Does Initial Velocity Effect Gravitational Accleration?

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Discussion Overview

The discussion centers around the effects of initial velocity on gravitational acceleration and the implications of Newtonian mechanics and special relativity. Participants explore how initial velocity may influence the final velocity upon impact with a massive body, as well as related concepts of free-fall experienced by astronauts.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant questions whether initial velocity affects the acceleration a mass receives due to gravity, proposing a scenario with two bodies of equal mass moving towards a massive body at different initial velocities.
  • Another participant asserts that initial velocity does not affect gravitational acceleration, referencing the gravitational force equation (f = GMm/r²) as independent of velocity.
  • A different viewpoint introduces Newton's observations about inertial systems, suggesting that the force needed to accelerate an object is the same regardless of its initial velocity, but challenges this with special relativity's assertion that mass increases with velocity.
  • One participant expresses gratitude for the clarification received regarding the effects of velocity on gravitational impact.
  • Follow-up questions are raised about the experience of astronauts in free-fall after rocket engines stop, with responses confirming that astronauts would experience weightlessness immediately upon cessation of thrust.
  • A participant acknowledges a misunderstanding about the forces involved with opposing velocity and expresses intent to share a blog on gravity for feedback.

Areas of Agreement / Disagreement

Participants present differing views on the relationship between initial velocity and gravitational acceleration, with some asserting it has no effect while others introduce complexities related to special relativity. The discussion remains unresolved regarding the implications of these differing perspectives.

Contextual Notes

Participants reference Newtonian mechanics and special relativity, indicating a potential dependence on definitions of mass and force, as well as assumptions about inertial frames. The discussion does not resolve the mathematical implications of these theories.

WCOLtd
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Does it's initial velocity effect the acceleration a mass receives due to the gravitational field?

If two bodies of equal mass were moving towards a massive body, and they started at the same radius from the surface but one went at 10 times the velocity of the other, when the bodies impact the surface would (Vf-Vi) of the faster body be less than that of the slower body of mass?
 
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WCOLtd said:
Does it's initial velocity effect the acceleration a mass receives due to the gravitational field?
No. f = GMm/r² so it is not a function of v.

WCOLtd said:
If two bodies of equal mass were moving towards a massive body, and they started at the same radius from the surface but one went at 10 times the velocity of the other, when the bodies impact the surface would (Vf-Vi) of the faster body be less than that of the slower body of mass?
Yes. The faster projectile will impact the planet in a shorter amount of time. Since a = Δv/Δt the smaller Δt implies a smaller Δv for the same a.
 
This is in fact the most basic of Newton's observations about inertial systems. His law in basis claims that the amount of force needed to similarly accelerate an object from no movement is the same as from any higher movement (relative a specific observer).
However this important Newtonian claim has been challenged by Special relativity, which asserts that mass increases with velocity. If this is so, when objects are thrown in speeds closer to the speed of light greater amount of force would be needed to accelerate them and thus vf-Vi would be noticeably smaller for the higher vf object.
 
Thank Dale; that was the answer I was looking for.
 
I have a followup question;

Does an astronaut experience zero g's the instant the rocket engines stop producing thrust?
 
WCOLtd said:
I have a followup question;

Does an astronaut experience zero g's the instant the rocket engines stop producing thrust?
As soon as the rocket engines stop the astronaut is in free-fall and would be able to "float" around the cabin.
 
Thank you so much, that's a huge help. I had thought that the vector of opposing velocity creates a force, I understand now that that is wrong.

I'm going to post blog on gravity, perhaps you could look it over and see whether I've got any wrong.
 
Sure, I would be glad to.
 
I just posted it it's entitled "Gravitational Kinematics Part I; Inertial Definitions"
 

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