253 Mathilde

253 Mathilde
	NASA image of 253 Mathilde
Discovery
Discovered by	Johann Palisa
Discovery date	November 12, 1885
Designations
Alternative names	A915 TN; 1949 OL1
Minor planet category	Main belt
Orbital characteristics
	Epoch January 30, 2005 (JD 2453400.5)
Aphelion	501.334 Gm; 3.35121 AU
Perihelion	290.564 Gm; 1.94230 AU
Semi-major axis	395.949 Gm; 2.64676 AU
Eccentricity	0.266157
Orbital period	1572.787 d ; (4.31 yr)
Average orbital speed	17.98 km/s
Mean anomaly	111.960°
Inclination	6.738°
Longitude of ascending node	179.633°
Argument of perihelion	157.475°
Physical characteristics
Dimensions	52.8 km; (66×48×46 km)
Mass	1.033(±0.044)×1017 kg
Mean density	1.3 g/cm³
Surface gravity	0.0025 m/s²
Escape velocity	16.2 m/s
Rotation period	17.406±0.010 d; (17 d 9 h 45 min)
Albedo	0.0436
Temperature	~174 K
Spectral type	Cb
Absolute magnitude (H)	10.20

253 Mathilde is a main belt asteroid found by Johann Palisa in 1885. It has a fairly elliptical orbit that takes more than four years to circle the Sun. This asteroid has an unusually slow rate of rotation, taking 17.4 days to complete a 360° revolution about its axis. It is a primitive C-type asteroid, which means the surface has lots of carbon; giving it a dark surface that reflects only 4% of the light that falls on it.^[9]

This asteroid was visited by the NEAR Shoemaker spacecraft during June 1997, on its way to asteroid 433 Eros. The spacecraft took pictures of one side of the asteroid, finding many big craters that have gouged out depressions in the surface. It is currently the biggest asteroid to be visited by a spacecraft, and the first C-type asteroid to be so explored.

↑ 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. p. 386. ISBN 0-387-94746-9.
↑ ^2.0 ^2.1 ^2.2 ^2.3 ^2.4 Unless otherwise noted, parameters are per: Yeomans, Donald K. (August 29, 2003). "253 Mathilde". JPL Small-Body Database Browser. NASA. Retrieved 2007-08-29.
↑ Cite error: The named reference icarus140 was used but no text was provided for refs named (see the help page).
↑ ^4.0 ^4.1 Cite error: The named reference Yeomans 1997 was used but no text was provided for refs named (see the help page).
↑ With asteroid mass m, radius r and G equal to the gravitational constant, Newton's law of universal gravitation gives an average surface gravity g of:
${\begin{aligned}g&=G{\frac {m}{r^{2}}}\\&=6.67\times 10^{-11}{\mbox{m}}^{3}/{\mbox{kg s}}^{2}\cdot {\frac {1.03\times 10^{17}\ {\mbox{kg}}}{(5.28\times 10^{4}\ {\mbox{m}})^{2}}}\\&=0.0025\ {\mbox{m/s}}^{2}\\\end{aligned}}$
↑ For surface gravity g and radius r, the escape velocity is:
${\begin{aligned}v_{e}&={\sqrt {2gr}}\\&={\sqrt {2\cdot 0.0025\ {\mbox{m/s}}^{2}\cdot 52800\ {\mbox{m}}}}\\&=16.2\ {\mbox{m/s}}\\\end{aligned}}$
↑ 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. Retrieved 2007-02-04.
↑ 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. p. 294. ISBN 978-0-12-088589-3.{{cite book}}: CS1 maint: multiple names: authors list (link)
↑ Cite error: The named reference flyby was used but no text was provided for refs named (see the help page).

[1] 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. p. 386. ISBN 0-387-94746-9.

[jpl-2] 2.0 ^2.1 ^2.2 ^2.3 ^2.4 Unless otherwise noted, parameters are per: Yeomans, Donald K. (August 29, 2003). "253 Mathilde". JPL Small-Body Database Browser. NASA. Retrieved 2007-08-29.

[icarus140-3] Cite error: The named reference icarus140 was used but no text was provided for refs named (see the help page).

[Yeomans_1997-4] 4.0 ^4.1 Cite error: The named reference Yeomans 1997 was used but no text was provided for refs named (see the help page).

[5] With asteroid mass m, radius r and G equal to the gravitational constant, Newton's law of universal gravitation gives an average surface gravity g of:
${\begin{aligned}g&=G{\frac {m}{r^{2}}}\\&=6.67\times 10^{-11}{\mbox{m}}^{3}/{\mbox{kg s}}^{2}\cdot {\frac {1.03\times 10^{17}\ {\mbox{kg}}}{(5.28\times 10^{4}\ {\mbox{m}})^{2}}}\\&=0.0025\ {\mbox{m/s}}^{2}\\\end{aligned}}$

[6] For surface gravity g and radius r, the escape velocity is:
${\begin{aligned}v_{e}&={\sqrt {2gr}}\\&={\sqrt {2\cdot 0.0025\ {\mbox{m/s}}^{2}\cdot 52800\ {\mbox{m}}}}\\&=16.2\ {\mbox{m/s}}\\\end{aligned}}$

[7] 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. Retrieved 2007-02-04.

[8] 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. p. 294. ISBN 978-0-12-088589-3.{{cite book}}: CS1 maint: multiple names: authors list (link)

[flyby-9] Cite error: The named reference flyby was used but no text was provided for refs named (see the help page).

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