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Does Initial Velocity Effect Gravitational Accleration?

  1. Aug 25, 2008 #1
    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?
     
  2. jcsd
  3. Aug 25, 2008 #2

    Dale

    Staff: Mentor

    No. f = GMm/r² so it is not a function of v.

    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.
     
  4. Aug 26, 2008 #3
    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.
     
  5. Aug 26, 2008 #4
    Thank Dale; that was the answer I was looking for.
     
  6. Aug 28, 2008 #5
    I have a followup question;

    Does an astronaut experience zero g's the instant the rocket engines stop producing thrust?
     
  7. Aug 28, 2008 #6

    Dale

    Staff: Mentor

    As soon as the rocket engines stop the astronaut is in free-fall and would be able to "float" around the cabin.
     
  8. Aug 28, 2008 #7
    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.
     
  9. Aug 28, 2008 #8

    Dale

    Staff: Mentor

    Sure, I would be glad to.
     
  10. Aug 28, 2008 #9
    I just posted it it's entitled "Gravitational Kinematics Part I; Inertial Definitions"
     
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