Posts Tagged ‘orbits’

Survey Orbit: A Truly Extaordinary View

Tuesday, June 3rd, 2014

By Marc Rayman
As NASA’s Dawn spacecraft makes its journey to its second target, the dwarf planet Ceres, Marc Rayman, Dawn’s chief engineer, shares a monthly update on the mission’s progress.

Dear Dawnosaurs,

Silently streaking through the main asteroid belt, emitting a blue-green beam of xenon ions, Dawn continues its ambitious interplanetary expedition. On behalf of creatures on distant Earth who seek not only knowledge and insight but also bold adventure, the spacecraft is heading toward its appointment with Ceres. In about 10 months, it will enter orbit around the ancient survivor from the dawn of the solar system, providing humankind with its first detailed view of a dwarf planet.

This month we continue with the preview of how Dawn will explore Ceres. In December we focused on the “approach phase,” and in January we described how the craft spirals gracefully into orbit with its extraordinary ion propulsion system. The plans for the first observational orbit (with a marvelously evocative name for a first examination of an uncharted world: RC3 — is that cool, or what?), at an altitude of 8,400 miles (13,500 kilometers), were presented in FebruaryLast month, we followed Dawn on its spiral descent from each orbital altitude to the next, with progressively lower orbits providing better views than the ones before. Now we can look ahead to the second orbital phase, survey orbit.

Survey orbit

This figure shows Dawn’s second observational orbit, “survey orbit,” at the same scale as the size of Ceres. At an altitude of 2,730 miles (4,400 kilometers), the spacecraft will make seven revolutions in about three weeks. Image credit: NASA/JPL-Caltech
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In survey orbit, Dawn will make seven revolutions at an altitude of about 2,730 miles (4,400 kilometers). At that distance, each orbit will take three days and three hours. Mission planners chose an orbit period close to what they used for survey orbit at Vesta, allowing them to take advantage of many of the patterns in the complex choreography they had already developed. Dawn performed it so beautifully that it provides an excellent basis for the Ceres encore. Of course, there are some adjustments, mostly in the interest of husbanding precious hydrazine propellant in the wake of the loss of two of the spacecraft’s four reaction wheels. (Although such a loss could have dire consequences for some missions, the resourceful Dawn team has devised a plan that can achieve all of the original objectives regardless of the condition of the reaction wheels.)

We had a preview of survey orbit at Vesta four years ago, and we reviewed the wonderfully successful outcome in September 2011. When we develop the capability to travel backwards in time, we will insert a summary of what occurred in survey orbit at Ceres here: _______…… Well, nothing yet. So, let’s continue with the preview.

As in all phases at Ceres (and Vesta), Dawn follows what space trajectory experts (and geeks) call a polar orbit. The ship’s course will take it above the north pole, and then it will sail south over the side bathed in the light of the sun. After flying over the south pole, Dawn will head north. Although the surface beneath it will be dark, the spacecraft will be high enough that it will not enter the dwarf planet’s shadow. The distant sun will constantly illuminate the large solar arrays.

The leisurely pace in survey orbit allows the explorer to gather a wealth of data during the more than 37 hours on the day side. It will train its science camera and visible and infrared mapping spectrometer (VIR) on the surface lit by the sun. The camera will collect hundreds of images using all seven of its color filters. It will reveal details three times finer than it observed in RC3 orbit and 70 times sharper than the best we have from the Hubble Space Telescope. VIR will acquire millions of spectra to help scientists determine the minerals present as well as the temperature and other properties of the surface. While the sensors are pointed at the surface, the main antenna cannot simultaneously be aimed at Earth, so the robot will store its pictures and spectra.

One Cerean day, the time it takes Ceres to rotate once on its axis, is a little over nine hours. (For comparison, Earth, as some of its residents and visitors know, takes 24 hours. Jupiter turns in just under 10 hours, Vesta in five hours and 21 minutes, and your correspondent’s cat Regulus in about 0.5 seconds when chasing a laser spot.) So as Dawn travels from the north pole to the south pole, Ceres will spin underneath it four times. Dawn will be close enough that even the wide field of view of its camera won’t capture the entire disc below, from horizon to horizon, but over the course of the seven orbits, the probe will see most of the surface. As in developing the plan for Vesta, engineers (like certain murine rodents and male humans) are keenly aware that as careful, as thorough, and as diligent as they are, their schemes don’t always execute perfectly. In the unknown, forbidding depths of space with a complex campaign to carry out, glitches can occur and events can go awry. The plan is designed with the recognition that some observations will not be achieved, but those that are promise great rewards.

Artist's concept of Dawn orbiting Ceres

Artist’s concept of Dawn in its survey orbit at dwarf planet Ceres. Image credit: NASA/JPL-Caltech

Most of the time, the spacecraft will gaze straight down at the alien terrain immediately beneath it. But on the first, second, and fourth passages over the day side of Ceres, it will spend some of the time looking at the limb against the blackness of space. Pictures with this perspective will not only be helpful for establishing the exact shape of the dwarf planet but they also will provide some very appealing views for eager sightseers on Earth.

In addition to using the camera and VIR, Dawn will measure space radiation with its gamma ray and neutron detector (GRaND). GRaND will still be too far from Ceres to sense the nuclear particles emanating from it, but recording the radiation environment will provide a valuable context for the sensitive measurements it will make at lower altitudes.

When Dawn’s orbit takes it over the dark side, it will turn away from the dwarf planet it is studying and toward the planet it left in 2007 where its human colleagues still reside. With its 5-foot (1.52-meter) main antenna, it will spend most of the day and a half radioing its precious findings across uncounted millions of miles (kilometers) of interplanetary space. (Well, you won’t have to count them, but we will.)

In addition to the instrument data it encodes, Dawn’s radio signal will allow scientists and engineers to measure how massive Ceres is. By observing the Doppler shift (the change in frequency caused by the spacecraft’s motion), they can determine how fast the ship moves in orbit. Timing how long the signals (traveling at the universal limit of the speed of light) take to make the round trip, navigators can calculate how far the probe is and hence where it is in its orbit. Combining these (and including other information as well) allows them to compute how strongly Ceres pulls on its orbital companion. The strength of its gravitational force reveals its heft.

By the end of survey orbit, Dawn will have given humankind a truly extraordinary view of a dwarf planet that has been cloaked in mystery despite more than 200 years of telescopic studies. As the exotic world of rock and ice begins to yield its secrets to the robotic ambassador from Earth, we will be transported there. We will behold new landscapes that will simultaneously quench our thirst for exploration and ignite our desire for even more. It is as humankind reaches ever farther into the universe that we demonstrate a part of what it means to be human, combining our burning need for greater understanding with our passion for adventure and our exceptional creativity, resourcefulness and tenacity. As we venture deeper into space, we discover much of what lies deep within ourselves.

Dawn is 7.2 million miles (12 million kilometers) from Ceres. It is also 1.87 AU (174 million miles, or 280 million kilometers) from Earth, or 695 times as far as the moon and 1.84 times as far as the sun today. Radio signals, traveling at the universal limit of the speed of light, take 31 minutes to make the round trip.

› Continue reading Marc Rayman’s May 31, 2014, Dawn Journal


Riding the Spiral: Navigating a New World

Wednesday, April 30th, 2014

By Marc Rayman
As NASA’s Dawn spacecraft makes its journey to its second target, the dwarf planet Ceres, Marc Rayman, Dawn’s chief engineer, shares a monthly update on the mission’s progress.

Artist's concept of the Dawn spacecraft
Dawn will use its ion propulsion system to change orbits at Ceres, allowing it to observe the dwarf planet from different vantage points. Image credit: NASA/JPL-Caltech
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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.

Illustration of Dawn's orbits from RC3 to survey orbit
RC3 to survey: Dawn will make five spiral loops during the month it will take to fly from its RC3 orbit (at 8,400 miles, or 13,500 kilometers) to survey orbit (at 2,700 miles, or 4,400 kilometers). Image credit: NASA/JPL-Caltech
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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.

Illustration of Dawn's orbits from HAMO to LAMO
HAMO to LAMO: Dawn will complete 160 revolutions in two months as it follows a tight spiral from HAMO (at 910 miles, or 1,470 kilometers) to LAMO (at 230 miles, or 375 kilometers). Image credit: NASA/JPL-Caltech
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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’ 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’ gravity field and the fields of those other worlds: Ceres’ 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.

› Continue reading Marc Rayman’s April 30, 2014, Dawn Journal


A Preview of Upcoming Attractions: Dawn Meets Ceres

Friday, February 28th, 2014

By Marc Rayman
As NASA’s Dawn spacecraft makes its journey to its second target, the dwarf planet Ceres, Marc Rayman, Dawn’s chief engineer, shares a monthly update on the mission’s progress.

Artist's concept of the Dawn spacecraft at the protoplanet Ceres
This artist’s concept of NASA’s Dawn spacecraft shows the craft orbiting high above Ceres, where the craft will arrive in early 2015 to begin science investigations. Image credit: NASA/JPL-Caltech
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Dear Ardawnt Readers,

Continuing its daring mission to explore some of the last uncharted worlds in the inner solar system, Dawn remains on course and on schedule for its rendezvous with dwarf planet Ceres next year. Silently and patiently streaking through the main asteroid belt between Mars and Jupiter, the ardent adventurer is gradually reshaping its orbit around the Sun with its uniquely efficient ion propulsion system. Vesta, the giant protoplanet it unveiled during its spectacular expedition there in 2011-2012, grows ever more distant.

In December, and January, we saw Dawn’s plans for the “approach phase” to Ceres and how it will slip gracefully into orbit under the gentle control of its ion engine. Entering orbit, gratifying and historic though it will be, is only a means to an end. The reason for orbiting its destinations is to have all the time needed to use its suite of sophisticated sensors to scrutinize these alien worlds.

Illustration of Dawn's approach phase and RC3 orbit
Following its gravitational capture by Ceres during the approach phase, Dawn will continue to use its ion propulsion system to spiral to the RC3 orbit at an altitude of 8,400 miles (13,500 kilometers). Image credit: NASA/JPL-Caltech
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As at Vesta, Dawn will take advantage of the extraordinary capability of its ion propulsion system to maneuver extensively in orbit at Ceres. During the course of its long mission there, it will fly to four successively lower orbital altitudes, each chosen to optimize certain investigations. (The probe occupied six different orbits at Vesta, where two of them followed the lowest altitude. As the spacecraft will not leave Ceres, there is no value in ascending from its fourth and lowest orbit.) All of the plans for exploring Ceres have been developed to discover as much as possible about this mysterious dwarf planet while husbanding the precious hydrazine propellant, ensuring that Dawn will complete its ambitious mission there regardless of the health of its reaction wheels.

All of its orbits at Ceres will be circular and polar, meaning the spacecraft will pass over the north pole and the south pole, so all latitudes will come within view. Thanks to Ceres’s own rotation, all longitudes will be presented to the orbiting observer. To visualize this, think of (or even look at) a common globe of Earth. A ring encircling it represents Dawn’s orbital path. If the ring is only over the equator, the spacecraft cannot attain good views of the high northern and southern latitudes. If, instead, the ring goes over both poles, then the combined motion of the globe spinning on its axis and the craft moving along the ring provides an opportunity for complete coverage.

Dawn will orbit in the same direction it did at Vesta, traveling from north to south over the side illuminated by the distant Sun. After flying over the south pole, it will head north, the surface directly beneath it in the dark of night. When it travels over the north pole, the terrain below will come into sunlight and the ship will sail south again.

Dawn’s first orbital phase is distinguished not only by providing the first opportunity to conduct intensive observations of Ceres but also by having the least appealing name of any of the Ceres phases. It is known as RC3, or the third “rotation characterization” of the Ceres mission. (RC1 and RC2 will occur during the approach phase, as described in December.)

During RC3 in April 2015, Dawn will have its first opportunity for a global characterization of its new residence in the asteroid belt. It will take pictures and record visible and infrared spectra of the surface, which will help scientists determine its composition. In addition to learning about the appearance and makeup of Ceres, these observations will allow scientists to establish exactly where Ceres’s pole points. The axis Earth rotates around, for example, happens to point very near a star that has been correspondingly named Polaris, or the North Star. [Note to editors of local editions: You may change the preceding sentence to describe wherever the axis of your planet points.] We know only roughly where Ceres’s pole is from our telescopic studies, but Dawn’s measurements in RC3 will yield a much more accurate result. Also, as the spacecraft circles in Ceres’s gravitational hold, navigators will measure the strength of the gravitational pull and hence its overall mass.

RC3 will be at an orbital altitude of about 8,400 miles (13,500 kilometers). From there, the dwarf planet will appear eight times larger than the moon as viewed from Earth, or about the size of a soccer ball seen from 10 feet (3.1 meters). At that distance, Dawn will be able to capture the entire disk of Ceres in its pictures. The explorer’s camera, designed for mapping unfamiliar extraterrestrial landscapes from orbit, will see details more than 20 times finer than we have now from the Hubble Space Telescope.

Although all instruments will be operated in RC3, the gamma-ray and neutron detector (GRaND) will not be able to detect the faint nuclear emissions from Ceres when it is this far away. Rather, it will measure cosmic radiation. In August we will learn more about how GRaND will measure Ceres’s atomic composition when it is closer.

It will take about 15 days to complete a single orbital revolution at this altitude. Meanwhile, Ceres turns on its axis in just over nine hours (more than two and a half times faster than Earth). Dawn’s leisurely pace compared to the spinning world beneath it presents a very convenient way to map it. It is almost as if the probe hovers in place, progressing only through a short arc of its orbit as Ceres pirouettes helpfully before it.

When Dawn is on the lit side of Ceres over a latitude of about 43 degrees north, it will point its scientific instruments at the unfamiliar, exotic surface. As Ceres completes one full rotation, the robot will fill its data buffers with as much as they can hold, storing images and spectra. By then, most of the northern hemisphere will have presented itself, and Dawn will have traveled to about 34 degrees north latitude. The spacecraft will then aim its main antenna to Earth and beam its prized findings back for all those who long to know more about the mysteries of the solar system. When Dawn is between 3 degrees north and 6 degrees south latitude, it will perform the same routine, acquiring more photos and spectra as Ceres turns to reveal its equatorial regions. To gain a thorough view of the southern latitudes, it will follow the same strategy as it orbits from 34 degrees south to 43 degrees south.

When Dawn goes over to the dark side, it will still have important measurements to make (as long as Darth Vader does not interfere). While the surface immediately beneath it will be in darkness, part of the limb will be illuminated, displaying a lovely crescent against the blackness of space. Both in the southern hemisphere and in the northern, the spacecraft will collect more pictures and spectra from this unique perspective. Dawn’s orbital dance has been carefully choreographed to ensure the sensitive instruments are not pointed too close to the Sun.

› Continue reading Marc Rayman’s February 2014 Dawn Journal


To Be in the Right Place, Dawn Catches Up With Time

Wednesday, May 1st, 2013

By Marc Rayman
As NASA’s Dawn spacecraft makes its journey to its second target, the dwarf planet Ceres, Marc Rayman, Dawn’s chief engineer, shares a monthly update on the mission’s progress.

The Dawn spacecraft's orbits
In this graphic of Dawn’s interplanetary trajectory, the thin solid lines represent the orbits of Earth, Mars, Vesta and Ceres. After leaving Vesta, Dawn’s orbit temporarily takes it closer to the Sun than Vesta, although in this view they are so close together the difference is not visible because of the thickness of the lines. Dawn will remain in orbit around Ceres at the end of its primary mission. Image credit: NASA/JPL-Caltech

Dear Dawnscerning Readers,

Nearly three times as far from Earth as the sun is, the Dawn spacecraft is making very good progress on its ambitious trek from Vesta to Ceres. After a spectacular adventure at the second most massive resident of the main asteroid belt between Mars and Jupiter, Dawn used its extraordinary ion propulsion system to leave it behind and undertake the long journey to a dwarf planet.

Ceres orbits the sun outside Vesta’s orbit, yet Dawn is now closer to the sun than both of these alien worlds. How can it be that as the probe climbs from one to the other, it seems to be falling inward? Perhaps the answer lies in the text below; let’s venture on and find out!

On Halloween we discussed why Dawn is heading in toward the sun, but this question is different. Vesta also is getting closer to the sun, but what’s of interest now is that Dawn, despite its more remote destination, has been approaching the sun more quickly. That earlier log stands out as the best one ever written on this exciting mission in the entire history of October 2012, but if you prefer not to visit it now, we can summarize here the explanation for the spacecraft moving toward the sun. Like all members of the sun’s entourage, Vesta and Ceres follow elliptical orbits, their distances from the master of the solar system growing and shrinking as they loop around it. Even Earth’s orbit, although nearly round, certainly is not perfectly circular. Our planet is a little closer to the sun in the northern hemisphere winter (southern hemisphere summer) than it is in the summer (southern hemisphere winter). Dawn’s orbit is elliptical as well, so it naturally moves nearer to the sun sometimes, and now is such a time. But that does not address why it is currently closer to the sun than Vesta, even though it is seeking out the more distant Ceres.

Because it will orbit Ceres, and not simply fly past it (which would be significantly easier but less valuable), Dawn must make its own orbit around the sun be identical to its target’s. But that is not the entire story. After spending 14 months orbiting Vesta, Dawn’s challenge is more than to change the shape of its orbit to match Ceres’s. The spacecraft also must be at the same place in Ceres’s heliocentric orbit that Ceres itself is.

It would not be very rewarding to follow the same looping path around the sun but always be somewhere else on that path. You can visualize this if you have one of the many defective — er, exotic clocks from the Dawn gift shop on your planet that have two minute hands. If the clock starts with one hand pointed at 12 and another pointed at 1, they will take the same repetitive route, but neither hand will ever catch up with the other. For Dawn’s goal of exploring Ceres, this would not prove satisfying. Therefore, part of the objective of the ion thrusting is to ensure the spacecraft arrives not only on the same heliocentric course as Ceres but is there when Ceres is also.

This is a problem familiar to all readers who have maneuvered in orbit, where the principles of orbital mechanics are the rules of the road. To solve it, we rely on one of the laws that we have addressed many times in these logs: objects in a lower orbit travel faster. We described this in more detail in February, and we can recall the essential idea here. The gravitational attraction of any body, whether it is the sun, Earth, a black hole, or anything else, is greater at shorter ranges. So to balance that strong inward pull, an orbiter is compelled to race around quickly. At higher orbits, where gravity is weaker, a more leisurely orbital pace suffices.

We can take advantage of this characteristic of orbits. If we drop to a slightly lower orbit, we travel along more swiftly. That is precisely what Dawn needs to do in order to ensure that when it finishes expanding and tilting its orbit in 2015 so that it is the same as Ceres’s, it winds up at the same location as its target. This would be like speeding up the minute hand that had begun at the 12, allowing it to catch up with the hand that would otherwise always be leading it.

› Continue reading Marc Rayman’s Dawn Journal


A Hard Day’s Flight: Dawn Achieves Orbital Velocity

Friday, March 1st, 2013

By Marc Rayman
As NASA’s Dawn spacecraft makes its journey to its second target, the dwarf planet Ceres, Marc Rayman, Dawn’s chief engineer, shares a monthly update on the mission’s progress.

Mosaic of Dawn's images of asteroid Vesta
Artist’s concept of NASA’s Dawn spacecraft. Image credit: NASA/JPL-Caltech

Dear Impordawnt Readers,

The indefatigable Dawn spacecraft is continuing to forge through the main asteroid belt, gently thrusting with its ion propulsion system. As it gradually changes its orbit around the sun, the distance to dwarf planet Ceres slowly shrinks. The pertinacious probe will arrive there in 2015 to explore the largest body between the sun and Neptune that has not yet been glimpsed by a visitor from Earth. Meanwhile, Vesta, the fascinating alien world Dawn revealed in 2011 and 2012, grows ever more distant. The mini-planet it orbited and studied in such detail now appears only as a pinpoint of light 15 times farther from Dawn than the moon is from Earth.

Climbing through the solar system atop a column of blue-green xenon ions, Dawn has a great deal of powered flight ahead in order to match orbits with faraway Ceres. Nevertheless, it has shown quite admirably that it is up to the task. The craft has spent more time thrusting and has changed its orbit under its own power more than any other ship from Earth. While most of the next two years will be devoted to still more thrusting, the ambitious adventurer has already accomplished much more than it has left to do. And now it is passing an interesting milestone on its interplanetary trek.

With all of the thrusting Dawn has completed, it has now changed its speed by 7.74 kilometers per second (17,300 mph), and the value grows as the ion thrusting continues. For space enthusiasts from Earth, that is a special speed, known as “orbital velocity.” Many satellites, including the International Space Station, travel at about that velocity in their orbits. So does this mean that Dawn has only now achieved the velocity necessary to orbit Earth? The short answer is no. The longer answer constitutes the remainder of this log.

We have discussed some of these principles before, but they are counterintuitive and questions continue to arise. Rather than send our readers on a trajectory through the history of these logs even more complicated than Dawn’s flight through the asteroid belt, we will revisit a few of the ideas here. (After substantial introspection, your correspondent granted and was granted permission to reuse not only past text but also future text.)

While marking Dawn’s progress in terms of its speed is a convenient description of the effectiveness of its maneuvering, it is not truly a measure of how fast it is moving. Rather, it is a measure of how fast it would be moving under very special (and unrealistic) circumstances. To understand this, we need to look at the nature of orbits in general and Dawn’s interplanetary trajectory in particular.

The overwhelming majority of craft humans have sent into space have remained in the vicinity of Earth, accompanying that planet on its annual revolutions around the sun. All satellites of Earth (including the moon) remain bound to it by its gravity. (Similarly, Dawn spent much of 2011 and 2012 as a satellite of distant Vesta, locked in the massive body’s gravitational grip.) As fast as satellites seem to travel compared to terrestrial residents, from the larger solar system perspective, their incessant circling of Earth means their paths through space are not very different from Earth’s itself. Consider the path of a car racing around a long track. If a fly buzzes around inside the car, to the driver it may seem to be moving fast, but if someone watching the car from a distance plotted the fly’s path, on average it would be pretty much like the car’s.

Everything on the planet and orbiting it travels around the sun at an average of 30 kilometers per second (67,000 mph), completing one full solar orbit every year. To undertake its interplanetary journey and travel elsewhere in the solar system, Dawn needed to break free of Earth’s grasp, and that was accomplished by the rocket that carried it to space more than five years ago. Dawn and its erstwhile home went their separate ways, and the sun became the natural reference for the spacecraft’s position and speed on its voyage in deep space.

Despite the enormous push the Delta II rocket delivered (with affection!) to Dawn, the spacecraft still did not have nearly enough energy to escape from the powerful sun. So, being a responsible resident of the solar system, Dawn has remained faithfully in orbit around the sun, just as Earth and the rest of the planets, asteroids, comets, and other members of the star’s entourage have.

Whether it is for a spacecraft or moon orbiting a planet, a planet or Dawn orbiting the sun, the sun orbiting the Milky Way galaxy, or the Milky Way galaxy orbiting the Virgo supercluster of galaxies (home to a sizeable fraction of our readership), any orbit is the perfect balance between the inward tug of gravity and the inexorable tendency of objects to travel in a straight path. If you attach a weight to a string and swing it around in a circle, the force you use to pull on the string mimics the gravitational force the sun exerts on the bodies that orbit it. The effort you expend in keeping the weight circling serves constantly to redirect its path; if you let go of the string, the weight’s natural motion would carry it away in a straight line (ignoring the effect of Earth’s gravity).

The force of gravity diminishes with distance, so the sun’s pull on a nearby body is greater than on a more distant one. Therefore, to remain in orbit, to balance the relentless tug of gravity, the closer object must travel faster, fighting the stronger pull. The same effect applies at Earth. Satellites that orbit very close (including, for example, the International Space Station, around 400 kilometers, or 250 miles, from the surface) must streak around the planet at about 7.7 kilometers per second (17,000 mph) to keep from being pulled down. The moon, orbiting almost 1000 times farther above, needs only to travel at about 1.0 kilometers per second (less than 2300 mph) to balance Earth’s weaker hold at that distance.

Notice that this means that for an astronaut to travel from the surface of Earth to the International Space Station, it would be necessary to accelerate to quite a high speed to rendezvous with the orbital facility. But then once in orbit, to journey to the much more remote moon, the astronaut’s speed eventually would have to decline dramatically. Perhaps speed tells an incomplete story in describing the travels of a spacecraft, just as it does with another example of countering gravity.

A person throwing a ball is not that different from a rocket launching a satellite (although the former is usually somewhat less expensive and often involves fewer toxic chemicals). Both represent struggles against Earth’s gravitational pull. To throw a ball higher, you have to give it a harder push, imparting more energy to make it climb away from Earth, but as soon as it leaves your hand, it begins slowing. For a harder (faster) throw, it will take longer for Earth’s gravity to stop the ball and bring it back, so it will travel higher. But from the moment it leaves your hand until it reaches the top of its arc, its speed constantly dwindles as it gradually yields to Earth’s tug. The astronaut’s trip from the space station to the moon would be accomplished by starting with a high speed “throw” from the low starting orbit, and then slowing down until reaching the moon.

The rocket that launched Dawn threw it hard enough to escape from Earth, sending it well beyond the International Space Station and even the moon. Dawn’s maximum speed relative to Earth on launch day was so high that Earth could not pull it back. As we saw in the explanation of the launch profile, Dawn was propelled to 11.46 kilometers per second (25,640 mph), well in excess of the space station’s orbital speed given three paragraphs above. But it has remained under the sun’s control.

Now we can think of the general problem of flying elsewhere in space as similar to climbing a hill. For terrestrial hikers, the rewards of ascent come only after doing the work of pushing against Earth’s gravity to reach a higher elevation. Similarly, Dawn is climbing a solar system hill with the sun at the bottom. It started part way up the hill at Earth; and its first rewards were found at a higher elevation, where Vesta, traveling around the sun at only about two thirds of Earth’s speed, revealed its fascinating secrets to the visiting ship. The ion thrusting now is propelling it still higher up the hill toward Ceres, which moves even more slowly to balance the still-weaker pull of the sun.

› Continue reading Marc Rayman’s Dawn Journal for more on how Dawn achieved orbital velocity