Abstract

A spherical particle, moving through an isotropic radiation field, will generally experience a small force that decreases its velocity because the Doppler effect causes a difference of radiation pressure between the front and back side of the particle. However, if the radiation is monochromatic, it is possible that certain particles, because of diffraction, can also absorb momentum from the radiation and increase their velocity. Numerical estimates are made to find the maximum possible effect of the radiation force on the velocity of a particle moving through an isotropic radiation field, such as that which exists inside a galaxy where the radiation from the stars is considered to be isotropic. These estimates indicate that the effects of this radiation generally take place over periods of time that are comparable to the age of the galaxies or longer.

© 1970 Optical Society of America

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References

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  1. R. Schlegel, Am. J. Phys. 28, 687 (1960).
    [Crossref]
  2. W. Rindler and D. W. Sciama, Am. J. Phys. 29, 643 (1961).
    [Crossref]
  3. J. Terrell, Am. J. Phys. 29, 644 (1961).
    [Crossref]
  4. E. T. Whittaker, Mat. Ann. 57, 347 (1903).
    [Crossref]
  5. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  6. H. P. Robertson, Monthly Notices Roy. Astron. Soc. 97, 423 (1937).
  7. H. P. Robertson and T. W. Noonan, Relativity and Cosmology (Saunders, Philadelphia, 1968).
  8. P. Debye, Ann. Physik 30, 57 (1909).
    [Crossref]
  9. W. M. Irvine, J. Opt. Soc. Am. 55, 16 (1965).
    [Crossref]
  10. J. L. Greenstein, Harvard Obs. Circ. 422, 10 (1937).
  11. C. W. Allen, Astrophysical Quantities (Athlone, London, 1963).
  12. F. Hoyle, Galaxies, Nuclei and Quasars (Harper and Row, New York, 1965).

1965 (1)

1961 (2)

W. Rindler and D. W. Sciama, Am. J. Phys. 29, 643 (1961).
[Crossref]

J. Terrell, Am. J. Phys. 29, 644 (1961).
[Crossref]

1960 (1)

R. Schlegel, Am. J. Phys. 28, 687 (1960).
[Crossref]

1937 (2)

J. L. Greenstein, Harvard Obs. Circ. 422, 10 (1937).

H. P. Robertson, Monthly Notices Roy. Astron. Soc. 97, 423 (1937).

1909 (1)

P. Debye, Ann. Physik 30, 57 (1909).
[Crossref]

1903 (1)

E. T. Whittaker, Mat. Ann. 57, 347 (1903).
[Crossref]

Allen, C. W.

C. W. Allen, Astrophysical Quantities (Athlone, London, 1963).

Debye, P.

P. Debye, Ann. Physik 30, 57 (1909).
[Crossref]

Greenstein, J. L.

J. L. Greenstein, Harvard Obs. Circ. 422, 10 (1937).

Hoyle, F.

F. Hoyle, Galaxies, Nuclei and Quasars (Harper and Row, New York, 1965).

Irvine, W. M.

Noonan, T. W.

H. P. Robertson and T. W. Noonan, Relativity and Cosmology (Saunders, Philadelphia, 1968).

Rindler, W.

W. Rindler and D. W. Sciama, Am. J. Phys. 29, 643 (1961).
[Crossref]

Robertson, H. P.

H. P. Robertson, Monthly Notices Roy. Astron. Soc. 97, 423 (1937).

H. P. Robertson and T. W. Noonan, Relativity and Cosmology (Saunders, Philadelphia, 1968).

Schlegel, R.

R. Schlegel, Am. J. Phys. 28, 687 (1960).
[Crossref]

Sciama, D. W.

W. Rindler and D. W. Sciama, Am. J. Phys. 29, 643 (1961).
[Crossref]

Terrell, J.

J. Terrell, Am. J. Phys. 29, 644 (1961).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Whittaker, E. T.

E. T. Whittaker, Mat. Ann. 57, 347 (1903).
[Crossref]

Am. J. Phys. (3)

R. Schlegel, Am. J. Phys. 28, 687 (1960).
[Crossref]

W. Rindler and D. W. Sciama, Am. J. Phys. 29, 643 (1961).
[Crossref]

J. Terrell, Am. J. Phys. 29, 644 (1961).
[Crossref]

Ann. Physik (1)

P. Debye, Ann. Physik 30, 57 (1909).
[Crossref]

Harvard Obs. Circ. (1)

J. L. Greenstein, Harvard Obs. Circ. 422, 10 (1937).

J. Opt. Soc. Am. (1)

Mat. Ann. (1)

E. T. Whittaker, Mat. Ann. 57, 347 (1903).
[Crossref]

Monthly Notices Roy. Astron. Soc. (1)

H. P. Robertson, Monthly Notices Roy. Astron. Soc. 97, 423 (1937).

Other (4)

H. P. Robertson and T. W. Noonan, Relativity and Cosmology (Saunders, Philadelphia, 1968).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

C. W. Allen, Astrophysical Quantities (Athlone, London, 1963).

F. Hoyle, Galaxies, Nuclei and Quasars (Harper and Row, New York, 1965).

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Figures (1)

Fig. 1
Fig. 1

Irvine’s graph of Qpr for n=1.33.

Equations (37)

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G μ = - ( T μ ν / x ν ) d V ,
x 1 = x ,             x 2 = y ,             x 3 = z ,             and             x 4 = c t .
T i 4 = c g i ,             T 44 = energy density , and             T i j = F i / A j + g i w j ,
g i = ( u d Ω / 4 π c ) cos α i ,             and             w i = c cos α i .
T i 4 = ( u d Ω / 4 π ) cos α i ,             T 44 = u ( d Ω / 4 π ) ,
T i j = ( u d Ω / 4 π ) cos α i cos α j .
G ¯ 3 = - ( T ¯ 31 x ¯ + T ¯ 32 y ¯ + T ¯ 33 z ¯ + T ¯ 34 c t ¯ ) d V ¯ .
G ¯ 3 = π a 2 c d t ¯ ( cos α ¯ 1 T ¯ 31 + cos α ¯ 2 T ¯ 32 + cos α ¯ 3 T ¯ 33 ) .
F ¯ z = c d P ¯ z / c d t ¯ = π a 2 ( cos α ¯ 1 T ¯ 31 + cos α ¯ 2 T ¯ 32 + cos α ¯ 3 T ¯ 33 ) .
T ¯ 31 = γ T 31 - β γ T 41 , T ¯ 32 = γ T 32 - β γ T 42 ,             and T ¯ 33 = γ 2 T 33 - 2 γ 2 β T 34 + β 2 γ 2 T 44 ;
cos ϕ = ( cos ϕ ¯ + β ) / ( 1 + cos ϕ ¯ ) ,
F z = F ¯ z = π a 2 u ( 1 - β 2 ) 2 cos ϕ ¯ ( 1 + β cos ϕ ¯ ) 4 d Ω ¯ 4 π .
F z r = a 2 u 4 Q p r ( a , λ ¯ ) ( 1 - β 2 ) 2 cos ϕ ( 1 + β cos ϕ ¯ ) 4 d Ω ¯ .
ν ¯ = ν ( 1 - β 2 ) 1 2 / ( 1 + β cos ϕ ¯ ) ,
F z = - 4 3 π a 2 u β / ( 1 - β 2 ) .
F z = c ( d / d t ) [ m 0 β ( 1 - β 2 ) 1 2 ] .
β 1 + ( 1 - β 2 ) 1 2 = β 0 1 + ( 1 - β 0 2 ) 1 2 exp ( - 4 π a 2 u t 3 m 0 c ) ,
v / v 0 = exp ( - 4 π a 2 u t / 3 m 0 c ) .
t e = ( 3 m 0 c ) / ( 4 π a 2 u ) ,
Q p r = m x ¯ + b = 2 π a m ν ¯ / c + b ,
F z = - ( u / 3 ) π a 2 ( 5 m x 0 + 4 b ) β .
Q p r = q ( x - x 0 ) 3 + m ( x - x 0 ) + h ,
β = [ - 5 ( m x 0 + 4 h ) / ( 3 q x 0 3 ) ] 1 2 .
Q p r 1 ( 14 / 3 ) ( 2 π a / λ ¯ ) 4
Q p r 2 ( 8 / 3 ) [ ( - 1 ) / ( + 1 ) ] 2 ( 2 π a / λ ¯ ) 4
F z 1 = - ( 7 / 3 ) × 2 8 π 5 a 6 ( u / 3 ) ( ν 4 / c 4 ) β ,
F z 2 = - ( 2 10 / 3 ) π 5 a 6 ( u / 3 ) ( ν 4 / c 4 ) [ ( - 1 ) / ( + 1 ) ] 2 β .
Q p r = 4 x ¯ F ( λ ¯ ) ,
F ( λ ¯ ) = 3 ( σ / ω ¯ ) / [ ( + 2 ) 2 + ( σ / ω ¯ ) 2 ] ,
Q p r = 4.3 x ¯ - 2.2 × 10 5 a .
Q p r = 3.0 x ¯ - 2.5 × 10 5 a
F = k β ,
v = v 0 exp ( k t / m 0 c ) ,
t e = c m 0 / k .
t e = ρ a c / u ,
u = 7 × 10 - 13 erg / cm 3 .
t e = ( 4 a c ρ ) / ( 5 u m x 0 + 4 u b ) .