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I'm not an astronomer but this question of measuring the sun's distance
got me thinking (uh oh). It seems it can be done if one can measure the
following:
1. Period of earth's orbit
2. Period of venus' orbit
3. Angle between venus and sun when it is as far from the sun (from our
viewpoint) as possible (sorry, I don't know the correct name for this)
Here's my thinking...assuming gravitational attraction between sun
and earth provides the centripetal force,
G M_sun / R_orbit^2 = (2*pi)^2 R_orbit / T_orbit^2
This is an equation with four unknowns (G, M_sun, R_orbit and T_orbit).
If we assume G can be measured in the lab, then we only have three
unknowns. Assuming we could measure the earth's orbital period,
we only have two unknowns.