# 超光速运动

## 解释

### 一些相反的证据

1993年 Thomson 等人提出，类星体3C273的外部喷流是几乎和观测者的视线是共线的。沿着3C273内部喷流观测到的超光速运动最高达到约9.6倍光速[3]

M87星系的喷流较内侧部分已观测到6倍光速的运动。如果要以运动方向和观测者视线夹角很小的模型来解释的话，喷流和视线方向夹角不能高于19°[4]。不过观测证据显示实际的夹角达到43°[5]。同组的科学家后来修改其结果，并宣称他们的观测结果支持喷流中的整体超光速运动[6]

## 数学推导

${\displaystyle AB\ =\ v\delta t}$
${\displaystyle AC\ =\ v\delta t\cos \theta }$
${\displaystyle BC\ =\ v\delta t\sin \theta }$
${\displaystyle t_{2}-t_{1}\ =\ \delta t}$
${\displaystyle t_{1}^{\prime }=t_{1}+{\frac {D_{L}+v\delta t\cos \theta }{c))}$
${\displaystyle t_{2}^{\prime }=t_{2}+{\frac {D_{L)){c))}$
${\displaystyle \delta t^{\prime }=t_{2}^{\prime }-t_{1}^{\prime }=t_{2}-t_{1}-{\frac {v\delta t\cos \theta }{c))=\delta t-{\frac {v\delta t\cos \theta }{c))=\delta t(1-\beta \cos \theta )}$, where ${\displaystyle \beta ={\frac {v}{c))}$
${\displaystyle \delta t={\frac {\delta t^{\prime )){1-\beta \cos \theta ))}$
${\displaystyle BC\ =\ D_{L}\sin \phi \approx \phi D_{L}=v\delta t\sin \theta \Rightarrow \phi D_{L}=v\sin \theta {\frac {\delta t^{\prime )){1-\beta \cos \theta ))}$

${\displaystyle \beta _{T}={\frac {v_{T)){c))={\frac {\beta \sin \theta }{1-\beta \cos \theta ))}$
${\displaystyle {\frac {\partial \beta _{T)){\partial \theta ))={\frac {\partial }{\partial \theta ))\left[{\frac {\beta \sin \theta }{1-\beta \cos \theta ))\right]={\frac {\beta \cos \theta }{1-\beta \cos \theta ))-{\frac {(\beta \sin \theta )^{2)){(1-\beta \cos \theta )^{2))}=0}$
${\displaystyle \Rightarrow \beta \cos \theta (1-\beta \cos \theta )^{2}=(1-\beta \cos \theta )(\beta \sin \theta )^{2))$

## 注释

1. ^
2. ^ Porcas, Richard. Superluminal motions: Astronomers still puzzled. Nature. 1983, 302 (5911): 753. Bibcode:1983Natur.302..753P. doi:10.1038/302753a0.
3. ^ Thomson, R. C.; MacKay, C. D.; Wright, A. E. Internal structure and polarization of the optical jet of the quasar 3C273. Nature. 1993, 365 (6442): 133. Bibcode:1993Natur.365..133T. doi:10.1038/365133a0.; Pearson, T. J.; Unwin, S. C.; Cohen, M. H.; Linfield, R. P.; Readhead, A. C. S.; Seielstad, G. A.; Simon, R. S.; Walker, R. C. Superluminal expansion of quasar 3C273. Nature. 1981, 290 (5805): 365. Bibcode:1981Natur.290..365P. doi:10.1038/290365a0.; Davis, R. J.; Unwin, S. C.; Muxlow, T. W. B. Large-scale superluminal motion in the quasar 3C273. Nature. 1991, 354 (6352): 374. Bibcode:1991Natur.354..374D. doi:10.1038/354374a0.
4. ^ Biretta, John A.; Junor, William; Livio, Mario. Nature. 1999, 401 (6756): 891. Bibcode:1999Natur.401..891J. doi:10.1038/44780. 缺少或|title=为空 (帮助) ; Biretta, J. A.; Sparks, W. B.; MacChetto, F. Hubble Space TelescopeObservations of Superluminal Motion in the M87 Jet. The Astrophysical Journal. 1999, 520 (2): 621. Bibcode:1999ApJ...520..621B. doi:10.1086/307499.
5. ^ Biretta, J. A.; Zhou, F.; Owen, F. N. Detection of Proper Motions in the M87 Jet. The Astrophysical Journal. 1995, 447: 582. Bibcode:1995ApJ...447..582B. doi:10.1086/175901.
6. ^ Biretta, J. A.; Sparks, W. B.; MacChetto, F. Hubble Space TelescopeObservations of Superluminal Motion in the M87 Jet. The Astrophysical Journal. 1999, 520 (2): 621. Bibcode:1999ApJ...520..621B. doi:10.1086/307499.
7. ^ Biretta, John A.; Junor, William; Livio, Mario. Nature. 1999, 401 (6756): 891. Bibcode:1999Natur.401..891J. doi:10.1038/44780. 缺少或|title=为空 (帮助)
8. Rees, M. J. (1966). "Appearance of Relativistically Expanding Radio Sources". Nature 211 (5048): 468–470. Bibcode:1966Natur.211..468R. doi:10.1038/211468a0.
9. Gubbay, J.S.; Legg, A.J.; Robertson, D.S.; Moffet, A.T.; Ekers, R.D.; Seidel, B. Variations of Small Quasar Components at 2,300 MHz. Nature. 1969, 224 (5224): 1094–1095. Bibcode:1969Natur.224.1094G. doi:10.1038/2241094b0.
10. ^ Cohen, M. H.; Cannon, W.; Purcell, G. H.; Shaffer, D. B.; Broderick, J. J.; Kellermann, K. I.; Jauncey, D. L. The Small-Scale Structure of Radio Galaxies and Quasi-Stellar Sources at 3.8 Centimeters. The Astrophysical Journal. 1971, 170: 207. Bibcode:1971ApJ...170..207C. doi:10.1086/151204.
11. ^ Whitney, AR; Shapiro, Irwin I.; Rogers, Alan E. E.; Robertson, Douglas S.; Knight, Curtis A.; Clark, Thomas A.; Goldstein, Richard M.; Marandino, Gerard E.; Vandenberg, Nancy R. Quasars Revisited: Rapid Time Variations Observed Via Very-Long-Baseline Interferometry. Science. 1971, 173 (3993): 225–30. Bibcode:1971Sci...173..225W. PMID 17741416. doi:10.1126/science.173.3993.225.
12. ^ Moffet, A.T.; Gubbay, J.; Robertson, D.S.; Legg, A.J. Evans, D.S, 编. External Galaxies and Quasi-Stelar Objects : IAU Symposium 44, held in Uppsala, Sweden 10-14 August 1970. Dordrecht: Reidel. 1972: 228. ISBN 9027701997.
13. ^ J. Anton Zensus and Timothy J Pearson (编). Superluminal Radio Sources : proceedings of a workshop in honor of Professor Marshall H. Cohen, held at Big Bear Solar Observatory, California, October 28-30, 1986. Cambridge New York: Cambridge University Press. 1987: 3. Bibcode:1987slrs.work....1P. ISBN 9780521345606.
14. ^ Mirabel, I.F.; Rodriguez, L.F. A superluminal source in the Galaxy. Nature. 1994, 371 (6492): 46–48. Bibcode:1994Natur.371...46M. doi:10.1038/371046a0.

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