5. Passage to Round Earth
The previous section showed how to find a quasi-analytical solution to the orbiting problem when the Earth is assumed to be flat and gravity constant. Here we present a method for transforming this solution back to a more realistic model with a round Earth and altitude-dependent gravity.
The equations of motion in the Round Earth are expressed using the polar coordinates (r, φ, v, γ) shown in figure
10
. Position is marked by radius r and polar angle φ, velocity is marked by its modulus v and local slope γ.
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Passage to Round Earth