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.
If we apply it to two planets (say, venus and earth) we get two equations
and four unknowns (M_sun, R_earth, R_venus, T_venus). However, we can get
an estimate of T_venus by measuring how long it takes between the times
when venus is seen at its highest point in the sky (I'm sorry, I don't
know the technical name for that). The value of T_venus would be the time
measured minus some correction to account for the motion of the earth.
Knowing T_venus, we now have two equations and three unknowns. However,
we can measure the angle above the horizon of venus when it is at its
highest point in the sky (i.e., angle between sun and venus). The tangent
of that angle should be R_venus/R_earth, which gives us a third equation.
So, what does everyone think? Is this a viable way of doing it?
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| Robert Cohen Department of Physics |
| East Stroudsburg University |
| bbq@esu.edu East Stroudsburg, PA 18301 |
| http://www.esu.edu/~bbq/ (570) 422-3428 |
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