Both a and b are true (after you fill in the missing information). With two objects it's only a matter of chosen frame (or point) of reference. I'd argue that since you're on Earth, b makes more sense.

The importance of the heliocentric model comes from the fact that there are more objects in the solar system. With multiple objects you could also hold any one of them still but it makes the model much more complicated and the attraction between the objects less intuitive.

b is ruled out to a "reasonable" person because the Earth is not an inertial reference frame, but is clearly the 'rotating' frame, while the Sun is (approximately) stationary.

This is confirmed through the phenomena of stellar parallax and stellar aberration, which are only visible from Earth because of its motion. Even back in the 1573, Thomas Digges and many successors realized they could prove the Earth was in motion using parallax (though had trouble detecting it), and in 1729 James Bradley gave the first proof of heliocentrism using aberration. Both of these observations were taken as proof by the scientific world that the Earth orbits the Sun, and not the other way around.

The difference is that when we say that the Earth revolves around the Sun, it's implied that we are using an inertial reference frame. Yes, you can take whichever reference point you want, but it's not the default assumption.

A tiny number of people saying "The Sun revolves around the Earth" have any idea of the subtleties of different frames of reference.

The Earth and the Sun both revolve around a separate point that is roughly in between them (ignoring pesky other planets). However this additional point in space happens to be located inside of the sun, so unless you are going to throw in non-inertial reference frames for some unstated reason, "the earth revolves around the sun" is rather unambiguously the 'correct' answer.

Well, they orbit each other, don't they? [Edit, well, to be precise, they are both orbiting the barycenter, which, given the great mass of the sun, is much closer to the center of the sun than the center of the earth]

For the Earth-Sun system, the center of mass is only shifted a few 100 km towards the earth, but the radius of the sun is 695500 km. So the offset is less than 1/1000 of the radius of the sun.

But we don't live in an Earth-Sun system. The point around which planets revolve in our solar system is often outside of the sun as can be seen here: http://en.wikipedia.org/wiki/File:Solar_system_barycenter.sv...

That wibble-wobbles around much faster than I would have expected.

It looks like Jupiter is way faster than I thought it was. My guestimate for gas giant orbits was skewed towards Uranus/Neptune (84/165 years), but Jupiter orbits in only 12!. It's crazy how close Jupiter is to us.

Thanks. That is a really cool diagram! I had no idea that it varied so much over time.

Stuff and nonsense! The only reason the lamestream media promulgates such poppycock, ist das it makes the maths easier!