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Eclipse Predictor - looking for improvements!

Off-topic Eclipse Moon
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Anton Viola avatar
Anton Viola avatar
I created an Excel model of the sun-earth-moon movements (see Astronomy Morsels), including tilt of the moon's orbit wrt. the orbit of the earth around the sun (descending, ascending nodes), as well as distance between moon and earth (perigee, apogee). This model allows for eclipse predictions, but results are not always accurate as the orbits in the model are circles and not ellipses. 

Any tips how to model the earth and moon orbits as ellipses? 

Anton
Oscar avatar
Oscar avatar
yes

it go like dis

(raises forefinger and draws an ellipse in the air)



Rate my amazing intelligence plz.
Bill McLaughlin avatar
Bill McLaughlin avatar
You could make one of these like I did.

NOTE: Nighskypictures.com website shown is no longer mine  since the video is 9 years old....

Ferguson's Paradox
Anton Viola avatar
Anton Viola avatar
So, I now know that I have to integrate Kepler's laws 1 and 2. So, I compiled a spreadsheet, illustrating all 3 laws, quite happy with it. You can find it on https://www.astronomy-morsels.ch/morsels.

Anton
Anton Viola avatar
Anton Viola avatar
Made an improvement: The spreadsheet now shows how the orbital velocity changes over time, quite nice to see!

Kepler's Laws - Spreadsheet

Anton
MaksPower avatar
MaksPower avatar
Mathematically, using ellipses will only give you a very rough approximation. It is not analytically possible to do better just using ellipses.

To obtain better accuracy you need to deal with the maths properly, including the perturbation series which affect both the earth and the moon. The standard textbook presenting this is by Jan Meeus https://www.amazon.com.au/dp/0943396220?ref_=mr_referred_us_au_au

Using Meeus' you can calculate eclipses to around 1 second in time, and the limits of the eclipse path to around 1km on earth; I used to do this with an HP41CX - and yes it could (just) manage the full series for the moons position, sun earth and do the trig.

I'm also fairly sure you can download the maths in Exel spreadsheet format somewhere - I have seen it advertised online before.

The second reference you will probably want is the USNO "Explanatory Supplement to the Astronomical Almanac"
https://aa.usno.navy.mil/publications/exp_supp
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Anton Viola avatar
Anton Viola avatar
Great, thanks! I’ll dive into this, have the textbook already.

Best,

Anton
Well Written