High speeds due to gravitaional forces

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Discussion Overview

The discussion revolves around the possibility of a massive body accelerating a 1 kg mass to speeds approaching light speed, exploring the necessary mass and distance involved. Participants express varying levels of understanding regarding relativistic effects and seek to analyze the problem using classical mechanics.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether a massive body can accelerate a 1 kg mass to light speed or near light speed, seeking a non-relativistic explanation.
  • Another participant notes that any inquiry about speeds close to light speed inherently involves relativistic considerations and emphasizes that exceeding light speed is impossible.
  • A participant suggests using Newtonian mechanics and provides a projectile motion equation to analyze the acceleration between two massive point particles.
  • One participant claims that the maximum velocity achievable by a body is equivalent to the escape velocity, which depends solely on the mass and radius of the massive body, referencing energy conservation principles.
  • A later reply challenges the previous claim, arguing that a projectile can exceed escape velocity if it is fired with sufficient kinetic energy, regardless of whether it is captured by the massive body.
  • Another participant acknowledges the importance of the initial velocity of the body in the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between escape velocity and the potential to exceed it, indicating a lack of consensus on this aspect of the discussion.

Contextual Notes

Participants reference concepts such as escape velocity and energy conservation without resolving the implications of relativistic effects or the conditions under which classical mechanics may apply.

joeyjo100
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Is it possible for a massive body to accelerate an object, say a 1kg mass, to a speed which is light speed or near light speed? What mass would this body have to be, and how far away would the 1 kg mass have to be?


I'm looking for an answer that doesn't involve relativistic stuff, mainly because i don't understand it... :)
 
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By definition, any time you're asking about getting close to the speed of light---thats relativistic. Also, note that you can never reach or exceed the speed of light.

You can do a Newtonian approximation to your question, the projectile motion equation for velocity is
[tex]V_f^2 = V_i^2 + 2ad[/tex]
for final velocity V_f, initial velocity V_i, acceleration a, and distance d.
Do you know how to find the acceleration between two massive point particles?
 
The maximum velocity you can get for a given body is the same as the escape velocity for that body. It will depend on the radius and mass of the massive body only. You can find it from energy conservation. You start with your 1 kg mass very far away (PE=0, KE=0) and then you approach the body till you reach the surface.
 
nasu said:
The maximum velocity you can get for a given body is the same as the escape velocity for that body. It will depend on the radius and mass of the massive body only. You can find it from energy conservation. You start with your 1 kg mass very far away (PE=0, KE=0) and then you approach the body till you reach the surface.

This isn't true. Fire a projectile at the Sun at a speed greater than the escape velocity of the Sun (about 600 km/s) and you'll of course accelerate to a speed faster than the escape velocity. The only issue is if you miss the Sun, it will fly off and never become captured by the Sun. However, if you aim right at it, you'll accelerate to quite a high speed!

And that's quite an extreme case, simply fire projectile with a kinetic energy greater than the potential energy of the object at whatever radii it is at and you'll achieve a speed greater than the escape velocity.
 
Right. I did not think the body having some velocity already.
 

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