Orbital Mechanics Vis Viva Equation Question

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SUMMARY

The discussion centers on the application of the Vis Viva equation in determining the orbital speed of a satellite in elliptical orbits. It confirms that the relative velocity calculated by the Vis Viva equation is equivalent to the orbital speed of the satellite. In elliptical orbits, the Vis Viva equation provides the orbital velocity Vo, which is distinct from the circular tangential velocity Vt. The relationship between circular tangential velocity, orbital speed, radial speed, and flight path angle is also validated, establishing that Φ = tan-1(r_dot/Vt).

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  • Knowledge of elliptical and circular orbits
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In the case of a satellite orbiting the Earth. Would the relative velocity calculated by the Vis Viva equation the same as the orbital speed of the satellite? If the satellite is in an ellipse, would Vis Viva give the circular tangential velocity Vt=rω, or would it give the orbital velocity Vo=Vt/cos(Φ), where Φ is the flight path angle?

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Additionally, is the following relationship between circular tangential velocity, Vt, orbital speed, Vo, radial speed, r_dot, and flight path angle, Φ, correct?
Vt2 + r_dot2 = Vo2
Therefore,
Φ = tan-1(r_dot/Vt)
 

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