Parabolic trajectory of a rocket

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    Rocket Trajectory
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SUMMARY

The trajectory of a rocket launched straight up is parabolic due to the influence of gravitational forces acting on it after engine cutoff. While rockets initially ascend vertically, they transition to a ballistic trajectory, which can be described as a segment of an ellipse, with the Earth’s center as one focus. The velocity of the rocket at launch plays a crucial role; if the velocity is less than the escape velocity, the rocket will follow this parabolic path. Understanding these dynamics is essential for analyzing rocket landings and trajectories.

PREREQUISITES
  • Understanding of basic physics concepts, particularly gravitational forces.
  • Familiarity with the principles of projectile motion.
  • Knowledge of orbital mechanics, specifically ellipses and their properties.
  • Awareness of rocket propulsion and thrust vectoring techniques.
NEXT STEPS
  • Study the principles of gravitational force and its effect on projectile motion.
  • Learn about the equations governing elliptical orbits and their applications in rocketry.
  • Research thrust vectoring techniques used in modern rockets for trajectory control.
  • Explore the concept of escape velocity and its implications for rocket launches.
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in the mechanics of rocket launches and trajectories will benefit from this discussion.

putongren
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Why is the trajectory of a rocket always parabolic if a rocket launches straight up in the air perpendicular to the ground? Doesn't a rocket just drop straight down back to the launch pad? I think the rocket lands away from the launch pad depending on the speed of the rocket.
 
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I would consider that to be a special case of a parabola or a limit condition. And it does drop straight down (ignoring the Earth's rotation).
 
Russ,

What do you mean by limiting condition? So a rocket like an ICBM lands far away because of thrust vectoring?
 
A limit condition is a simplified special case - like a circle is to an ellipse.

And now I see your confusion - real rockets on launch pads tend to start off straight up. Yes, these rockets are steered. They don't end up on a ballistic (parabolic) trajectory until after their engines are stopped.
 
If v of the rocket is high. But v < \sqrt{\frac{2GM}{R}}
where M is the mass of Earth
R is the radius of Earth
The trajectory of the rocket is a part of ellipse because g is change accordingly to h (likes the trajectory of planet). One focus of this ellipse is the center of earth.
 

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