Summary for : (76) Freia

DynT.TT.BT T.L B T.DDensity (g/cm^3)Δρ/ρDiameter (km)ΔD/DMass (kg)ΔM/MRefAvg.M
MBAPX- | -C1.76 ± 1.37   (D)78 %166.7 ± 10.06.0 %4.27e+18 ± 3.24e+1876 %SEVM
MBAPX- | -C2.13 ± 1.15   (D)54 %169.5 ± 9.15.4 %5.43e+18 ± 2.80e+1852 %Sw.avg
MBAC0.79 ± 1.69   (E)214 %167.9 ± 8.75.2 %1.97e+18 ± 4.20e+18213 %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

DesignationDiameter / Err (km)ΔD/DMethodYearRefNχ2Use
(76) Freia183.66 ± 4.002.2 % STM2004D932 18.06 1
(76) Freia161.68 ± 5.233.2 % STM2010D64 0.91 2
(76) Freia192.41 ± 8.574.5 % NEATM2010D64 9.03 3
(76) Freia158.67 ± 4.963.1 % Occ2011D95 2.59 4
(76) Freia168.36 ± 1.951.2 % STM2011D83 0.76 5
(76) Freia158.57 ± 8.025.1 % NEATM2011D72 1.02 6

plot, average diameter and derived density

All

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).

NEATM : Near-Earth Asteroid Thermal Model. Occ : Stellar occultation. STM : Standard Thermal Model.


EVM diam. average D = (166.7 ± 10.04) km   (ΔD/D = 6%, SNR = 16.60) Derived bulk density ρ = (1.76 ± 1.37) g/cm3   (Δρ/ρ = 78%, SNR = 1.3)


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.
D95(2011):Dunham, D.W., Herald, D., Frappa, E., Hayamizu, T., Talbot, J., Timerson, B., 2011. Asteroid Occultations. NASA Planetary Data System. EAR-A-3-RDR-OCCULTATIONS-V9.0.

Mass estimates

DesignationMass / Err (kg)ΔM/MMethodYearRefNχ2Use
(76) Freia4.12e+17 ± 2.13e+18517 %Deflec 2011M973.28 1
(76) Freia6.72e+17 ± 2.06e+18307 %Deflec 2011M973.05 2
(76) Freia1.43e+19 ± 9.03e+1863 %Deflec 2011M971.23 3
(76) Freia7.56e+18 ± 7.95e+1711 %OrbFitN 2014M12317.07 4
(76) Freia9.34e+18 ± 2.78e+1830 %Deflec 2015M1243.32 5
(76) Freia4.24e+18 ± 1.49e+1835 %Deflec 2017M1250.00 6
(76) Freia3.24e+18 ± 1.35e+1842 %Ephem 2019M1260.58 7

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 = (4.272 ± 3.239) × 1018 kg   (ΔM/M = 76%, SNR = 1.3) Derived bulk density ρ = (1.76 ± 1.37) g/cm3   (Δρ/ρ = 78%, SNR = 1.3)


References
M97(2011):Zielenbach, W., 2011. Mass Determination Studies of 104 Large Asteroids. Astronomical Journal 142, 120–128.
M123(2014):Goffin, E., 2014. Astrometric asteroid masses: a simultaneous determination. Astronomy & Astrophysics, Volume 565, id.A56, 8 pp.
M124(2015):Kretlow, M., 2015. https://astro.kretlow.de .
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,