To get an own measure of the Astronomical Unit by means of the following
formula for the Sun's parallax (see the
related paper (in German or in English)
By evaluating pictures taken during the transit of Venus (or Mercury, respectively) you get all results relative to the sun's angular radius ρ_{S} . For instance, by comparison of simultaneously taken pictures of different observers you get the relative parallax effect f. To be able to derive its absolute value Δβ you must know the angular radius of the Sun:
Δβ = f ρ_{S}
Of course, you know ρ_{S} roughly (about 15 arcminutes) and you can find its exact value - even for the day of interest. But:
There are, at least, two simple possibilities for this measurement:
Sunspots on the ground | Light rays causing the spots on the ground |
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Mounting of a binocular for observing and measuring the sun's movement | The both projection of the Sun (during an eclipse | Projection with ... | ... Solarscope |
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Having the optical system fixed you will soon remark that the Sun's picture tends to wander over the sheet.
Determine the speed of this movement. The most exact procedure for that is to draw a circle on the sheet, slightly larger than the projection picture, and to measure the time, which the picture needs to completely leave the circle (from "third contact" t_{1} to "fourth contact" t_{2} ):
Start | "Third contact": t_{1} | "Fourth contact": t_{2} |
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Therefore, the angular radius of the Sun must be:
While the hour angle increases by Δτ the Sun is moving at the celestial sphere by rcosδ_{S}Δτ. The corresponding central angle is, therefore, cosδ_{S} Δτ. |
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The situation of the above picture, but now projected to the plane of meridian. |
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Editors: | Udo Backhaus |
last update: 01.04.2012 | |||
Stephan Breil |