Relation between Mass and distance between two objects

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Discussion Overview

The discussion centers on the relationship between mass and the distance between two objects, particularly in the context of gravitational attraction and the limits of speed an object can reach when falling towards another object. Participants explore concepts from Newtonian gravity and General Relativity, as well as specific formulas related to gravitational acceleration and escape velocity.

Discussion Character

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

Main Points Raised

  • Some participants question whether an object falling towards another can accelerate indefinitely and if there is a limit to its speed, suggesting that the speed of light is the ultimate limit.
  • One participant proposes a formula for the maximum speed of a falling object, V = √(2GM/r), where G is the gravitational constant, M is the mass attracting the object, and r is the distance to that mass, noting that this applies under the assumption that the falling object's mass is negligible compared to the other mass.
  • Another participant mentions that the maximum speed an object can reach when falling towards Earth from a long distance is approximately 11 km/sec, regardless of the initial distance.
  • Some participants introduce the concept of barycenters and Lagrange points as relevant to the discussion of safe distances between objects under gravitational influence.
  • There is mention of Newtonian gravity and Einstein's General Relativity as theories that explain the gravitational interactions between masses.

Areas of Agreement / Disagreement

Participants express differing views on the limits of speed for falling objects and the implications of gravitational theory, with no consensus reached on the broader implications of these concepts.

Contextual Notes

Participants reference various theories and formulas without resolving the complexities of gravitational interactions, including assumptions about mass and distance that may not be universally applicable.

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I have a question about Mass of an objects and distance between them. If a object is pulled by gravity it accelerates. Is there a limit on the speed till which object will speed.
If a object is falling towards Earth from a long distance then it will accelarate indefinitely ?
Is there a safe distance between two objects if there is no other force to interfere ? Do anyone know any theory which explains this
 
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shunya said:
If a object is pulled by gravity it accelerates. Is there a limit on the speed till which object will speed.

The maximum speed at which an object can move is the speed of light. Look up the theory of relativity.


Is there a safe distance between two objects if there is no other force to interfere ?

The barycenter is the distance from mass m:

[tex]d_{barycenter}=\frac{m}{M+m}r[/tex]

where r is the separation between the two objects.
 
shunya said:
I have a question about Mass of an objects and distance between them. If a object is pulled by gravity it accelerates. Is there a limit on the speed till which object will speed.
Yes. If you are talking about one object falling towards another due to gravity. Assuming the two objects start at rest with respect to each other, then the maximum speed the falling object could reach before striking the second, no matter how far apart they started, is

[tex]V= \sqrt{\frac{2GM}{r}}[/tex]

where G is the gravitational constant
M is the mass that is attracting the object
r is the the radius of mass M.

The one caveat is that that we are assuming that the falling object's mass is very small when compared to the other mass.

If a object is falling towards Earth from a long distance then it will accelarate indefinitely ?
for the Earth, this velocity turns out to be just about 11 km/sec. Meaning that even if the object fell form an infinite distance, it could only be moving at 11 km/sec when it strikes the surface of the Earth.
 
Janus got it right. That's also the escape velocity formula for a given distance r.
 
Janus said:
Assuming the two objects start at rest with respect to each other, then the maximum speed the falling object could reach before striking the second, no matter how far apart they started, is

[tex]V= \sqrt{\frac{2GM}{r}}[/tex]

I interpreted the question as being more general (i.e. for the minimum possible radius of an object), but of course this is correct for an individual gravitating mass.
 
Welcome to Physics Forums shunya!
Do anyone know any theory which explains this
The theories are Newtonian gravity/mechanics and (for 'high' speeds, 'huge' masses, etc) Einstein's General Relativity - which is so close to the Newtonian equations in 'ordinary' circumstances as to be indistinguishable.
 
shunya said:
Is there a safe distance between two objects if there is no other force to interfere ? Do anyone know any theory which explains this


Lagrange points come to mind
This should illustrate it better: http://www.physics.montana.edu/faculty/cornish/lagrange.html and the math itself: http://scienceworld.wolfram.com/physics/LagrangePoints.html
 
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