What does General Relativity Seek to Describe?The basic idea of general relativity is that space and time can be curved. Matter acts as the source of space time curvature, in a way described by Einstein¡¦s field equation: Gμν=KTμνWithout going into too much detail, the right hand side describes the masses and the left hand side the curvature of space - more detail will follow in later sections.
It is a common image, but it is still a good visualization tool - space time is like a taught rubber sheet. A bowling ball placed in the middle of the sheet will lead the sheet curving quite sharply.
As an aside, we will also study the vacuum equations Gμν=0, which has solutions like ripples in a rubber sheet ¡V gravity without any mass present! This is a novel effect of general relativity, showing how it is much richer than Newtonian gravity.
When we throw a ball up in the air, it is really moving in a "straight line." Its path looks curved to us because we are not aware of the curvature of space.
Imagine an "intelligent ant" (these intelligent ants exist only in the worlds of general relativity lectures, but seem to inhabit every relativity course ever given) on the curved rubber sheet somewhere above our bowling ball. If we tell the ant to walk in a straight line, the ant will follow curved path around the depression, because it is not aware of the curvature of space. Locally, the ant is walking in a straight line, but the curvature of space carries it around.
Similarly, as the Earth goes round the sun, its inertia simply carries it in a straight line along the curved space, causing it to orbit. To us on the surface of the Earth, there is little evidence that the Earth is doing anything other than coasting along in a straight line. From outside the solar system, the circular nature of the Earth's path is quite apparent (unless one allows for the curvature of space, then it is a straight line).