Can you straighten this out for me? (no pun intended) I'm still having trouble thinking of gravity as the curvature of space-time instead of as a force. If it is really curvature, then:

The earth does not orbit around the sun, correct? The earth and moon travel in a straight line, but the curvature of space-time makes it seem like we're going around the sun. Like drawing a line on a piece of paper and then making a cone out of the paper so that both ends of the line touch. The line is still straight based on the 2-dimensional plane on the paper, but is a circle (somewhat) to a three-dimensional observer.

But if we travel in a straight line through curved space-time, then our orbit around the sun should not be affected by velocity.

But if the earth actually orbits in a circle, and not a straight line, that means that there has to be something pulling us toward the center of the circle. How can curvature of space-time "pull" on an object without using a force? It should merely warp the path of a moving object, but not draw it into the center, and at the same rate regardless of the velocity.

What am I missing here?

Thanks in advance!