I think it is highly unlikely NASA faked the moon landing and lied about the size of Africa. I have never heard about a problem with the size of Africa before in connection with NASA, but if they were to make an error this is not the same as lying. And we do not have to trust NASA that the Earth is round, there is plenty of evidence!
I see three clear ways of looking at this:
1) The idea that the Earth is round came about long before NASA even existed in about 500 BC. The ancient Greeks were masters in the mathematics known as geometry – which is the study of angles and shapes, they applied their knowledge of geometry to the shadows cast by the sun on the Earth and the moon. Even though they incorrectly placed the Earth at the centre of the solar system they came to the correct conclusion that the Earth was a sphere.
2) If you want nice photos of the spherical Earth from space you don’t just have to trust NASA, many other organisations have entered space. Russia, China, Europe and India all have their own space programs; as well as many private companies and research institutes – those that launch satellites and fly high altitude planes. High altitude weather balloons can see the curvature of the Earth for example. You can also see signs of it yourself if you have ever seen ships sinking below the horizon.
3) If the Earth is not (roughly) spherical, how would you explain the solar system? The movement of planets round the sun? For if you accept the current theories of gravity the shape of the planets is also explained. How could a flat [or any other shape] Earth be stable? How would satellites phones or GPS work the same as they do when we model the Earth to be a sphere when we design them? How would satellites orbit the Earth? The best way to show your disapproval of something is to come up with something better. The current laws of physics are the best we have so far, and pretty impressive!
It’s not just NASA who says that the Earth is round. Humans have known the Earth isn’t flat for quite a long time. The simplest illustration of this is: if the Earth were flat and you saw something, like a ship with sails, coming toward you, the whole ship would appear at once on the horizon. Instead, the sails appear first. Also, the Moon landings weren’t faked. It would have taken more sophisticated video technology than existed at the time to fake the moon landings that it did to make them happen for real. Video tech was very primitive at the time. Watch this: https://www.youtube.com/watch?v=dWBYAxhH3u4
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