The acceleration thing is a scam theory brought up by The Flat Earth Society.
I do not know flat earth organizations, is The Flat Earth Society in line with the rest of the flat earth community? (eg some people dont like Autism Speaks).
I would say it isn't. Some believe that this organization is created to make flat earthers look stupid with some stupid theories most FEs don't believe.
But because of its name globe earthers tend to think that this is what FEs believe. FEs think that the earth is a flat motionless plane and don't believe there is a space.
But rather that space (other planets for example) would be other places on the flat plane and exists beyond Antarctica (some believe there is more out there, not all)
I still think its all crazy, but thank you for the calm explanation.
