Simplified geodesic equation

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In this video, we start with the regular form of the geodesic equation to write it in a very compact and smart way in terms of the covariant derivative.

The geodesic equation gives us a spacetime path along which any freely falling object moves. Freely falling infers that there are no other forces except gravitational force acting on that object.

For example, a rocket being launched from the surface of the Earth is not moving along a geodesic since there are forces other than the gravitational force, such as a force by the rocket engine and atmosphere.

Any planet moving around the Sun moves along a geodesic. But remember that the orbit we will draw on paper for that planet will simply be a projection of 4D geodesic in 3D space.

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