The flyby anomaly: a multivariate analysis approach

[EN] The flyby anomaly is the unexpected variation of the asymptotic post-encounter velocity of a spacecraft with respect to the pre-encounter velocity as it performs a slingshot manoeuvre. This effect has been detected in, at least, six flybys of the Earth but it has not appeared in other recent flybys. In order to find a pattern in these, apparently contradictory, data several phenomenological formulas have been proposed but all have failed to predict a new result in agreement with the observations. In this paper we use a multivariate dimensional analysis approach to propose a fitting of the data in terms of the local parameters at perigee, as it would occur if this anomaly comes from an unknown fifth force with latitude dependence. Under this assumption, we estimate the range of this force around 300 km .Acedo Rodríguez, L. (2017). The flyby anomaly: a multivariate analysis approach. Astrophysics and Space Science. 362(2):1-7. doi:10.1007/s10509-017-3025-zS173622Acedo, L.: Adv. Space Res. 54, 788 (2014). 1505.06884Acedo, L.: Universe 1, 422 (2015a)Acedo, L.: Galaxies 3, 113 (2015b)Acedo, L.: Mon. Not. R. Astron. Soc. 463(2), 2119 (2016)Acedo, L., Bel, L.: Astron. Nachr. (2016). 1602.03669Adler, S.L.: Int. J. Mod. Phys. A 25, 4577 (2010). 0908.2414 . doi: 10.1142/S0217751X10050706Adler, S.L.: In: Proceedings of the Conference in Honour of Murray Gellimann’s 80th Birthday, p. 352 (2011). doi: 10.1142/9789814335614_0032Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G.: Phys. Rev. D 65(8), 082004 (2002). gr-qc/0104064 . doi: 10.1103/PhysRevD.65.082004Anderson, J.D., Campbell, J.K., Ekelund, J.E., Ellis, J., Jordan, J.F.: Phys. Rev. Lett. 100(9), 091102 (2008). doi: 10.1103/PhysRevLett.100.091102Atchison, J.A., Peck, M.A., Streetman, B.J.: J. Guid. Control Dyn. 33, 1115 (2010). doi: 10.2514/1.47413Border, J.S., Pham, T., Bedrossian, A., Chang, C.: 2015 Delta Differential One-way Ranging in Dsn Telecommunication Link Design Handbook (810-005). http://deepspace.jpl.nasa.gov/dsndocs/810-005/210/210A.pdf . Accessed: 2016-11-17Burns, J.A.: Am. J. Phys. 44(10), 944 (1976). doi: 10.1119/1.10237Busack, H.-J.: arXiv e-prints 1312.1139 (2013)Butrica, A.J.: In: From Engineering Science to Big Science: The NACA and NASA Collier Trophy Research Project Winners, p. 251 (1998)Cahill, R.T.: arXiv e-prints 0804.0039 (2008)Chamberlin, A., Yeomans, D., Giorgini, J., Chodas, P.: 2016 Horizons Ephemeris System. http://ssd.jpl.nasa.gov/horizons.cgi . Accessed: 2016-10-27Danby, J.M.A.: Fundamentals of Celestial Mechanics, 2nd edn. Willmann-Bell, Richmond (1988)Dickey, J.O., Bender, P.L., Faller, J.E., Newhall, X.X., Ricklefs, R.L., Ries, J.G., Shelus, P.J., Veillet, C., Whipple, A.L., Wiant, J.R., Williams, J.G., Yoder, C.F.: Science 265, 482 (1994). doi: 10.1126/science.265.5171.482Feng, J.L., Fornal, B., Galon, I., Gardner, S., Somolinsky, J., Tait, T.M.P., Tanedo, P.: Phys. Rev. Lett. 117, 071803 (2016). doi: 10.1103/PhysRevLett.117.071803Fischbach, E., Buncher, J.B., Gruenwald, J.T., Jenkins, J.H., Krause, D.E., Mattes, J.J., Newport, J.R.: Space Sci. Rev. 145, 285 (2009). doi: 10.1007/s11214-009-9518-5Folkner, W.M., Williamns, J.G., Boggs, D.H., Park, R.S., Kuchynka, P.: IPN Progress Report 42(196) (2014)Franklin, A., Fischback, E.: The Rise and Fall of the Fifth Force. Discovery, Pursuit, and Justification in Modern Physics, 2nd edn. Springer, New York (2016)Hackmann, E., Lämmerzahl, C.: In: 38th COSPAR Scientific Assembly. COSPAR Meeting, vol. 38, p. 3 (2010)Hafele, J.C.: arXiv e-prints 0904.0383 (2009)Iorio, L.: Sch. Res. Exch. 2009 807695 (2009). 0811.3924 . doi: 10.3814/2009/807695Iorio, L.: Astron. J. 142, 68 (2011a). 1102.4572 . doi: 10.1088/0004-6256/142/3/68Iorio, L.: Mon. Not. R. Astron. Soc. 415, 1266 (2011b). 1102.0212Iorio, L.: Galaxies 1, 192 (2013). 1306.3166Iorio, L.: Int. J. Mod. Phys. D 24, 1530015 (2015). 1412.7673Jouannic, B., Noomen, R., van den IJSel, J.A.A.: In: Proceedings of the 25th International Symposium on Space Flight Dynamics ISSFD, Munich (Germany), 2015Krasinsky, G.A., Brumberg, V.A.: Celest. Mech. Dyn. Astron. 90, 267 (2004)Lämmerzahl, C., Preuss, O., Dittus, H.: In: Dittus, H., Lämmerzahl, C., Turyshev, S.G. (eds.) Lasers, Clocks and Drag-Free Control: Exploration of Relativistic Gravity in Space. Astrophysics and Space Science Library, vol. 349, p. 75 (2008). doi: 10.1007/978-3-540-34377-6_3McCulloch, M.E.: Mon. Not. R. Astron. Soc. 389, 57 (2008). 0806.4159 . doi: 10.1111/j.1745-3933.2008.00523.xPinheiro, M.J.: Phys. Lett. A 378, 3007 (2014). 1404.1101Pinheiro, M.J.: Mon. Not. R. Astron. Soc. 461(4), 3948 (2016)Rievers, B., Lämmerzahl, C.: Ann. Phys. 523, 439 (2011). 1104.3985 . doi: 10.1002/andp.201100081Thompson, P.F., Abrahamson, M., Ardalan, S., Bordi, J.: In: 24th AAS/AIAA Space Flight Mechanics Meeting, Santa Fe, New Mexico, January 26–30, 2014, 2014. http://hdl.handle.net/2014/45519Turyshev, S.G., Toth, V.T.: Living Rev. Relativ. 13, 4 (2010). 1001.3686 . doi: 10.12942/lrr-2010-4Turyshev, S.G., Toth, V.T., Kinsella, G., Lee, S.-C., Lok, S.M., Ellis, J.: Phys. Rev. Lett. 108(24), 241101 (2012). 1204.2507 . doi: 10.1103/PhysRevLett.108.241101Vallado, D.A.: Fundamentals of Astrodynamics and Applications, 2nd edn. (2004)Williams, J.G., Turyshev, S.G., Boggs, D.H.: Phys. Rev. Lett. 93(26), 261101 (2004). gr-qc/0411113 . doi: 10.1103/PhysRevLett.93.26110