down to “survey orbit,” about 2,700 miles (4,400 kilometers) above the surface. During that month-long descent, it will make only about five revolutions. After three weeks surveying Ceres from that new vantage point, Dawn will follow a tighter spiral down to the (misleadingly named) high altitude mapping orbit (HAMO) at 910 miles (1,470 kilometers). In the six-week trip to HAMO, the craft will wind around almost 30 times. It will devote two months to performing extensive observations in HAMO. And finally as 2015 draws to a close, it will fly an even more tightly wound course to reach its low altitude mapping orbit (LAMO) at 230 miles (375 kilometers), where it will collect data until the end of the mission. The ship will loop around 160 times during the two months to go from HAMO to LAMO. (We will preview the plans for survey orbit, HAMO and LAMO in May, July and August of this year, and if all goes well, we will describe the results in 2015 and 2016.)
Designing the spiral trajectories is a complex and sophisticated process. It is not sufficient simply to activate the thrust and expect to arrive at the desired destination, any more than it is sufficient to press the accelerator in your car and expect to reach your goal. You have to steer carefully (and if you don’t, please don’t drive near me), and so does Dawn. As the ship revolves around Ceres, it must constantly change the pointing of the blue-green beam of high velocity xenon ions to stay on precisely the desired winding route to the targeted orbit. The mission control team at JPL will program the ship to orient its thruster in just the right direction at the right time to propel itself on the intended spiraling course.
Aiming a thruster in the direction needed to spiral around Ceres requires turning the entire spacecraft. Each thruster is mounted on its own gimbal with a limited range of motion. In normal operation, the gimbal is positioned so that the line of thrust goes through the center of the ship. When the gimbal is swiveled to another direction, the gentle force from the ion engine causes the ship to rotate slowly. This is similar to the use of an outboard motor on a boat. When it is aligned with the centerline of the boat, the craft travels straight ahead. When the motor is turned, it continues to propel the boat but also turns it. In essence, Dawn’s steering of its thrust is accomplished by pivoting the ion engine.
A crucial difference between the boat and our interplanetary ship is that with the former, the farther the motor is turned, the tighter the curving course. (Another difference is that the spacecraft wouldn’t float.) Dawn doesn’t have that liberty. For our craft, the gimballing of the thruster needs to be carefully coordinated with the orbital motion, as if the motorboat operator needed to compensate for a curving current. This has important implications at Ceres. Sophisticated as it is, Dawn knows its own location in orbit only by virtue of information mission controllers install onboard to predict where it will be at any time. That is based on their best computations of Ceres’s gravity, the planned operation of the ion propulsion system, and many other considerations, but it will never be perfectly accurate. Let’s take a look at two of the reasons.
Ceres, like Vesta, Earth, the moon, Mars, and other planets or planetary-type bodies, has a complex gravity field. The distribution of materials of different densities within the interior creates variations in the strength of the gravitational force, so Dawn will feel a slightly changing tug from Ceres as it travels in orbit. But there is a noteworthy difference between Ceres’s gravity field and the fields of those other worlds: Ceres’s field is unknown. We will have to measure it as we go. The subtle irregularities in gravity as Dawn descends will cause small deflections from the planned trajectory. Our ship will be traversing unknown, choppy waters.
Other phenomena will lead to slight discrepancies as well. The ion propulsion system will be responsible for changing the orbit, so even tiny deviations from the intended thrust eventually may build up to have a significant effect. This is no different from any realistic electrical or mechanical system, which is sure to have imperfections. If you planned a trip in which you would drive 60.0 miles (96.6 kilometers) at 60.0 mph (96.6 kilometers per hour), you could expect to arrive in exactly 60.0 minutes. (No surprises there, as it isn’t exactly rocket science.) But even if you maintained the speedometer as close to 60 as you could, it would not be accurate enough to indicate the true speed. If your actual speed averaged 60.4 mph (97.2 kilometers per hour), you would arrive 24 seconds early. Perhaps that difference wouldn’t matter to you (and if it did, you might consider replacing your car with a spaceship), but such minuscule errors, when compounded by Dawn’s repeated spirals around Ceres, would make a difference in achieving its carefully chosen orbit.
As a result of these and other effects, mission controllers will need to adjust the complex flight plan as Dawn travels from one observational orbit to another. So it will thrust for a few days and then stop to allow navigators to get a new fix on its position. When it points its main antenna to Earth, the Doppler shift of its radio signal will reveal its speed, and the time for radio signals (traveling, as all readers know so well, at the universal limit of the speed of light) to make the round trip will yield its distance. Combining those measurements with other data, mission controllers will update the plan for where to point the thruster at each instant during the next phase of the spiral, check it, double check it, and transmit it to the faraway robot, which will then put it into action. This intensive process will be repeated every few days as Dawn maneuvers to lower orbits.
The flight team succeeded brilliantly in performing this kind of work at Vesta, but they will encounter some differences at Ceres. Sunlight is even weaker in that remote part of the asteroid belt. The giant solar arrays will generate less electrical power for the ion propulsion system, so the whisper-like thrust will be even fainter. In addition, Ceres is more massive than Vesta, so its gravitational hold is stronger. Of course, the team has developed plans to account for these and other differences as they guide Dawn from one orbit to another.
The reward for these particularly challenging parts of the mission will be new perspectives on Ceres. The distant landscapes, barely even hinted at by observations for more than two centuries, will come into sharper and sharper focus as Dawn spirals closer. At each new orbital perch, the explorer will reveal exciting new details, allowing new discoveries and new insights. Everyone who is curious about the cosmos is welcome to join the journey as human ingenuity and curiosity take us far, far from home to an uncharted world.
Dawn is 9.2 million miles (15 million kilometers) from Ceres. It is also 1.61 AU (149 million miles, or 241 million kilometers) from Earth, or 620 times as far as the moon and 1.60 times as far as the sun today. Radio signals, traveling at the universal limit of the speed of light, take 27 minutes to make the round trip.
Dr. Marc D. Rayman
4:00 p.m. PDT April 30, 2014
P.S. This is the 100th Dawn Journal, so this seems like a good time to end. This will be the last one.
P.P.S. Until next month.
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