More on the bending of light !

See I. I. Shapiro, Science 157

1970

Earlier work this paper cites.

See, for example, Handbook of Mathematical Functions

1972

Earlier work this paper cites.

Let us note here that a few presentations do go beyond a consideration of ( 14

1973

Earlier work this paper cites.

See, for example, M. J. Jaklitsch, C.Hellaby and D. R. Matravers, GRG 21

1989

Earlier work this paper cites.

The text by B. O’Neill, Semi-Riemannian Geometry

2001

Cited alongside, same era.

K. Lake, Phys. Rev. D 65

2002

Cited alongside, same era.

See, S. S. Shapiro, J. L. Davis, D. E. Lebach and J. S. Gregory, Phys. Rev Lett. 92

2004

Cited alongside, same era.

The fact that ( 3

2005

Cited alongside, same era.

Electronic Address: lake@astro.queensu.ca

Cited in the paper.

The constancy of u Σ u_{\Sigma} (as regards Λ \Lambda ), for grazing incidence, is set by junction conditions on the deflector as explained in lake . Since we have assumed that u ≤ u Σ u\leq u_{{}_{\Sigma}} , the form ( 4

Cited in the paper.

For 1 / 4 ≤ u Σ < 1 / 3 1/4\leq u_{{}_{\Sigma}}<1/3 , l ( u ) > 2 u Σ ( 1 − 3 u Σ ) > 0 l(u)>2u_{{}_{\Sigma}}(1-3u_{{}_{\Sigma}})>0 and for u Σ ≤ 1 / 4 u_{{}_{\Sigma}}\leq 1/4 , l ( u ) > u Σ ( 1 − 2 u Σ ) > 0 l(u)>u_{{}_{\Sigma}}(1-2u_{{}_{\Sigma}})>0

Cited in the paper.

The limit u = 0 u=0 plays a central role in most arguments and this limit deserves special consideration for Λ > 0 \Lambda>0 . If the emitter lies within the cosmological horizon we have the restriction u ≥ u ℋ u\geq u_{\mathcal{H}} where u ℋ ∼ Λ ​ m 2 / 3 u_{\mathcal{H}}\sim\sqrt{\Lambda m^{2}/3} for Λ > 0 \Lambda>0 jhm . Using current limits on Λ \Lambda , for a solar mass deflector, we have u ℋ < 2.2 10 − 26 u_{\mathcal{H}}<2.2\;10^{-26} . This does not change in any significant way any argument in this paper (but see Appendix B)

Cited in the paper.

We use the following adopted

Cited in the paper.

The notation comes from the fact that the factor 1 2 \frac{1}{2} is exact

Cited in the paper.

Note that 2 ​ Δ o ​ u ​ t 2\Delta_{out} increases monotonically with distance even though this is not clear in the Table because of number . See also Appendix C

Cited in the paper.

For the planets I have used the semi-major axis

Cited in the paper.

C. R. Keeton and A. O. Petters, Phys. Rev D 72

2005

Later among the works it cites.

See C. M. Will, “The Confrontation between General Relativity and Experiment”, Living Rev. Relativity 9

2006

Later among the works it cites.

This is sometimes referred to as “Eddington’s method”. See, for example, J. Plebański and A. Krasiński, General Relativity and Cosmology

2006

Later among the works it cites.

W. Rindler and M. Ishak, Phys. Rev. D 76

2007

Closest in time.