[wvenable]

> the earth is standing still, it's not moving... it is moving in a straight line

Wait, is the earth moving or not? I also can't figure out what definition of orbit you are using. Your comment feels far too clever for it's own good.

[lutusp]

The OP is trying to argue that there's a preferred frame of reference in a physical theory (relativity) that explicitly disallows preferred frames of reference. If you took a position roughly 200 million miles (about 320 million kilometers) above the sun's north pole, and watched from there, you would certainly see the earth orbit the sun. The reason? Different curvature from that perspective.

The OP could have simply said that, in relativity, there's no force called gravity, instead planets orbit their parent bodies because of curved four-dimensional spacetime. He then could have quoted physicist John Wheeler, who famously said, "Matter tells space how to curve, and space tells matter how to move."

After the OP correctly said that the earth is moving through curved spacetime in a straight line, IMHO he should have turned in his golf clubs.

> Your comment feels far too clever for it's own good.

You got that exactly right. The OP's intention is to confuse, not enlighten.

[Iftheshoefits]

It is too clever, by half. From my perspective it's a long-winded and self-contradictory (as you note) attempt at punning with curvature tensors and metrics, only not doing it right.