# 253 Mathilde

Discovery[1] NASA image of 253 Mathilde Johann Palisa November 12, 1885 Mathilde Leowy 1949 OL1, A915 TN Main belt Epoch August 27, 2011 (JD 2455800.5) 3.35085789 AU (501.334 Gm) 1.9394293 AU (290.564 Gm) 2.645134617 AU (395.949 Gm) 0.26679620 4.30211572 yr (1571.347765 d) 17.98 km/s[2] 118.514244° 6.743283° 179.61628° 157.36198° 52.8[3] km (66×48×46 km[4]) 1.033(±0.044)×1017[5] kg 1.3[5] g/cm³ 0.00993 m/s² 22.9 m/s 17.406±0.010[6] d (17 d 9 h 45 min) 0.0436[3] ≈ 174[7] K Cb[3] 10.20[3]

253 Mathilde is a main-belt asteroid about 50 km in diameter that was discovered by Johann Palisa in 1885. It has a relatively elliptical orbit that requires more than four years to circle the Sun. This asteroid has an unusually slow rate of rotation, requiring 17.4 days to complete a 360° revolution about its axis. It is a primitive C-type asteroid, which means the surface has a high proportion of carbon; giving it a dark surface that reflects only 4% of the light that falls on it.[8]

This asteroid was visited by the NEAR Shoemaker spacecraft during June 1997, on its way to asteroid 433 Eros. During the flyby, the spacecraft imaged a hemisphere of the asteroid, revealing many large craters that have gouged out depressions in the surface. Until 21 Lutetia was visited in 2010, it was the largest asteroid to be visited by a spacecraft and the first C-type asteroid to be explored.

## Observation history

In 1880, Johann Palisa, the director of the Austrian Naval Observatory, was offered a position as an assistant at the newly completed Vienna Observatory. Although the job represented a demotion for Johann, it gave him access to the new 27-inch (690 mm) refractor, the largest telescope in the world at that time. By this point Johann had already discovered 27 asteroids, and he would employ the Vienna 27-inch (690 mm) and 12-inch (300 mm) instruments to find an additional 94 asteroids before he retired.[9]

Among his discoveries was the asteroid 253 Mathilde, found on November 12, 1885. The initial orbital elements of the asteroid were then computed by V. A. Lebeuf, another Austrian astronomer working at the observatory. The name of the asteroid was suggested by Lebeuf, after Mathilde, the wife of Moritz Leowy—who was the vice director of the Paris Observatory.[1][10]

In 1995, ground-based observations determined that 253 Mathilde is a C-type asteroid. It was also found to have an unusually long period of rotation.[10]

On June 27, 1997, the NEAR Shoemaker spacecraft passed within 1,212 km of 253 Mathilde while moving at a velocity of 9.93 km/s. This close approach allowed the spacecraft to capture over 500 images of the surface,[8] and provided data for more accurate determinations of the asteroid's dimensions and mass (based on gravitational perturbation of the spacecraft).[5] However, only one hemisphere of 253 Mathilde was imaged during the fly-by.[11] This was only the third asteroid to be imaged from a nearby distance, following 951 Gaspra and 243 Ida.

## Description

Damodar, a 20km-wide crater on 253 Mathilde.

253 Mathilde is very dark, with an albedo comparable to fresh asphalt,[12] and is thought to share the same composition as CI1 or CM2 carbonaceous chondrite meteorites, with a surface dominated by phyllosilicate minerals.[13] The asteroid has a number of extremely large craters, with the individual craters being named for coal fields and basins around the world.[14] The two largest craters, Ishikari (29.3 km) and Karoo (33.4 km), are as wide as the asteroid's average radius.[4] The impacts appear to have spalled large volumes off the asteroid, as suggested by the angular edges of the craters.[8] No differences in brightness or colour were visible in the craters and there was no appearance of layering, so the asteroid's interior must be very homogeneous. There are indications of material movement along the downslope direction.[4]

The density measured by NEAR Shoemaker, 1,300 kg/m³, is less than half that of a typical carbonaceous chondrite; this may indicate that the asteroid is very loosely packed rubble pile.[5] The same is true of several C-type asteroids studied by ground-based telescopes equipped with adaptive optics systems (45 Eugenia, 90 Antiope, 87 Sylvia and 121 Hermione). Up to 50% of the interior volume of 253 Mathilde consists of open space. However, the existence of a 20-km-long scarp may indicate that the asteroid does have some structural strength, so it could contain some large internal components.[11] The low interior density is an inefficient transmitter of impact shock through the asteroid, which also helps to preserve the surface features to a high degree.[4]

Mathilde's orbit is eccentric, taking it to the outer reaches of the main belt. Nonetheless, the orbit lies entirely between the orbits of Mars and Jupiter; it does not cross the planetary orbits. It also has one of the slowest rotation periods of the known asteroids—most asteroids have a rotation period in the range of 2–24 hours.[15] Because of the slow rotation rate, NEAR Shoemaker was only able to photograph 60% of the asteroid's surface. The slow rate of rotation may be accounted for by a satellite orbiting the asteroid, but a search of the NEAR images revealed none larger than 10 km in diameter out to 20 times the radius of 253 Mathilde.[16]

## References

1. ^ a b Moore, Sir Patrick (1999). The Wandering Astronomer. CRC Press. ISBN 0-7503-0693-9.
2. ^ For semi-major axis a, orbital period T and eccentricity e, the average orbital speed is given by:
\begin{align} v_o & = \frac{2\pi a}{T}\left[1-\frac{e^2}{4}-\frac{3e^4}{64} - \dots \right] \\ & = 18.31\ \mbox{km/s} \left[ 1 - 0.0177 - 0.00008 - \cdots \right] \\ & \approx 17.98\ \mbox {km/s} \\ \end{align}\!\,
For the circumference of an ellipse, see: H. St̀eocker, J. Harris (1998). Handbook of Mathematics and Computational Science. Springer. p. 386. ISBN 0-387-94746-9.
3. Unless otherwise noted, parameters are per: Yeomans, Donald K. (August 29, 2003). "253 Mathilde". JPL Small-Body Database Browser. NASA. Retrieved 2007-08-29.
4. ^ a b c d J. Veverka et al (1999). "NEAR Encounter with Asteroid 253 Mathilde: Overview". Icarus 140 (1): 3–16. Bibcode:1999Icar..140....3V. doi:10.1006/icar.1999.6120.
5. ^ a b c d D. K. Yeomans et al (1997). "Estimating the mass of asteroid 253 Mathilde from tracking data during the NEAR flyby". Science 278 (5346): 2106–9. Bibcode:1997Sci...278.2106Y. doi:10.1126/science.278.5346.2106. PMID 9405343. Archived from the original on 1 October 2007. Retrieved 2007-08-29.
6. ^ Stefano Mottola et al (1995). "The slow rotation of 253 Mathilde". Planetary and Space Science 43 (12): 1609–1613. Bibcode:1995P&SS...43.1609M. doi:10.1016/0032-0633(95)00127-1.
7. ^ For asteroid albedo α, semimajor axis a, solar luminosity $L_0$, Stefan-Boltzmann constant σ and the asteroid's infrared emissivity ε (≈ 0.9), the approximate mean temperature T is given by:
\begin{align} T & = \left ( \frac{(1 - \alpha) L_0}{\epsilon \sigma 16 \pi a^2} \right )^{\frac{1}{4}} \\ & = \left ( \frac{(1 - 0.0436) (3.827 \times 10^{26}\ \mbox{W})} {0.9 (5.670 \times 10^{-8}\ \mbox{W/m}^2\mbox{K}^4) 16 \cdot 3.142 (3.959 \times 10^{11}\ \mbox{m})^2} \right )^{\frac{1}{4}} \\ & = 173.7\ \mbox{K} \end{align}
See: Torrence V. Johnson, Paul R. Weissman, Lucy-Ann A. McFadden (2007). Encyclopedia of the Solar System. Elsevier. p. 294. ISBN 0-12-088589-1.
8. ^ a b c Williams, David R. (December 18, 2001). "NEAR Flyby of Asteroid 253 Mathilde". NASA. Archived from the original on 18 August 2006. Retrieved 2006-08-10.
9. ^ Raab, Herbert (2002). "Johann Palisa, the most successful visual discoverer of" (PDF). Astronomical Society of Linz. Archived from the original on 28 September 2007. Retrieved 2007-08-27.
10. ^ a b Savage, D.; Young, L.; Diller, G.; Toulouse, A. (February 1996). "Near Earth Asteroid Rendezvous (NEAR) Press Kit". NASA. Retrieved 2007-08-29.
11. ^ a b Cheng, Andrew F. (2004). "Implications of the NEAR mission for internal structure of Mathilde and Eros". Advances in Space Research 33 (9): 1558–1563. Bibcode:2004AdSpR..33.1558C. doi:10.1016/S0273-1177(03)00452-6.
12. ^ Pon, Brian (June 30, 1999). "Pavement Albedo". Heat Island Group. Archived from the original on 29 August 2007. Retrieved 2007-08-27.
13. ^ Kelley, M. S.; Gaffey, M. J.; Reddy, V. (March 12–16, 2007). "Near-IR Spectroscopy and Possible Meteorite Analogs for Asteroid (253)". 38th Lunar and Planetary Science Conference. League City, Texas: Lunar & Planetary Institute. p. 2366. Retrieved 2007-08-29.
14. ^ Blue, Jennifer (August 29, 2007). "Categories for Naming Features on Planets and Satellites". USGS. Archived from the original on 24 August 2007. Retrieved 2007-08-29.
15. ^ Lang, Kenneth R. (2003). "2. Asteroids and meteorites, Size, color and spin". NASA's Cosmos. NASA. Retrieved 2007-08-29.
16. ^ W. J. Merline et al (1998). "Search for Satellites of 253 Mathilde from Near-Earth Asteroid Rendezvous Flyby Data". Meteoritics & Planetary Science 33 (1): A105. Bibcode:1998M&PSA..33..105M.