The shape of Earth

[polymath257]

Really? How do they stay up there?

Is this the only explanation for GPS technology? Or could it be that our phones rely on ground based towers?

How high are they?

They stay up using basic orbital mechanics. You can derive the motion using Newtonian mechanics as a good first approximation. I have gone through the mathematics.

Yes, it is. Ground based towers can't do the triangulation required, especially in a moving vehicle away from towers. You can get GPS signal even if you can't use your phone for a call or text message. I have done such.

How far up? About 12,600 miles: they are in orbits that take half of a sidereal day to complete. I have watched satellites in real time through binoculars.

As for the shape of the Earth:

I have watched a lunar eclipse and have seen the shadow of the Earth on the moon.

I have traveled to different places and have seen the change in which stars are visible.

I have learned about how gravity works, including basic experiments, and have verified that something the size and mass of the Earth would become spherical, slightly modified by centrifugal forces into an ellipsoid.

I have seen other planets and have verified that they are spherical (basically--elliptical in more detail). Given orbital mechanics, the Earth is a planet and would be expected to be spherical as well.

I have seen multiple photos that I trust showing the shape and size of the Earth from orbiting satellites, from non-orbiting satellites, from the moon, etc. I trust them because the information given agrees with what i can personally verify only in much more detail.

I also know the history associated with trying to understand the shape of the Earth. Even Aristotle understood it to be basically spherical. Eratosthenes managed to figure out its size 2200 years ago (although later measurements weren't as accurate--Eratosthenes was lucky).