Relation between Mass and distance between two objects

In summary, the maximum speed an object can reach due to gravity is the speed of light and this can be explained by the theory of relativity. The safe distance between two objects can be determined by calculating the barycenter, which depends on the mass and separation of the objects. If the objects are falling towards each other due to gravity, the maximum speed the falling object can reach is determined by the gravitational constant, the mass of the attracting object, and the distance between them. This can be further understood through Newtonian gravity/mechanics and Einstein's General Relativity. Lagrange points also provide a theory for determining safe distances between objects.
  • #1
shunya
1
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
Janus got it right. That's also the escape velocity formula for a given distance r.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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 [Broken] and the math itself: http://scienceworld.wolfram.com/physics/LagrangePoints.html
 
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What is the relation between mass and distance between two objects?

The relation between mass and distance between two objects is described by the law of universal gravitation. This law states that the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the force of gravity decreases, and as the mass of one or both objects increases, the force of gravity increases.

How does the distance between two objects affect their gravitational attraction?

The distance between two objects directly affects their gravitational attraction. The force of gravity decreases as the distance between two objects increases. This is because the gravitational force is spread out over a larger distance, resulting in a weaker force of attraction between the two objects.

Does the mass of one object have a greater effect on the gravitational force than the other object?

No, both objects in a gravitational system contribute equally to the force of gravity. The force of gravity is directly proportional to the mass of both objects, so if one object has a greater mass, it will have a greater influence on the gravitational force. However, the distance between the two objects also plays a crucial role in determining the strength of the gravitational force.

Can the distance between two objects affect their mass?

No, the distance between two objects does not affect their mass. Mass is an intrinsic property of an object and does not change based on its position or distance from other objects. However, the gravitational force between two objects is affected by their distance, as described by the law of universal gravitation.

How does the relation between mass and distance between two objects impact the motion of objects in space?

The relation between mass and distance between two objects has a significant impact on the motion of objects in space. The gravitational force between two objects determines their orbital motion, and the distance between them affects the strength of this force. Objects with larger masses and closer distances will have a stronger gravitational force, resulting in faster and more stable orbital motion.

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