Can You Achieve a Circular Orbit with Non-Perpendicular Launch Velocities?

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SUMMARY

To achieve a circular orbit around a planet, the required velocity must be Sqrt[Gm/R] and directed perpendicular to the radius vector. Launching at an angle results in a velocity vector that has both perpendicular and parallel components, leading to an elliptical orbit rather than a circular one. The perpendicular component must still equal Sqrt[Gm/R] for a circular orbit, but any deviation from this direction introduces an eccentricity, resulting in a non-circular ellipse.

PREREQUISITES
  • Understanding of gravitational mechanics
  • Familiarity with orbital dynamics
  • Knowledge of velocity vector components
  • Basic principles of conic sections in physics
NEXT STEPS
  • Study the principles of elliptical orbits in orbital mechanics
  • Learn about the effects of launch angles on orbital trajectories
  • Explore the mathematical derivation of orbital velocity equations
  • Investigate the role of eccentricity in orbital shapes
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Aerospace engineers, physics students, and anyone interested in orbital mechanics and satellite trajectory planning.

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If you are at the distance R from a planet and you want to achieve a circular orbit your velocity must be Sqrt[Gm/R] perpendicular to the radius vector.

But what if you launch at an angle (ie no longer perpendicular to the radius)? Is it still possible to achieve a circular orbit if the perpendicular component is still Sqrt[Gm/R]?
 
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Mt guess is that you will end up with some sort of ellipse.
 
You will definitely have a non-circular ellipse.
 

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