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The pinnacle of the theory is equation~\ref{einstein}, actually a set of 10 equations called {\bf Einstein's Field Equations}.   These equations describe gravitation as a result of space-time being curved by matter and energy.   Space and time can be measured using the so-called metric tensor (a tensor is a mathematical object analogous to but more general than a vector), which enters through the quantity $G_{\mu\nu}$. The metric tensor is, so-to-speak, a complex ruler with a clock attached. The equation states that the result of making a measurement using the metric tensor doesn't only depends on space time itself, as expected in Newtonian mechanics. Instead mass and energy enter the picture via the quantity $T_{\mu\nu}$, also called the stress-energy tensor. The stress-energy tensorbasically  measures the density and flux of energy and momentum. So the curvature of space-time is zero only if there is no mass and energy. As soon as mass and energy are present, space and time are affected. The orbit of the Earth around the Sun is then explained by the curved space-time produced by the large mass of our star. The resulting orbital motion of our planet simply follows as a change in the metric in accordance with Equations~\ref{einstein}. Gravity is not a force that is added on top of space-time, as in Newton's description. Gravity is just an emerging property of space-time in the presence of mass and energy. Simple, elegant, beautiful.