Guidelines for measuring solar radius with Baily beads analysis

Abstract

By inspection of central eclipses videorecords, data of Baily beads timings are retrievable. Knowing the lunar limb profile at the moment of the eclipse we evaluate the excess or defect of solar limb when the Sun is assumed at its standard radius. Two procedures of data analysis are here presented: one based on limb heights and the other on times. While these methods are based upon Occult 4 software, they can be used with other ephemerides and new lunar profiles. The example of 2006 total eclipse data, with its remarkably negative value of ΔR= -0.41"± 0.04", is presented.

The Reflecting Heliometer of Rio de Janeiro after 6 years of activity

“…This angle has been measured also with a fixed wooden reference rod, with special pinhole masks to focus the rod at finite distance on the focal plane of the telescope designed for sources at infinity. The Reflecting Heliometer was carried to Easter Island for the total eclipse of 2009 to calibrate the heliometric angle with the Baily beads method Sigismondi (2009). After the least squares method applied to the measures made in periods with the same filter's configuration have been compared with corresponding eclipse data showing the stability of the configuration.…”

Long term variations of solar radius

“…Nothing will change in their timings which are the main issues of these observational data. Once we have a set of Baily beads identified from a video of a suitable grazing eclipse [12], let say N , we could calculate the radius of a circle of which are known N points, or of an ellipse to include also oblateness effects. The accuracy increases proportionally to √ N , improving by a factor √ N /2 the measurements based only on the totality duration (equivalent to N = 2).…”

Baily’s Beads Atlas in 2005 – 2008 Eclipses

“…For more than two-thousand years it has been a challenge for astronomers to measure the diameter of the Sun (Sigismondi and Oliva, 2005). Francis Baily (1774 -1844) (Hockey, 2007) pointed out that, if the observer's position varies by a few hundred yards from the shadow's path limit of a central eclipse, tiny points of light were visible on the lunar edge.…”

“…Baily's beads can last for a significant length of time on the edges of the umbral path of the eclipse. There the eclipses are called grazing (Sigismondi and Oliva, 2006). The observation of this phenomenon provides one of the most precise methods to determine the angular diameter of the Sun (Bode, Büchner, and Mushardt, 1995), because the timing of such beads is not affected by atmospheric turbulence: It depends only on the space geometry along the line of sight solar limb -lunar limb -observer.…”

“…There are various methods of analysis, based on different software such as SOLRAD (D.W. Dunham), Occult 4 (D. Herald, 2008), and Sunbeads2 (R. Büchner), and usually observations are interpreted only by a single method. The differences among them is in the ephemerides used, but all of them are based upon the Watts atlas, and all recover the solar diameter as the one that minimizes residuals between observed and calculated heights of the solar limb above lunar valleys (Sigismondi, 2008c).…”