Posts Tagged ‘trajectory’

So Close, Yet So Far Away: Dawn’s Trajectory Explained

Monday, March 31st, 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
Artist’s concept depicting the Dawn spacecraft thrusting with its ion propulsion system as it travels from Vesta (lower right) to Ceres (upper left). The galaxies in the background are part of the Virgo supercluster. Dawn, Vesta and Ceres are currently in the constellation Virgo from the perspective of viewers on Earth. Image credit: NASA/JPL
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Dear Correspondawnts,

Powering its way through deep space, Dawn draws ever closer to dwarf planet Ceres. To reach its destination, the interplanetary spaceship gently reshapes its path around the sun with its extraordinary ion propulsion system. In about a year, the spacecraft will gracefully slip into orbit so it can begin to unveil the nature of the mysterious world of rock and ice, an intriguing protoplanetary remnant from the dawn of the solar system.

Even as Dawn ascends the solar system hill, climbing farther and farther from the sun, penetrating deeper into the main asteroid belt between Mars and Jupiter, its distance to Earth is shrinking. This behavior may be perplexing for readers with a geocentric bias, but to understand it, we can take a broader perspective.

The sun is the conductor of the solar system symphony. Its gravity dictates the movements of everything that orbits it: Earth as well as the other planets, Vesta, Ceres, and myriad smaller objects, including asteroids and Dawn. (Actually, the gravity of every single body affects how all of the others move, but with more than 99 percent of the entire solar system’s mass concentrated in the gargantuan sun, it dominates the gravitational landscape.)

Whether it is for a planet or Dawn orbiting the sun, a spacecraft or moon orbiting a planet, the sun or other stars orbiting the Milky Way (the Milky Way galaxy, that is, not your correspondent’s cat Milky Way), or the Milky Way galaxy orbiting the Virgo supercluster of galaxies (home to an appreciable 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 line. 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 course, forcing it to curve; if you release the string, the weight’s natural motion would take it away in a straight line (we are ignoring here the effect of Earth’s gravity on the weight).

The force of gravity dwindles as the distance increases, so the sun pulls harder on a nearby body than on a farther one. Therefore, to remain in orbit, to balance the relentless gravitational lure, the closer object must travel at higher speed, resisting the stronger attraction. The same effect applies at Earth. Satellites that orbit very close (including, for example, the International Space Station, 250 miles, or 400 kilometers, above the surface) must streak around the planet at about 17,000 mph (7.6 kilometers per second) to avoid being drawn down. The moon, orbiting almost a thousand times farther above, needs only to travel at less than 2300 mph (about 1.0 kilometers per second) to balance Earth’s weaker hold at its remote location.

For that reason, Mercury zips around the sun faster than any of the other planets. Mars travels more slowly than Earth, and the still more distant residents of the asteroid belt, whether natural (all of them but one) or a product of human ingenuity (one: Dawn), proceed at an even more leisurely pace. As Earth makes its relatively rapid annual trip around the sun, the distance to the spacecraft that left it behind in 2007 alternately shrinks and grows.

We can visualize this with one of the popular models of clocks available in the Dawn gift shop on your planet, in which the hour hand is longer than the minute hand. Imagine the sun as being at the center of the clock. The tip of the short minute hand represents Earth, and the end of the hour hand represents Dawn. Some of the time (such as between noon and shortly after 12:30), the distance between the ends of the hands increases. Then the situation reverses as the faster minute hand begins moving closer and closer to the hour hand as the time approaches about 1:05.

The Dawn spacecraft's trajectory
This graphic shows the Dawn spacecraft’s interplanetary trajectory from launch through its arrival at Ceres next year. The positions of the spacecraft and Earth are shown on April 10, 2014, when their independent orbits bring them relatively close together. Image credit: NASA/JPL-Caltech

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Earth and Dawn are exhibiting the same repetitive behavior. Of course, their relative motion is more complicated than that of the clock hands, because Dawn’s ion thrusting is constantly changing its solar orbit (and so the distance and speed at which it loops around the sun), but the principle is the same. They have been drawing closer since August 2013. Earth, coming from behind, is now about to pass Dawn and move ahead. The stalwart probe will not even take note however, as its sights remain firmly set on an unexplored alien world.

On April 10, the separation will be 1.56 AU (1.56 times the average distance between Earth and the sun, which means 145 million miles, or 233 million kilometers), an almost inconceivably large distance (well in excess of half a million times farther than the International Space Station, which orbits Earth, not the sun) but less than it has been since September 2011. (The skeptical reader may verify this by reviewing the concluding paragraph of each log in the intervening months.) Enjoy the upcoming propinquity while you can! As the ship sails outward from the sun toward Ceres, it will never again be this close to its planet of origin. The next time Earth, taking an inside track, overtakes it, in July 2015 (by which time Dawn will be orbiting Ceres), they will only come within 1.94 AU (180 million miles, or 290 million kilometers) of each other.

By the way, Vesta, the endlessly fascinating protoplanet Dawn unveiled in 2011-2012, will be at its smallest separation from Earth of 1.23 AU (114 million miles, or 183 million km) on April 18. Ceres, still awaiting a visitor from Earth, despite having first been glimpsed from there in 1801, will attain its minimum distance on April 15, when it will be 1.64 AU (153 million miles, or 246 million km) away. It should not be a surprise that Dawn’s distance is intermediate; it is between them as it journeys from one to the other.

Finder chart showing the locations of Vesta and Ceres
This finder chart can help you locate Vesta and Ceres (and even Dawn, although it is too small to see) in the constellation Virgo. Click it for a larger version. Image credit: Sky & Telescope Magazine
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Not only is each one nearly at its shortest geocentric range, but from Earth’s point of view, they all appear to be near each other in the constellation Virgo. In fact, they also look close to Mars, so you can locate these exotic worlds (and even the undetectably small spacecraft) in the evening sky by using the salient red planet as a signpost. In June, the coincidental celestial alignment will make Vesta and Ceres appear to be separated by only one third the diameter of the full Moon, although these behemoths of the asteroid belt will be 0.57 AU (52 million miles, or 85 million kilometers) from each other.

We mentioned above that by constantly modifying its orbit under the persistent pressure of its ion engine, Dawn complicates the simple clock-like behavior of its motion relative to Earth. On Halloween 2012, we were treated to the startling fact that to rendezvous with Ceres, at a greater distance from the sun, Dawn had to come in toward the sun for a portion of its journey; quite a trick! In that memorable log (which is here, for those readers who didn’t find every detail to be so memorable), we observed that it would not be until May 2014 that Dawn would be as far from the sun as it was on Nov. 1, 2012. Sure enough, having faithfully performed all of the complex and intricate choreography since then, it will fly to more than 2.57 AU from the solar system’s star in May, and it will continue heading outward.

With the sun behind it and without regard to where Earth or most other residents of the solar system are in their orbits, Dawn rises to ever greater heights on its extraordinary expedition. Distant though it is, the celestial ambassador is propelled by the burning passion for knowledge, the powerful yearning to reach beyond the horizon, and the noble spirit of adventure of the inhabitants of faraway Earth. The journey ahead presents many unknowns, promising both great challenges and great rewards. That, after all, is the reason for undertaking it, for such voyages enrich the lives of all who share in the grand quest to understand more about the cosmos and our humble place in it.

Dawn is 11 million miles (18 million kilometers) from Ceres. It is also 1.57 AU (146 million miles, or 235 million kilometers) from Earth, or 625 times as far as the moon and 1.57 times as far as the sun today. Radio signals, traveling at the universal limit of the speed of light, take 26 minutes to make the round trip.

› Read more from Marc Rayman’s 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


For Dawn, a Time to Thrust and and a Time to Coast

Thursday, October 31st, 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 All Hallows’ Dawns,

Deep in the main asteroid belt between Mars and Jupiter, Dawn is continuing its smooth, silent flight toward dwarf planet Ceres. Far behind it now is the giant protoplanet Vesta, which the spacecraft transformed from a tiny splotch in the night sky to an exotic and richly detailed world.

The voyage from Vesta to Ceres will take the pertinacious probe 2.5 years. The great majority of spacecraft coast most of the time (just as planets and moons do), each one following a trajectory determined principally by whatever momentum they started with (usually following release from a rocket) and the gravitational fields of the sun and other nearby, massive bodies. In contrast, Dawn spends most of its time thrusting with its ion propulsion system. The gentle but efficient push from the high velocity xenon ions gradually reshapes its orbit around the sun. In September 2012, as it departed Vesta after 14 months of scrutinizing the second most massive resident of the asteroid belt, Dawn’s heliocentric orbit was the same as the rocky behemoth’s. Now they are very far apart, and by early 2015, the robotic explorer’s path will be close enough to Ceres’s that they will become locked in a gravitational embrace.

Without ion propulsion, Dawn’s unique mission to orbit two extraterrestrial destinations would be impossible. No other spacecraft has attempted such a feat. To accomplish its interplanetary journey, the spaceship has thrust more than 96 percent of the time since propelling itself away from Vesta last year. Whenever it points its ion engine in the direction needed to rendezvous with Ceres, its main antenna cannot also be aimed at Earth. Dawn functions very well on its own, however, communicating only occasionally with its terrestrial colleagues. Once every four weeks, it interrupts thrusting to rotate so it can use its 5-foot (1.52-meter) antenna to establish contact with NASA’s Deep Space Network, receiving new instructions from the Dawn operations team at JPL and transmitting a comprehensive report on all its subsystems. Then it turns back to the orientation needed for thrusting and resumes its powered flight.

During its years of interplanetary travel, Dawn has reliably followed a carefully formulated flight plan from Earth past Mars to Vesta and now from Vesta to Ceres. We discussed some of the principles underlying the development of the complex itinerary in a log written when Dawn was still gravitationally anchored to Earth. To carry out its ambitious adventure, Dawn should thrust most of the time, but not all of the time. Indeed, at some times, thrusting would be unproductive.

We will not delve into the details here, but remember that Dawn is doing more than ascending the solar system hill, climbing away from the sun. More challenging than that is making its orbit match the orbit of its targets so that it does not fly past them for a brief encounter as some other missions do. Performing its intricate interplanetary choreography requires exquisite timing with the grace and delicacy of the subtly powerful ion propulsion.

Of course Dawn does not thrust much of the time it is in orbit at Vesta and Ceres; rather, its focus there is on acquiring the precious pictures and other measurements that reveal the detailed nature of these mysterious protoplanets. But even during the interplanetary flight, there are two periods in the mission in which it is preferable to coast. Sophisticated analysis is required to compute the thrusting direction and schedule, based on factors ranging from the physical characteristics of the solar system (e.g., the mass of the sun and the masses and orbits of Earth, Mars, Vesta, Ceres and myriad other bodies that tug, even weakly, on Dawn) to the capabilities of the spacecraft (e.g., electrical power available to the ion thrusters) to constraints on when mission planners will not allow thrusting (e.g., during spacecraft maintenance periods).

The first interval that interplanetary trajectory designers designated as “optimal coast” was well over four years and 1.8 billion miles (2.8 billion kilometers) ago. Dawn coasted from October 31, 2008, to June 8, 2009. During that time, the ship took some of Mars’s orbital energy to help propel itself toward Vesta. (In exchange for boosting Dawn, Mars slowed down by an amount equivalent to about 1 inch, or 2.5 centimeters, in 180 million years.)

The second and final interval when coasting is better than thrusting begins next month. From Nov. 11 to Dec. 9, Dawn will glide along in its orbit around the sun without modifying it. The timing of this coast period is nearly as important to keeping the appointment with Ceres as is the timing of the thrusting. In next month’s log, we will describe some of the special assignments the sophisticated robot will perform instead of its usual quiet cruise routine of accelerating and emitting xenon ions. We also will look ahead to some interesting celestial milestones and alignments in December.

While the spacecraft courses through the asteroid belt, the flight team continues refining the plans for Ceres. In logs in December and several months in 2014, we will present extensive details of those plans so that by the time Dawn begins its mission there, you will be ready to ride along and share in the experience.

In the meantime, as the stalwart ship sails on, it is propelled not only by ions but also by the promise of exciting new knowledge and the prospects of a thrilling new adventure in exploring an uncharted alien world.

Dawn is 16 million miles (26 million kilometers) from Vesta and 25 million miles (39 million kilometers) from Ceres. It is also 3.07 AU (286 million miles, or 460 million kilometers) from Earth, or 1,200 times as far as the moon and 3.10 times as far as the sun today. Radio signals, traveling at the universal limit of the speed of light, take 51 minutes to make the round trip.

– Dr. Marc D. Rayman

P.S. This log is posted early enough to allow time for your correspondent to don his Halloween costume. In contrast to last year’s simple (yet outlandish) costume, this year’s will be more complex. He is going in double costume, disguised as someone who is only pretending to be passionate about the exploration of the cosmos and the rewards of scientific insight.

› Read more entries from Marc Rayman’s Dawn Journal