253 Mathilde

253 Mathilde
	253 Mathilde as seen by NEAR in 1997
Discovery
Discovered by	J. Palisa
Discovery site	Vienna Obs.
Discovery date	12 November 1885
Designations
MPC designation	(253) Mathilde
Pronunciation	/məˈtɪldə/
Named after	Mathilde Loewy
Alternative designations	A885 VA, 1915 TN; 1949 OL1
Minor planet category	Main belt
Orbital characteristics
	Epoch 31 July 2016 (JD 2457600.5)
	Uncertainty parameter 0
Observation arc	130.38 yr (47622 d)
Aphelion	3.35003411 AU (501.157970 Gm)
Perihelion	1.9467702 AU (291.23268 Gm)
Semi-major axis	2.648402147 AU (396.1953219 Gm)
Eccentricity	0.26492652
Orbital period (sidereal)	4.31 yr (1574.3 d)
Average orbital speed	17.98 km/s
Mean anomaly	170.584348°
Mean motion	0° 13m 43.248s / day
Inclination	6.7427122°
Longitude of ascending node	179.58936°
Argument of perihelion	157.39642°
Earth MOID	0.939032 AU (140.4772 Gm)
Jupiter MOID	2.06073 AU (308.281 Gm)
TJupiter	3.331
Physical characteristics
Dimensions	52.8 km; (66×48×46 km)
Mass	(1.033±0.044)×1017 kg
Mean density	1.3 g/cm3
Equatorial surface gravity	0.00989 m/s2
Equatorial escape velocity	22.9 m/s
Synodic rotation period	417.7 h (17.40 d); 17.406 ± 0.010 d; (17 d 9 h 45 min)
Geometric albedo	0.0436±0.004
Temperature	≈ 174 K
Spectral type	Cb
Absolute magnitude (H)	10.3

253 Mathilde is an asteroid in the intermediate asteroid belt, approximately 50 kilometers in diameter, that was discovered by Austrian astronomer Johann Palisa at Vienna Observatory on 12 November 1885. It has a relatively elliptical orbit that requires more than four years to circle the Sun. This tumbling 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]

Mathilde was visited by the NEAR Shoemaker spacecraft during June 1997, on its way to asteroid 433 Eros. During the little flyby, the spacecraft imaged a hemisphere of the asteroid, revealing many large craters that had gouged out depressions in the surface. It was the first carbonaceous asteroid to be explored and, until 21 Lutetia was visited in 2010, it was the largest asteroid to be visited by a spacecraft.

^ Cite error: The named reference moore was invoked but never defined (see the help page).
^ ^a ^b ^c ^d ^e ^f Unless otherwise noted, parameters are per: Yeomans, Donald K. (29 August 2003). "253 Mathilde". JPL Small-Body Database Browser. NASA. Retrieved 12 May 2016.
^ For semi-major axis a, orbital period T and eccentricity e, the average orbital speed is given by:
${\begin{aligned}v_{o}&={\frac {2\pi a}{T}}\left[1-{\frac {e^{2}}{4}}-{\frac {3e^{4}}{64}}-\dots \right]\\&=18.31\ {\mbox{km/s}}\left[1-0.0177-0.00008-\cdots \right]\\&\approx 17.98\ {\mbox{km/s}}\\\end{aligned}}\!\,$
For the circumference of an ellipse, see: H. St̀eocker; J. Harris (1998). Handbook of Mathematics and Computational Science. Springer. pp. 386. ISBN 0-387-94746-9.
^ Cite error: The named reference icarus140 was invoked but never defined (see the help page).
^ ^a ^b Cite error: The named reference Yeomans 1997 was invoked but never defined (see the help page).
^ 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.
^ 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:
${\begin{aligned}T&=\left({\frac {(1-\alpha )L_{0}}{\epsilon \sigma 16\pi a^{2}}}\right)^{\frac {1}{4}}\\&=\left({\frac {(1-0.0436)(3.827\times 10^{26}\ {\mbox{W}})}{0.9(5.670\times 10^{-8}\ {\mbox{W/m}}^{2}{\mbox{K}}^{4})16\cdot 3.142(3.959\times 10^{11}\ {\mbox{m}})^{2}}}\right)^{\frac {1}{4}}\\&=173.7\ {\mbox{K}}\end{aligned}}$
See: Torrence V. Johnson; Paul R. Weissman; Lucy-Ann A. McFadden (2007). Encyclopedia of the Solar System. Elsevier. pp. 294. ISBN 978-0-12-088589-3.
^ Cite error: The named reference flyby was invoked but never defined (see the help page).

[moore-1] Cite error: The named reference moore was invoked but never defined (see the help page).

[jpl-2] ^ ^a ^b ^c ^d ^e ^f Unless otherwise noted, parameters are per: Yeomans, Donald K. (29 August 2003). "253 Mathilde". JPL Small-Body Database Browser. NASA. Retrieved 12 May 2016.

[3] For semi-major axis a, orbital period T and eccentricity e, the average orbital speed is given by:
${\begin{aligned}v_{o}&={\frac {2\pi a}{T}}\left[1-{\frac {e^{2}}{4}}-{\frac {3e^{4}}{64}}-\dots \right]\\&=18.31\ {\mbox{km/s}}\left[1-0.0177-0.00008-\cdots \right]\\&\approx 17.98\ {\mbox{km/s}}\\\end{aligned}}\!\,$
For the circumference of an ellipse, see: H. St̀eocker; J. Harris (1998). Handbook of Mathematics and Computational Science. Springer. pp. 386. ISBN 0-387-94746-9.

[icarus140-4] Cite error: The named reference icarus140 was invoked but never defined (see the help page).

[Yeomans_1997-5] Cite error: The named reference Yeomans 1997 was invoked but never defined (see the help page).

[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:
${\begin{aligned}T&=\left({\frac {(1-\alpha )L_{0}}{\epsilon \sigma 16\pi a^{2}}}\right)^{\frac {1}{4}}\\&=\left({\frac {(1-0.0436)(3.827\times 10^{26}\ {\mbox{W}})}{0.9(5.670\times 10^{-8}\ {\mbox{W/m}}^{2}{\mbox{K}}^{4})16\cdot 3.142(3.959\times 10^{11}\ {\mbox{m}})^{2}}}\right)^{\frac {1}{4}}\\&=173.7\ {\mbox{K}}\end{aligned}}$
See: Torrence V. Johnson; Paul R. Weissman; Lucy-Ann A. McFadden (2007). Encyclopedia of the Solar System. Elsevier. pp. 294. ISBN 978-0-12-088589-3.

[flyby-8] Cite error: The named reference flyby was invoked but never defined (see the help page).

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