# Relation between Mass and distance between two objects

1. Mar 19, 2005

### shunya

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

2. Mar 19, 2005

### SpaceTiger

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

The barycenter is the distance from mass m:

$$d_{barycenter}=\frac{m}{M+m}r$$

where r is the separation between the two objects.

3. Mar 19, 2005

### Janus

Staff Emeritus
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

$$V= \sqrt{\frac{2GM}{r}}$$

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.

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. Mar 19, 2005

### tony873004

Janus got it right. That's also the escape velocity formula for a given distance r.

5. Mar 19, 2005

### SpaceTiger

Staff Emeritus
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. Mar 23, 2005

### Nereid

Staff Emeritus
Welcome to Physics Forums shunya!
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. Mar 23, 2005

### cronxeh

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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