Orbits Around Small Irregularly Shaped Bodies

Recently there has been a lot of interest in spacecraft missions that visit the smaller objects in the solar system, such as asteroids and comets. These types of objects are essentially debris scattered across interplanetary space, which are fragments left over from the processes that formed the Sun and planets. And therein lies their attraction as targets of scientific interest for spacecraft probes.

Asteroids, sometimes called minor planets, are usually solid bodies which vary in size from around 900 km (560 miles) in diameter to tiny boulders a few meters across. The majority of these objects travel in orbits between Mars and Jupiter, although many of the smaller objects can be found almost anywhere in the inner solar system. Comets are also small objects, typically about 1 to 10 km in diameter, composed mostly of ice and dust. The current view is that these "dirty snowballs'' originate from a region of space distant from the Sun, called the Oort cloud, around tens of thousands of AU away from the Sun. Periodically, a comet will be knocked out of the cloud by the gravitational disturbances of a passing star, causing it to fall into the inner solar system. As it does so, once it is closer than about 5 AU from the Sun, the ice begins to react to solar heating, causing plumes of gas and dust. This produces the characteristic appearance of comets—a compact nucleus and a long tail, shining magnificently by reflected sunlight. In past times, they were often greeted with a mixture of awe and suspicion, and were sometimes regarded as an omen of some impending disaster. Fortunately, the public is now better informed, although a strong reaction can still be evoked by a bright comet.

These small bodies are believed to contain crucial clues to aid understanding of the origin and early evolution of our solar system, which is why there has been growing interest in sending spacecraft to investigate them. The first orbital mission around an asteroid was achieved by the Near Earth Asteroid Rendezvous (NEAR) Shoemaker spacecraft, which entered orbit around its target asteroid Eros in February 2000. The spacecraft was not designed to land on the asteroid's surface, but the mission was finished off in February 2001 with a rather ad hoc descent and touchdown on Eros's surface, making for a first in astronautical history. The other high-profile mission in progress at the time of this writing is the European Space Agency's Rosetta mission to orbit and land on a comet. Rosetta's rendezvous with its intended target will not occur until May 2014. On arrival, the Rosetta spacecraft will enter orbit around the small comet 67P/Churyumov-Gerasimenko, finally deploying a small instrument package to make a soft landing on the comet's nucleus.

If we think about orbits around asteroids and comets, they do not fall into the ideal-orbit category discussed in Chapters 2 and 3. You may recall that a so-called ideal orbit is one that results from the motion of a spacecraft in a pure inverse square law gravity field. This produces the familiar trajectory shapes called conic sections: the circle, the ellipse, the parabola, and the hyperbola. The main reason why orbits around asteroids and comets do not fall into this category is that these objects are usually irregular in shape, so that their gravitational fields are nothing like that described by Newton's inverse square law. This affects the orbital motion significantly.

You may also remember from Chapter 2 that the motion of a spacecraft in an ideal circular or elliptical orbit takes place in a fixed plane, and is periodic in the sense that after each orbital revolution the vehicle returns to the same position with the same orbital speed. For the motion of a spacecraft around an irregularly shaped body, neither of these things is true. Figure 4.7 shows an orbit around an asteroid where the track of the spacecraft around the object does not join up, and in fact varies on each orbital rotation. This departure from ideal motion is particularly significant for close orbits around the object. Given that the orbit track is not repeated on each revolution around the object, it is possible that, after a number of orbits, the spacecraft may impact the surface. Care is required to choose a close orbit

Figure 4.7: A close orbit around a small, irregularly shaped body is perturbed by the nonspherical distribution of mass in the asteroid. The picture is of the asteroid Ida, imaged by the Galileo spacecraft in August 1993. (Backdrop image courtesy of NASA/JPL-Caltech.)

that has long-term stability. On the other hand, if the spacecraft were to orbit some distance away, say 20 asteroid diameters, then the irregularities in the bodies shape become less influential, and the spacecraft's motion approximates well to an ideal orbit.

For missions like Rosetta, the process of deploying a lander on a comet can be quite torturous, given that the spacecraft has to be in fairly close orbit around the nucleus to successfully achieve this deployment. The first issue for the spacecraft designer is that the surrounding environment and the size of the comet are not known before the spacecraft gets there. This means that the spacecraft systems and payloads have to be designed to successfully and safely accommodate a range of conditions. The fact that the size, mass, and shape of the comet are unknown at the spacecraft design stage means that a gradual approach to a close orbit is required. As a consequence the spacecraft is inserted into an initial orbit with a large radius compared to the size of the comet.

For the sake of argument, let's suppose the comet nucleus is a fairly average 5 km (3 miles) in diameter, with a density about that of water. If we make the initial orbit radius equal to about 20 comet diameters, then the orbit would approximate well to an ideal circular orbit with a radius of around 100 km (62 miles). The speed of the spacecraft in this initial orbit is about 20 cm/sec (8 inches/sec), which compared to a brisk walking speed of around 4 mph or 1.8 m/sec (5.9 feet/sec) is an amazingly sedate speed for a spacecraft! This gives a first insight into the way mission orbit activities are carried out in proximity to a comet; it can be describe as a low-energy environment where things move slowly, and take a long time to happen. The other implication of this low orbital speed is the precision with which the entry into orbit has to be made. In this circular orbit the escape velocity is only 30 cm/sec (1 ft/sec), compared to about 11 km/sec for Earth, so an error in speed in excess of just 10 cm/sec in orbit insertion speed would result in the spacecraft's disappearing from the comet altogether!

The next job for the mission analysis team is to try to lower the orbit radius to, say, 2 comet diameters (10 km) to allow the lander to be detached from the spacecraft and begin its descent to the surface. However, to fly the spacecraft that close to an irregularly shaped comet would require the team to have detailed knowledge of the gravity field to facilitate accurate prediction of the spacecraft's trajectory. As mentioned above, without this knowledge it is possible over a number of orbital revolutions for the spacecraft to impact the surface. To acquire this knowledge, the comet is examined from the initial high orbit using imaging sensors to acquire detailed information about its shape. At the same time, the spacecraft is tracked precisely in order to detect the small perturbing forces that provide a clue to how the object's gravity field differs from an inverse square law. These data, on shape and perturbations, allow a first estimate of the gravity field of the comet to be made by the mission analysis team. With this information, the orbit radius can be lowered further to, say, 5 comet diameters (25 km), where the process can be repeated, allowing a further refinement in knowledge of the gravity field. Finally, once the team is confident that it has sufficient knowledge of the gravity field, the spacecraft can be inserted into its final close orbit, from which the lander can be deployed. The orbital speed in the 10 km radius orbit is around 60 cm/sec (2 feet/sec), still much slower than our brisk walking pace. In a real project situation, the choice of this orbit radius is difficult to pin down. On the one hand, it has to be small enough so that the descent time of the lander is not too long, but it also has to be large enough so that the orbiting spacecraft is not damaged or contaminated by the near-comet environment. The near-comet space is a dynamic environment, particularly when the comet is close to the Sun. Solar heating causes the surface of the comet to evaporate in plumes of gas and dust, from which the orbiting spacecraft needs to keep a distance. There is always a conflict between the engineers and scientists in these situations. The engineers want to keep the spacecraft a safe distance from hazards, whereas the scientists want it to be "where the action is.'' Clearly a compromise has to be struck between the value of the science and the risk to the spacecraft.

Let's suppose the lander is an instrument package with landing legs, having a total mass of, say, 100 kg. The next task is to detach it from the orbiting spacecraft, so that it can begin its descent to the surface. The simplest way of doing this is to push the lander out the back of the spacecraft, with an ejection speed equal to the spacecraft's forward orbital speed (how this is done is not really relevant to the story here, but it would probably be most easily done with a calibrated spring mechanism). If the backward speed of the lander matches the forward speed of the spacecraft—around 60 cm/sec in this case—then the lander is left momentarily motionless above the comet's surface. The comet's weak gravity will then cause it to fall steadily toward the surface. Because the gravity of the comet is so weak, this trip to the surface takes quite some time, around 4.4 hours in our example, and when the lander finally approaches the surface its descent speed is only around 1.6 m/sec (just a shade less than our brisk walking speed of 4 mph). On final approach to the surface, contamination of the surface by spraying it with rocket engine exhaust gases may not be a good idea from the point of view of the science objectives of the mission. This may prevent the use of a rocket engine to slow the descent, so that the structure of the lander may need to be able to withstand the 1.6 m/sec impact speed.

Perhaps the major issue with the touchdown is preventing the lander from bouncing back off the surface, and possibly going back into orbit. This is a real possibility, as the 100-kg-mass spacecraft will weigh only about 1/10th of a Newton on the surface, which is about 1/10th the weight of a small apple! And of course the nature of the surface, whether it's bouncy, or sticky, or somewhere in between, is unknown until touchdown. To prevent such a bounce happening, the lander will either have to fire an upward directed rocket motor or mechanically grapple the surface somehow, on touchdown.

Figure 4.8 shows the European Space Agency's Rosetta lander after what is hoped to be a successful touchdown on comet 67P/Churyumov-Gerasi-menko in around 2014. The complexities of the orbital aspects of such a mission are not to be underestimated, where the central body is no longer a nice uniform sphere, but has a shape resembling a potato.

Figure 4.8: Artist's impression of the Rosetta lander after a successful touchdown on comet 67P/Churyumov-Gerasimenko. (Image courtesy of the European Space Agency [ESA].)

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