Let’s say an asteroid is about to enter earth’s atmosphere(it will burn up of course). The initially sitting is at:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]point = [x_{0},y_{0},z_{0},t_{0}] = [r_{0},\\theta_{0},\\phi_{0},t_{0}][/tex]

With a 4-velocity:

[tex]V = [v_{1},v_{2},v_{3},v_{4}][/tex]

The momentum at 0+

[tex]p_{0+} = mass*V = mass*[v_{1},v_{2},v_{3},v_{4}][/tex]

The Riemann Geometry is Riemann Space with Torsion = 0. The metric is the Schwarzchild metric. Affinity is the Christoffel Symbol. Curvature is non-zero. And, the Ricci tensor is null.

My question is how do you formulate [tex]x^{i}[/tex] to attempt solve for the path, "s" in the second-order geodesic differential equation from the given initial 4-velocity vector and starting point?

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# Solution help for the Geodesic Equation

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