Hi Doug, not sure how much time you've spent digging into this, but are you familiar with the case for a flat earth? A dear friend of mine has been studying it out and is intrigued by it. Would you be so kind to share what you have found?

My first instinct is not to reply to this Q. ("Can he be serious?!") These folks also claim the the moon landings were faked. And they fall for other conspiracy theories, too. I need to focus on the more serious questions. However... to help you help your friend to focus on things that matter...

I imagine the primary (driving) motive for holding to a flat earth -- a notion that by about 700 AD had been discarded, at least in European society -- is religious. That is, some biblical passages indicate a flat earth -- with corners, atop pillars, under the solid hemispherical dome called the firmament, etc. Other passages indicate a rising and setting sun. We know that in passages like Ecc 1:5 the Lord never intended to teach us earth science. God did not bother to instruct the ancients about other galaxies, DNA, or quantum physics. To do so would have interfered with the biblical message -- which is relational and moral and theological. So it's a huge mistake in biblical interpretation to seek truth where no truth was being put forward. In the same vein, the Bible doesn't teach us anything about Chinese pottery, or hydraulic engineering, or the moons of Saturn. You get the idea...

But in the spirit of fun, here's my evidence for a spherical earth:

  • When you go up in a hot air balloon, you can see the curvature of the earth.
  • At sea the last thing you see as a ship goes over the horizon is the mast. 
  • When there's a lunar eclipse, the shape of the earth is visible in the shadow on the moon. It's always an arc -- wherever on the planet you are -- suggesting sphericity.
  • If the earth were flat, then everyone on the earth would experience sunrise and sunset at the same time – and everyone who respects time zones would have to be in on the conspiracy – including all my Facebook friends “around” the world. (Or should I be saying “across the world?”)
  • I've flown around the entire globe a number of times. You really can get back to where you started from!