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Summary for : (532) Herculina

Dyn	T.T	T.B	T T.L B	T.D	Density (g/cm^3)	Δρ/ρ	Diameter (km)	ΔD/D	Mass (kg)	ΔM/M	Ref	Avg.M
MBA	S	S	- \| -	S	2.77 ± 1.57 (D)	56 %	215.2 ± 11.8	5.5 %	1.45e+19 ± 7.82e+18	54 %	S	EVM
MBA	S	S	- \| -	S	2.25 ± 1.77 (D)	79 %	212.9 ± 9.3	4.4 %	1.14e+19 ± 8.82e+18	78 %	S	w.avg
MBA	S				2.12 ± 0.53 (C)	25 %	217.5 ± 5.1	2.3 %	1.15e+19 ± 2.80e+18	24 %	C	?

Average asteroid densities (g/cm^3):
C = 1.3 ± 0.6, B = 2.4 ± 0.5, S = 2.7 ± 0.5, M = 3.5 ± 1.0, P = 2.8 ± 1.6, X = 1.9 ± 0.8, Xc = 4.9 ± 0.9, Xk = 4.2 ± 0.7 (Ref)

Object is a Gaia target for mass determination !

Additional resources:

3D Model | JPL New Horizons | Minor Planet Center | Wikipedia (these auto-generated links might not work)

Note: The density estimates have been ranked from (A) to (E), corresponding to the relative error: (B) less than 20%, (C) between 20 and 50%, (D) between 50 and 100%, and (E) more than 100%. (A) stands for (presumably) reliable estimates (accuracy better than 20%), based on more than 5 mass estimates and 5 diameter estimates, or a spacecraft encounter. Apparently unrealistic densities (ρ > 8) are tagged with (X).

EVM: average by using the Expected Value Method (Ref). w.avg: weighted average (with w = 1/err^2).

T.T: Tholen Tax Class. T.B: Bus & Binzel Tax Class. T T.L: S3OS2 Lazarro (Tholen) Tax Class. T.L B: S3OS2 Lazarro (Bus & Binzel) Tax Class. T.D: DeMeo Tax Class.

Ref: S = SiMDA, C = Carry (2012)

Diameter estimates

Designation	Diameter / Err (km)	ΔD/D	Method	Year	Ref	χ²	Use
(532) Herculina	222.38 ± 4.19	1.9 %	STM	2004	D93	2.97	1
(532) Herculina	217.34 ± 9.10	4.2 %	STM	2010	D64	0.06	2
(532) Herculina	241.26 ± 8.50	3.5 %	NEATM	2010	D64	9.42	3
(532) Herculina	216.77 ± 2.96	1.4 %	STM	2011	D83	0.29	4
(532) Herculina	203.00 ± 14.23	7.0 %	NEATM	2011	D72	0.73	5
(532) Herculina	191.00 ± 4.00	2.1 %	ADAM	2017	D100	36.50	6

plot, average diameter and derived density

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Notes (N):
1: This estimate is discarded for the average diameter (and derived density) calculation in Carry (2012).
2: This estimate is discarded for the average diameter (and derived density) calculation in SiMDA (catalog).

ADAM : All-Data Asteroid Modeling. NEATM : Near-Earth Asteroid Thermal Model. STM : Standard Thermal Model.

EVM diam. average D = (215.2 ± 11.85) km (ΔD/D = 6%, SNR = 18.16) Derived bulk density ρ = (2.77 ± 1.57) g/cm³ (Δρ/ρ = 56%, SNR = 1.8)

References

D64	(2010):	Ryan, E.L., Woodward, C.E., 2010. Rectified Asteroid Albedos and Diameters from IRAS and MSX Photometry Catalogs. Astronomical Journal 140, 933–943.
D72	(2011):	Masiero, J.R., Mainzer, A.K., Grav, T., Bauer, J.M., Cutri, R.M., Dailey, J., Eisenhardt, P.R.M., McMillan, R.S., Spahr, T.B., Skrutskie, M.F., Tholen, D., Walker, R.G., Wright, E.L., DeBaun, E., Elsbury, D., Gautier, IV, T., Gomillion, S., Wilkins, A., 2011. Main Belt Asteroids with WISE/NEOWISE. I. Preliminary Albedos and Diameters. Astrophysical Journal 741, 68.
D83	(2011):	Usui, F., Kuroda, D., Müller, T.G., Hasegawa, S., Ishiguro, M., Ootsubo, T., Ishihara, D., Kataza, H., Takita, S., Oyabu, S., Ueno, M., Matsuhara, H., Onaka, T., 2011. Asteroid Catalog Using Akari: AKARI/IRC Mid-Infrared Asteroid Survey. Publications of the Astronomical Society of Japan 63, 1117–1138.
D93	(2004):	Tedesco, E.F., Noah, P.V., Noah, M.C., Price, S.D., 2004. IRAS Minor Planet Survey. NASA Planetary Data System. IRAS-A-FPA-3-RDR-IMPS-V6.0.
D100	(2017):	Hanuš, J., Viikinkoski, M., Marchis, F., et al., 2017. Volumes and bulk densities of forty asteroids from ADAM shape modeling. Astronomy and Astrophysics 601, A114 (2017). DOI: 10.1051/0004-6361/201629956

Mass estimates

Designation	Mass / Err (kg)	ΔM/M	Method	Year	Ref	N	χ²	Use
(532) Herculina	3.34e+19 ± 5.57e+18	17 %	Deflec	2004	M42	12	11.55	1
(532) Herculina	1.09e+19 ± 1.99e+17	2 %	Ephem	2009	M80		322.31	2
(532) Herculina	1.33e+19 ± 1.33e+18	10 %	Ephem	2009	M86		0.78	3
(532) Herculina	5.76e+18 ± 1.51e+18	26 %	Ephem	2010	M93	12	33.29	4
(532) Herculina	1.46e+19 ± 6.92e+18	47 %	Deflec	2010	M92		0.00	5
(532) Herculina	9.89e+18 ± 5.59e+18	57 %	Ephem	2011	M103		0.67	6
(532) Herculina	1.25e+19 ± 6.31e+18	50 %	Deflec	2011	M97		0.10	7
(532) Herculina	1.81e+19 ± 4.46e+18	25 %	Deflec	2011	M97		0.66	8
(532) Herculina	1.75e+19 ± 4.33e+18	25 %	Deflec	2011	M97		0.49	9
(532) Herculina	2.26e+19 ± 8.76e+18	39 %	Deflec	2011	M97		0.86	10
(532) Herculina	5.75e+18 ± 1.91e+18	33 %	Ephem	2011	M100		20.86	11
(532) Herculina	2.07e+19 ± 7.95e+17	4 %	OrbFitN	2014	M123	2	60.96	12
(532) Herculina	3.60e+19 ± 7.32e+18	20 %	Deflec	2017	M125	2	8.64	13
(532) Herculina	2.98e+19 ± 1.15e+19	39 %	Deflec	2017	M125	2	1.78	14
(532) Herculina	3.42e+19 ± 6.18e+18	18 %	Deflec	2017	M125	3	10.19	15
(532) Herculina	8.16e+18 ± 1.02e+18	13 %	Ephem	2019	M126		38.36	16

plot, average mass and derived density

All

Notes (N):
1: This estimate is discarded for the average mass (and derived density) calculation in Carry (2012).
2: This estimate is discarded for the average mass (and derived density) calculation in SiMDA (catalog).
3: This estimate is an average of individual solutions listed before under the same reference (e.g. M125).

Deflec : Orbital deflection (close encounter) of one or several test asteroids (classical LSQ). Ephem : Planetary ephemeris solution. OrbFitN : Simultaneous multi-asteroid astrometric orbit solution (similar to 'Ephem').

EVM mass average M = (1.447 ± 0.782) × 10¹⁹ kg (ΔM/M = 54%, SNR = 1.9) Derived bulk density ρ = (2.77 ± 1.57) g/cm³ (Δρ/ρ = 56%, SNR = 1.8)

References

M42	(2004):	Kochetova, O.M., 2004. Determination of Large Asteroid Masses by the Dynamical Method. Solar System Research 38, 66–75.
M80	(2009):	Fienga, A., Laskar, J., Morley, T., Manche, H., Kuchynka, P., Le Poncin-Lafitte, C., Budnik, F., Gastineau, M., Somenzi, L., 2009. INPOP08, a 4-D planetary ephemeris: from asteroid and time-scale computations to ESA Mars Express and Venus Express contributions. Astronomy and Astrophysics 507, 1675–1686.
M86	(2009):	Folkner, W.M., Williams, J.G., Boggs, D.H., 2009. The planetary and lunar ephemeris de 421. IPN Progress Report 42, 1–34.
M92	(2010):	Somenzi, L., Fienga, A., Laskar, J., Kuchynka, P., 2010. Determination of asteroid masses from their close encounters with Mars. Planetary and Space Science 58, 858–863.
M93	(2010):	Fienga, A., Manche, H., Kuchynka, P., Laskar, J., Gastineau, M., 2010. INPOP10a. Scientific Notes.
M97	(2011):	Zielenbach, W., 2011. Mass Determination Studies of 104 Large Asteroids. Astronomical Journal 142, 120–128.
M100	(2011):	Fienga, A., Kuchynka, P., Laskar, J., Manche, H., Gastineau, M., 2011. Asteroid mass determinations with INPOP planetary ephemerides. EPSC-DPS Joint Meeting 2011 , 1879.
M103	(2011):	Konopliv, A.S., Asmar, S.W., Folkner, W.M., Karatekin, Ö., Nunes, D.C., Smrekar, S.E., Yoder, C.F., Zuber, M.T., 2011. Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters. Icarus 211, 401–428.
M123	(2014):	Goffin, E., 2014. Astrometric asteroid masses: a simultaneous determination. Astronomy & Astrophysics, Volume 565, id.A56, 8 pp.
M125	(2017):	Baer, J., Chesley, S.R., 2017. Simultaneous Mass Determination for Gravitationally Coupled Asteroids. The Astronomical Journal, Volume 154, Issue 2, article id. 76, 11 pp.
M126	(2019):	Fienga, A., et. al, 2019. INPOP19a planetary ephemeris. Notes Scientifiques et Techniques de l'Institut de mécanique céleste,

Size, Mass and Density of Asteroids (SiMDA)

Summary for : (532) Herculina

Diameter estimates

Mass estimates