I was revising for an exam the other day in the physics resource room and somehow we ended up having a short conversation about conspiracy theorists and the one name I remember cropping up was the Flat Earth Society. So I have decided to do a bit of a rant/proof on this. This post will just be a bit on the shape of the Earth and I will go into the evidence later in the week.
Long ago people assumed the Earth was flat, perfectly reasonable since apart from all the hills and valleys no overall curving trend was observable to the people at the time living their day to day lives. Even today a flat Earth is a sufficiently good local approximation for people who don't travel exceptionally long distances, although there are plenty technologies that do rely on it to work but I'm discussing direct observation at this stage so that's beyond the point.
Things started to change around 330BC when the first evidence started to emerge for a spherical Earth, this was an important discovery because long distance navigation such as crossing oceans is going to be substantially different depending on if the ocean is flat or curved and yes by the time Columbus came along everyone knew full well the Earth was certainly not flat, give the people of the time a little credit.
That is all well and good and for most of us this will be the most accurate model we need but it is not the end of the story, a more accurate picture, and one important for satellites was first proposed by Newton in 1689. Since the Earth rotates there will be a 'centrifugal force' that will push the material outwards more strongly the further it is from the axis of rotation(actually its not a force as such, just inertia, the material further from the axis is moving faster so it is harder to change its direction). The end result of this is that the radius of the earth to one of the poles is 6 356.8km but the radius to the equator is 6 378.1km. This means the polar diameter is about 40km less than the equatorial diameter, this slightly flattened sphere is called an oblate spheroid.
It is even possible to make more detailed observations which have found that the South pole is 40m closer to the centre of the Earth that the North pole, so it actually has a very slight pear-shape, with various lumps and dents roughly matching the continents and oceans. However having said that its relative variations from an oblate spheroid(0.17%) are less than a pool ball from a perfect sphere(0.22%).
All that is actually a nice example of how science works, start with a basic idea, such as "as far as I can see directly the earth is flat" and then develop the idea "actually its a sphere it just looks flat when your standing on it because its bloody huge" and further development "wait its a slightly squashed sphere" and this continues to whatever accuracy is needed. Since the maths involved gets evil very fast as the idea is refined the secret is to use the simplest model that is detailed enough for the task at hand. Treating the Earth as an oblate spheroid is vital to keep satellites where they are needed, but its a bit of a headache when you just want to find somewhere on a map of your town, at that level even the gross oversimplification(to the point of outright wrong) of a flat Earth will do the job. Of course the key point of it being science it you also have to prove the ideas.
http://www.scientificamerican.com/article.cfm?id=earth-is-not-round an article covering spherical Earth onwards
http://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-002-physics-and-chemistry-of-the-terrestrial-planets-fall-2008/lecture-notes/MIT12_002f08_lec27_28.pdf the kind of maths involved in getting this lovely detailed understanding of the Earths shape.
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