> The Sun is centered in your animation, but is that also the case for its
> position in the Local Group? Probably not. Does that not introduce a
> "deformation" in the way the group is viewed from the outside?

Dont exactly understand what do you mean with that.
"Local Group" most of the time is used when talking about galaxies.
And yes, the sun ist centered only in my animation. Beside of that she is the
center of virtually nothing. Not the Local Cloud, the Local Bubble or anything
else.

Here the english Wikipedia-Site of the Local Bubble.
https://en.wikipedia.org/wiki/Local_Bubble

Also you can check out the german site.
It has a few nice drawings of our surrounding.
https://de.wikipedia.org/wiki/Lokale_Blase

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