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                                      Michael Lee's Mathematics and Physics

Astronomy

 

                "Supermoon," January 20, 2019. 18:11 MST Edmonton, Alberta, Canada. Photograph by Michael Guy Lee

 

The Astronomical Unit (AU) or the distance from the Earth to the Sun.

 

It's intriguing the great seventeenth century Dutch mathematician, physicist and astronomer Christiaan Huygens managed to accurately measure the Astronomical Unit or the distance from the Earth to the Sun in 1659.  He thought it to be 1.023 multiplied by today's measurements of 1.530386217e11 metres; that's amazingly good. They say he, like Galileo, noticed the phases of Venus and he reasoned that whenever Venus is 'half lit' it means the Sun, Venus and the Earth form a right-angled triangle. Using trigonometry, if we had a reasonable estimate of the distance of Venus to the Earth during this configuration (length x), it would be easy to calculate the Astronomical Unit.  His difficulty was observing Venus half lit, like a quarter moon, would be next to impossible.  However, he must have reasoned that angle theta shown below, reaches a maximum magnitude of 46.2 degrees,  when that happens, the planets are in the following configuration.  All angle measurements are in radians.

 

 

 

 
Huygens made one critical assumption which later turned out to be almost entirely true. In order to estimate the distance of Venus to the Earth (length x) when Venus is 'half lit,' he had to know the diameter of Venus.  He, dare I say, 'guessed' that the diameter of Venus and the Earth are the same. This could have arisen from the now known incorrect belief that Venus and the Earth are both inhabitable worlds. Here is a bust of Christiaan Huygens (1629-1695) in Delft, Netherlands.

 

I'm curious to see how this could be recreated as a little project.   First, I need a program that will tell me the angle between any two points in the celestial sphere given their coordinates (i.e. the angular separation), so I put together an Excel spreadsheet that does so.   You are free to use and share it.   If you like it, please make a small contribution to your local animal shelter.

 

Angular Separation Calc.  (Excel spreadsheet) of any two points in the celestial sphere.

 

 Here is an article published by Harvard University about Huygens' measurement.