Posts Tagged ‘orbit’

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


It’s All About Grace Under Pressure for Dawn’s Drop Into Orbit

Friday, January 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 at the dwarf planet Ceres
Artist’s concept of NASA’s Dawn spacecraft thrusting with its ion propulsion system as it approaches the dwarf planet Ceres. Image credit: NASA/JPL-Caltech

Dear Rendawnvous,

Dawn is continuing its trek through the main asteroid belt between Mars and Jupiter. Leaving behind a blue-green wake of xenon from its ion propulsion system, its sights are set on dwarf planet Ceres ahead. The journey has been long, but the veteran space traveler (and its support team on distant Earth) is making good progress for its rendezvous early next year.

Last month, we had a preview of many of the activities the probe will execute during the three months that culminate in settling into the first observational orbit at Ceres in April 2015. At that orbit, about 8,400 miles (13,500 kilometers) above the alien landscapes of rock and ice, Dawn will begin its intensive investigations. Nevertheless, even during the “approach phase,” it will often observe Ceres with its camera and one of its spectrometers to gain a better fix on its trajectory and to perform some preliminary characterizations of the mysterious world prior to initiating its in-depth studies. The discussion in December did not cover the principal activity, however, which is one very familiar not only to the spacecraft but also to readers of these logs. The majority of the time in the approach phase will be devoted to continuing the ion-powered flight. We described this before Vesta, but for those few readers who don’t have perfect recall (we know who you are), let’s take another look at how this remarkable technology is used to deliver the adventurer to the desired orbit around Ceres.

Thrusting is not necessary for a spacecraft to remain in orbit, just as the moon remains in orbit around Earth and Earth and other planets remain in orbit around the sun without the benefit of propulsion. All but a very few spacecraft spend most of their time in space coasting, following the same orbit over and over unless redirected by a gravitational encounter with another body. In contrast, with its extraordinarily efficient ion propulsion system, Dawn’s near-continuous thrusting gradually changes its orbit. Thrusting since December 2007 has propelled Dawn from the orbit in which the Delta rocket deposited it after launch to orbits of still greater distance from the sun. The flight profile was carefully designed to send the craft by Mars in February 2009, so our celestial explorer could appropriate some of the planet’s orbital energy for the journey to the more distant asteroid belt, of which it is now a permanent resident. In exchange for Mars raising Dawn’s heliocentric orbit, Dawn lowered Mars’s orbit, ensuring the solar system’s energy account remained balanced.

While spacecraft have flown past a few asteroids in the main belt (although none as large as the gargantuan Vesta or Ceres, the two most massive objects in the belt), no prior mission has ever attempted to orbit one, much less two. For that matter, this is the first mission ever undertaken to orbit any two extraterrestrial destinations. Dawn’s exclusive assignment would be quite impossible without its uniquely capable ion propulsion system. But with its light touch on the accelerator, taking nearly four years to travel from Earth past Mars to Vesta, and more than two and a half years from Vesta to Ceres, how will it enter orbit around Ceres? As we review this topic in preparation for Ceres, bear in mind that this is more than just a cool concept or neat notion. This is real. The remarkable adventurer actually accomplished the extraordinary feats at Vesta of getting into and out of orbit using the delicate thrust of its ion engines.

Whether conventional spacecraft propulsion or ion propulsion is employed, entering orbit requires accompanying the destination on its own orbit around the sun. This intriguing challenge was addressed in part in February 2007. In February 2013, we considered another aspect of what is involved in climbing the solar system hill, with the sun at the bottom, Earth partway up, and the asteroid belt even higher. We saw that Dawn needs to ascend that hill, but it is not sufficient simply to reach the elevation of each target nor even to travel at the same speed as each target; the explorer also needs to travel in the same direction. Probes that leave Earth to orbit other solar system bodies traverse outward from (or inward toward) the sun, but then need to turn in order to move along with the body they will orbit, and that is difficult.

Those of you who have traveled around the solar system before are familiar with the routine of dropping into orbit. The spacecraft approaches its destination at very high velocity and fires its powerful engine for some minutes or perhaps even about an hour, by the end of which it is traveling slowly enough that the planet’s gravity can hold it in orbit and carry it around the sun. These exciting events may range from around 1,300 to 3,400 mph (0.6 to 1.5 kilometers per second). With ten thousand times less thrust than a typical propulsion system on an interplanetary spacecraft, Dawn could never accomplish such a rapid maneuver. As it turns out, however, it doesn’t have to.

Dawn’s method of getting into orbit is quite different, and the key is expressed in an attribute of ion propulsion that has been referred to 63 times (trust or verify; it’s your choice) before in these logs: it is gentle. (This example shows just how gentle the acceleration is.) With the gradual trajectory modifications inherent in ion propulsion, sharp changes in direction and speed are replaced by smooth, gentle curves. The thrust profiles for Dawn’s long interplanetary flights are devoted to the gradual reshaping of its orbit around the sun so that by the time it is in the vicinity of its target, its orbit is nearly the same as that of the target. Rather than hurtling toward Vesta or Ceres, Dawn approaches with grace and elegance. Only a small trajectory adjustment is needed to let its new partner’s gravity capture it, so even that gentle ion thrust will be quite sufficient to let the craft slip into orbit. With only a nudge, it transitions from its large, slow spiral away from the sun to an inward spiral centered around its new gravitational master.

illustration of Dawn's orbit
This graphic shows the planned trek of NASA’s Dawn spacecraft from its launch in 2007 through its arrival at the dwarf planet Ceres in early 2015. Note how Dawn spirals outward to Vesta and then still more to Ceres. Image credit: NASA/JPL-Caltech

To get into orbit, a spacecraft has to match speed, direction and location with its target. A mission with conventional propulsion first gets to the location and then, using the planet’s gravity and its own fuel-guzzling propulsion system, very rapidly achieves the required speed and direction. By spiraling outward from the sun, first to the orbit of Vesta and now to Ceres, Dawn works on its speed, direction and location all at the same time, so they all gradually reach the needed values at just the right time.

To illustrate this facet of the difference between how the different systems are applied to arrive in orbit, let’s imagine you want to drive your car next to another traveling west at 60 mph (100 kilometers per hour). The analogy with the conventional technology would be similar to speeding north toward an intersection where you know the other car will be. You arrive there at the same time and then execute a screeching, whiplash-inducing left turn at the last moment using the brakes, steering wheel, accelerator and adrenaline. When you drive an ion propelled car (with 10 times higher fuel efficiency), you take an entirely different path from the start, one more like a long, curving entrance ramp to a highway. As you enter the ramp, you slowly (perhaps even gently) build speed. You approach the highway gradually, and by the time you have reached the far end of the ramp, your car is traveling at the same speed and in the same direction as the other car. Of course, to ensure you are there when the other car is, the timing is very different from the first method, but the sophisticated techniques of orbital navigation are up to the task.

› Continue reading Marc Rayman’s January 2014 Dawn Journal


NASA’s Dawn Spacecraft Celebrates Six Years in Space

Friday, September 27th, 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.

Artist's concept of the Dawn spacecraft
Artist’s concept of NASA’s Dawn spacecraft between the giant asteroid Vesta and the dwarf planet Ceres. Image credit: NASA/JPL-Caltech

Dear Dawnniversaries,

On the sixth anniversary of leaving Earth to embark on a daring deep-space expedition, Dawn is very, very far from its erstwhile planetary residence. Now humankind’s only permanent resident of the main asteroid belt between Mars and Jupiter, the seasoned explorer is making good progress toward the largest object in that part of the solar system, the mysterious dwarf planet Ceres. The voyage is long, and the intrepid but patient traveler will not reach its next destination until half a year after its seventh anniversary of departing Earth.

On its fifth anniversary, Dawn was still relatively close to Vesta, the giant protoplanet that had so recently held the craft in its gravitational grip. The only probe ever to orbit a main belt asteroid, Dawn spent 14 months (including its fourth anniversary) accompanying Vesta on its way around the sun. After more than two centuries of appearing to astronomers as little more than a fuzzy blob of light among the stars, the second most massive body in the asteroid belt has been revealed as a fascinating, complex, alien world more closely related to terrestrial planets (including Earth) than to typical asteroids.

Most of the ship’s first four years of spaceflight were devoted to using its ion propulsion system to spiral away from the sun, ascending the solar system hill from Earth to Vesta. Now it is working to climb still higher up that hill to Ceres.

For those who would like to track the probe’s progress in the same terms used on previous (and, we boldly predict, subsequent) anniversaries, we present here the sixth annual summary, reusing the text from last year with updates where appropriate. Readers who wish to cogitate about the extraordinary nature of this deep-space expedition may find it helpful to compare this material with the logs from its first, second, third, fourth, and fifth anniversaries.

In its six years of interplanetary travels, the spacecraft has thrust for a total of 1,410 days, or 64 percent of the time (and about 0.000000028 percent 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 318 kilograms (701 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 8.7 kilometers per second (19,500 mph). As previous logs have described (see here for one of the more extensive discussions), 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 about three-quarters of the thrust time planned for its entire mission, Dawn has already far exceeded the velocity change achieved by any other spacecraft under its own power. (For a comparison with probes that enter orbit around Mars, refer to this earlier log.)

Since launch, our readers who have remained on or near Earth have completed six revolutions around the sun, covering about 37.7 AU (5.6 billion kilometers or 3.5 billion miles). Orbiting farther from the sun, and thus moving at a more leisurely pace, Dawn has traveled 27.4 AU (4.1 billion kilometers or 2.5 billion miles). As it climbed away from the sun to match its orbit to that of Vesta, it continued to slow down to Vesta’s speed. It will have to slow down still more to rendezvous with Ceres. Since Dawn’s launch, Vesta has traveled only 24.2 AU (3.6 billion kilometers or 2.2 billion miles), and the even more sedate Ceres has gone 22.8 AU (3.4 billion kilometers or 2.1 billion miles).

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. In order to make the table below comprehensible (and to fulfill our commitment of environmental responsibility), we recycle some more text here on the nature of orbits.

› Continue reading Marc Rayman’s Dawn Journal