Contents:
1. Introduction
2. Discovery
3. Scientists explore Toutatis
- Rotation of the asteroid
- Nature of the asteroid
4. Orbital elements
5. The last passage of the asteroid
6. Our observations of Toutatis
7. Exercise”Let’s make an asteroid”
8. Conclusion
9. Bibliography

Fig.1 Team: Trayan Petkov – 16 years old
Leader: Veselka Radeva
Astronomical Observatory, Varna, Bulgaria

1.Introduction:
The asteroid Toutatis is one of the few asteroids that passed at a dangerously short distance from our planet in 2004. Each year astronomers find and track asteroids that pass very near the Earth. Scientists call these asteroids Near Earth Objects. Scientists have made a scale that they use to estimate the degree of danger an asteroid to hit the Earth. When one finds such a near and dangerous asteroid, scientists use all possible means to examine the asteroid. In this way they receive very important information for the asteroid’s nature and can estimate the degree of danger for the Earth. We were impressed by the words of the famous Dr. Don Yeomans of NASA's Jet Propulsion Laboratory (JPL), Pasadena, Calif., manager of NASA's Near Earth Objects Program Office. He has said:”This is the closest Toutatis will come for another 500 years, and its orbit is very known. What this fly-by provides is an opportunity to study one for our closest solar system neighbors.”

From High Resolution Goldstone Images
These are 8 of the "high resolution" Goldstone images that are being used to produce a higher-resolution 3D model of Toutatis. (From Ostro et al., Science 270:80-83, 1995--© Copyright 1995 by the AAAS) [2]

Shaded Relief Map of Asteroid 4179 Toutatis
This is a shaded relief map of asteroid 4179 Toutatis. As with all maps, it is the cartographer's interpretation and not all features are necessarily certain given the limited data available. This interpretation stretches the data as far as is feasible. (Courtesy Phil Stooke, NSSDC, and NASA)

Scientists have made a computer model of the Earth-orbit-crossing asteroid Toutatis. These views of the asteroid show shallow craters, linear ridges, and a deep topographic "neck" whose geologic origin is not known. It may have been sculpted by impacts into a single, coherent body, or Toutatis might actually consist of two separate objects that came together in a gentle collision. (Courtesy Scott Hudson, Washington State University)[2]

Fig.3. Computer Model
of Toutatis
Scott Hudson, Washington State University

Fig.4. The rotation of
the asteroid
Copyright 1995 by the AAAS

We were most interested in the rotation of the asteroid. This image shows the shape and non-principal-axis spin state of asteroid 4179 Toutatis rendered at a particular instant. The red, green, and blue axes are the principal axes of inertia; the magenta axis is the angular momentum vector; the yellow axis is the spin vector. If a flashlamp was attached to the short axis of inertia (the red axis) and flashed it every 15 minutes for a month, it would trace out the intricate path indicated by the small spheres stacked end-to-end. If this process was continued forever the path would never repeat. Toutatis's spin state differs radically from those of the vast majority of solar system bodies that have been studied. (© Copyright 1995 by the AAAS)

For us it was very interesting to understand how the asteroid turns on Nine Successive Days. This image shows the non-principal-axis spin state of asteroid 4179 Toutatis at one-day intervals (from left to right, top to bottom). The red, green, and blue axes are the principal axes of inertia; the magenta axis is the angular momentum vector; the yellow axis is the spin vector. Toutatis does not spin about a single axis. Instead, its spin vector traces a curve around the asteroid's surface once every 5.41 days. During this time the object rotates once about its long axis, and every 7.35 days, on average, the long axis precesses about the angular momentum vector. The combination of these two motions with different periods give Toutatis its bizarre "tumbling" rotation. (Courtesy Scott Hudson, Washington State University)[2]

Fig.5. Axes of rotation
Copyright 1995 by the AAAS

4.Orbital elements
In the Minor Planet Center that is lead by the famous astronomer Brian Marsden there are 1317 observations at 13 oppositions for the period 1976-2004. The astronomers at the Center have calculated the orbital elements of the asteroid.[E] They are as follows:

(4179) Toutatis
Orbital Elements

In December 1992, Toutatis made a close approach to Earth. At the time, it was an average of about 4 million kilometers (2.5 million miles) from Earth. Images of Toutatis were acquired using radar carried out at the Goldstone Deep Space Communications Complex in California's Mojave desert. For most of the work, a 400,000-watt coded radio transmission was beamed at Toutatis from the Goldstone main 70-meter (230-foot) antenna. The echoes, which took as little as 24 seconds to travel to Toutatis and back, were received by the new 34-meter (112-foot) antenna and relayed back to the 70-meter (230-foot) station, where they were decoded and processed into images. [3]

The most important facts drawn from the observations of scientists:

The images of Toutatis reveal two irregularly shaped, cratered objects about 4 and 2.5 kilometers (2.5 and 1.6 miles) in average diameter which are probably in contact with each other. These "contact binaries" may be fairly common since another one, 4769 Castalia, was observed in 1989 when it passed near the Earth. Numerous surface features on Toutatis, including a pair of half-mile-wide craters, side by side, and a series of three prominent ridges -- a type of asteroid mountain range -- are presumed to result from a complex history of impacts.
Toutatis is one of the strangest objects in the solar system, with a highly irregular shape and an extraordinarily complex "tumbling" rotation. Both its shape and rotation are thought to be the outcome of a history of violent collisions. "The vast majority of asteroids, and all the planets, spin about a single axis, like a football thrown in a perfect spiral, but Toutatis tumbles like a flubbed pass," said Dr. Scott Hudson of Washington State University. One consequence of this strange rotation is that Toutatis does not have a fixed north pole like the Earth. Instead, its north pole wanders along a curve on the asteroid about every 5.4 days. "The stars viewed from Toutatis wouldn't repeatedly follow circular paths, but would crisscross the sky, never following the same path twice," Hudson said.
"The motion of the Sun during a Toutatis year, which is about four Earth years, would be even more complex," he continued. "In fact, Toutatis doesn't have anything you could call a 'day.' Its rotation is the result of two different types of motion with periods of 5.4 and 7.3 Earth days, that combine in such a way that Toutatis's orientation with respect to the solar system never repeats."
The rotations of hundreds of asteroids have been studied with optical telescopes. The vast majority of them appear to be in simple rotation with a fixed pole and periods typically between one hour and one day, the scientists said, even though the violent collisions these objects are thought to have experienced would mean that every one of them, at some time in the past, should have been tumbling like Toutatis.[2]

1996 Nov. 29.96

0.0354

2000 Oct. 31.19

0.0739

2004 Sept.29.5

0.0104

2008 Nov. 9.50

0.0503

5. The last passage of the asteroid
29 September 2004
Toutatis, a potato-shaped asteroid about 4.6 km (3 miles) in its longest extent, will pass within 1,550,000 km (963,000 miles) of the Earth's center on Wednesday, September 29, 2004 - reaching its closest approach at 13:35:28 GMT (06:35:28 PDT). This is roughly four times the distance from the Earth to the moon and closer than this asteroid has come to Earth since at least the twelfth century. Toutatis will not pass this closely again for the next 500 years. The passage is the closest Earth approach this century for a known asteroid of this size. Because of an extensive set of optical and radar observations, the orbit for Toutatis is one of the best determined of any asteroid and there is no chance that this object will collide with the Earth during this encounter - or any other encounter for at least 5 centuries.[5]
Let’s compare our asteroid Toutatis with the Eros asteroid
The data for Eros has given scientists clues about the history of the solar system. Eros is considered a geologic relic from the infancy of the solar system, which formed about 4.5 billion years ago. It could also prevent a future catastrophe. The 21-mile-long (34-km) Eros belongs to a group of large asteroids with orbits relatively close to Earth, like the one that scientists speculate slammed into Earth and killed the dinosaurs 67 million years ago.
Scientists warn that there is a remote risk another such killer asteroid will someday hit Earth. Learning about Eros could offer them clues to prevent such a catastrophic collision. Both Toutatis and Eros are potentially dangerous for our planet, which is one of the reasons we chose Toutatis for our project.[1],[2],[3],[6],[7]

Animation of Toutatis - http://www.solarviews.com/cap/ast/toutspin.htm
Animation of Eros - http://www.solarviews.com/cap/eros/eros10.htm

6. Our observations of the asteroid
We made observations of the asteroid in the summer of 2004 during the National astronomical summer school in the National Astronomical Observatory – Rozhen. Due to the fact that we are very interested in astronomy, we were taught to observe with large telescopes. The telescope that we used for our observations of the asteroid has diameter of the mirror 50 cm and focal length of 172 cm. At the focus of the Schmidt telescope was CCD– ST8. We received several images of the asteroid that we processed with the software of the CCD camera. We received the following images:

For us it was extremely interesting to make an exercise with our friends from the astronomical courses in the Observatory in Varna.

Fig.9. The class
photo by Nadezhda Radeva

Fig.10. Explanation of the rotation of the asteroids
photo by Nadezhda Radeva

Objective: Most asteroids are not spherical like planets. Students will mode the 3D from of asteroids Toutatis and a paper model of asteroid Eros.
Necessary materials: plasticine, wooden sticks, scissors, glue, a sheet of paper with the shape of the asteroid Eros that will be made during the lesson.
Estimated Time: Depending on the ability level of your students this could take from 20 to 40 minutes.

Fig.11 The model of Toutatis
photo by Nadezhda Radeva

Fig.12 The model of Toutatis
photo by Nadezhda Radeva

Procedure:
Step1: The teacher has to present to students short information about the discovery of the asteroid and to show the movement of the asteroid around the Sun. The students discuss the moments of the passage of the asteroid through perihelion, the speed of the asteroid in perihelion and aphelion and the slope of the asteroid’s orbit.
Step 2: Students look at photos of the asteroid that have been obtained by different observatories in the Internet. They make a 3D model of the asteroid from plasticine. By using the maps of the surface of the asteroid they make the craters and the swellings on it. They discuss the real size of the asteroid that has been obtained by radio observations. They watch animations of Toutatis and show the movement of the asteroid around its 5 axes. The 5 axes are made from the wooden sticks that have to be put in the plasticine.
Step 3: Students look at photos and animations of the asteroid Eros. They discuss its size, parameters of its orbit and its rotation. Then, they put together the asteroid Eros from paper and compare the two objects’ orbital elements, size and rotation around their axes.

Fig.13.The paper model of the asteroid Eros
photo by Nadezhda Radeva

Fig.14.The paper models of the asteroid Eros
photo by Nadezhda Radeva

Fig.15. Trayan explains the orbit of Toutatis
photo by Nadezhda Radeva

8. Conclusion:
Sometimes people call the small bodies “the garbage of the Solar system”. However, we think that asteroids will be very important for the future. People will examine them very well and they will learn to use them in order to receive different chemical products and will start producing various products in the asteroid belt. When we gathered information about the asteroid Toutatis we understood how important it is we to know the movement of asteroids in the Solar system. It turns out that there are many asteroids that can pass dangerously close to the Earth and to endanger life on our planet. Asteroids are very interesting and their exploration is and will be very important for the future of humanity.