Parabolic trajectory of a rocket

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    Rocket Trajectory
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Discussion Overview

The discussion centers on the trajectory of a rocket, specifically addressing why it is considered parabolic when launched straight up and the implications of its landing position relative to the launch pad. The scope includes theoretical considerations of motion, the effects of thrust vectoring, and the influence of gravitational forces on trajectory shape.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why a rocket's trajectory is always parabolic if it launches straight up, suggesting that it lands away from the launch pad depending on its speed.
  • Another participant proposes that the straight-up launch can be seen as a special case of a parabolic trajectory, noting that the rocket does drop straight down when ignoring Earth's rotation.
  • A participant seeks clarification on the term "limiting condition" and connects it to the concept of thrust vectoring in ICBMs, implying that this affects the landing distance.
  • One participant explains that a limit condition refers to a simplified case, comparing it to the relationship between a circle and an ellipse, and clarifies that rockets are steered and only follow a ballistic trajectory after engine cutoff.
  • A later contribution introduces the idea that if the rocket's velocity is below a certain threshold, its trajectory can be part of an ellipse, influenced by changing gravitational acceleration with altitude.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the rocket's trajectory, with some supporting the parabolic model while others introduce elliptical trajectories under specific conditions. The discussion remains unresolved regarding the implications of thrust vectoring and the exact nature of the trajectory during ascent and descent.

Contextual Notes

There are limitations in the assumptions made about gravitational effects and the simplifications regarding the rocket's motion, particularly in relation to thrust vectoring and the conditions under which different trajectory shapes apply.

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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