Ballance egg on end on winter solstice

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lortech
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Well, I missed the opportunity to try this.

Seems, within the first one two two minutes, you can balance a egg on its end when the Earth is at its solar minimum called the winter solstice..the shortest day of the year.

Now, I figure, the Earth's gravitational constant in relation to the sun and moon have a play in this phenomena? Anyone care to explain what is happening in this case with physics math?
 
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Not much to explain. That "balancing an egg at the equinox" is an urban legend--no basis in fact.

Here's a video from Phil Plait (BadAstronomy.com) showing how he balances an egg:

https://www.youtube.com/watch?v=RrhdR0G2PQ0