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Re: sun's distance as lab exercise?



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)

maximum elongation

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

Nice for circular orbits. I assume you mean the analog for real
planetary orbits.

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.

G isn't that easy to measure in the lab. It was first achieved by
Cavendish in (I think) 1792. He published under the flambuoyant
title "Weighing the Earth". By that time a value of the au was
available with a smaller uncertainty than Cavendish's measured
uncertainty in G.

Leigh