Posts Tagged ‘gravity’

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 July, 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


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


Getting the Lowdown on Asteroid Vesta

Monday, December 5th, 2011

By Marc Rayman

As NASA’s Dawn spacecraft investigates its first target, the giant asteroid Vesta, Marc Rayman, Dawn’s chief engineer, shares a monthly update on the mission’s progress.

Still from a 3-D video incorporating images from NASA's Dawn spacecraft
This 3-D video incorporates images from the framing camera instrument aboard NASA’s Dawn spacecraft from July to August 2011. The images were obtained as Dawn approached Vesta and circled the giant asteroid during the mission’s survey orbit phase. Survey orbit took place at an altitude of about 1,700 miles (2,700 kilometers). To view this video in 3-D use red-green, or red-blue, glasses (left eye: red; right eye: green/blue). Image credit: NASA/JPL-Caltech/UCLA/MPS/DLR/IDA
› See video

Dear Dawnward Spirals,

Continuing its ambitious campaign of exploration deep in the asteroid belt, Dawn has spent most of the past month spiraling ever closer to Vesta. Fresh from the phenomenal success of mapping the alien world in detail in October, the spacecraft and its human team members are engaged in one of the most complicated parts of the mission. The reward will be the capability to scrutinize this fascinating protoplanet further.

Thanks to the extraordinary performance of its ion propulsion system, Dawn can maneuver to different orbits that are best suited for conducting each of its scientific observations. The probe is now headed for its low altitude mapping orbit (LAMO), where the focus of its investigations will be on making a census of the atomic constituents with its gamma ray and neutron sensors and on mapping the gravity field in order to determine the interior structure of this protoplanet.

As secondary objectives, Dawn will acquire more images with its camera and more spectra with its visible and infrared mapping spectrometer. As we will see in a future log, these measurements will receive a smaller share of the resources than the high priority studies. The spectacular pictures obtained already will keep scientists happy for years, and you can continue to share in the experience of marveling at the astonishing discoveries by seeing some of the best views here, including scenes captured during the spiral to LAMO.

Planning the low altitude mapping orbit around massive Vesta, with its complicated gravity field, required a great deal of sophisticated analysis. Before Dawn arrived, mission designers studied a range of possible gravitational characteristics and honed the methods they would use for plotting the actual orbit once the details of the protoplanet’s properties were ascertained. In the meantime, the team used a tentative orbit at an altitude over the equator of 180 kilometers (110 miles). As explained in a previous log, the altitude varies both because the orbit is not perfectly circular and because Vesta displays such exceptional topography. The highest elevations turn out to be at the equator, and the average altitude of that orbit would be 200 kilometers (125 miles).

Now that navigators have measured Vesta’s gravity, they have the knowledge to refine the design for LAMO, and they decided to raise it by 10 kilometers (6 miles). The target then is an average altitude of 210 kilometers (130 miles). But there is more to the specification of the orbit than simply its height. To meet all of the scientific objectives, the orientation of this orbit needs to be different from the orientation of the previous orbits, the high altitude mapping orbit (HAMO) and survey orbit.

› Continue reading Marc Rayman’s Dawn Journal