Would you care to point to where the earth centre of mass is on your pear. So we can confirm your mathematical configurations, to be more then just metaphors.
You keep asking me that, and I keep pointing you to the internationally recognised standards and I'm not sure what other answer you're looking for. Let's try again.
The centre of mass of the earth is below you. It's down. That's not a joke, wherever all the 'down's meet, that's the centre of mass. I mean, where else would it be?
A huge amount of effort has been put into accurately measuring the geoid over the years because of it's value to surveying, meteorology, cartography and many other things. As always, this information isn't a secret that you need to pry out of me, it's
on the internet. The geoid is the gravitational surface of the earth rather than the physical one. The earth isn't a uniform density, nor is it -as you are fond of pointing out- a perfect sphere. That means that gravity is
slightly variable in strength and direction as you move around the surface - if a dense area is to your right, gravity will be slightly off to the right, if the dense area is the other side of the world, gravity will be a little weaker. However, it still all comes down to a point. The centre of mass.
Are you unsure about
how an irregular shape can
have a centre of mass? Or do you want me to say that it's 40 miles beneath Nairobi? Or what? You ask where it is, but the answer never seems to satisfy. If none of that was enlightening, instead of asking for a fourth time, maybe tell me what's inadequate about the previous answers.