5 Summary

In this paper I have investigated the potential of trigonometry on cosmological scales for determining the cosmological parameters $\Omega _{\rm M}$and $\Omega _\Lambda$. In particular, I have considered the possibility of measuring the redshift of an object at cosmological distance as seen by another distant object. I have shown that a single such measurement generally constrains a linear combination of the form $C = \Omega _\Lambda + m \Omega _{\rm M}$ and that m can take almost any value depending on the constellation of the objects involved. Further I found that $\sigma_C$decreases from $\sim$ $100 \sigma_{z_2'}$ to $\sim$ $0.1 \sigma_{z_2'}$ for z₁ = 0.1 to 1.5. Finally I showed that the stereoscopic view afforded by combining the 2dFGRS and 2QZ with similar surveys undertaken from a galaxy at z = 0.01 would enable us to constrain  $\Omega _{\rm M}$ and $\Omega _\Lambda$ to within $\sim$1%.