Centre of Mass of two Gravitating bodies from rest

In summary, the centre of mass is a point that represents the average location of the mass of an object or system of objects. It can be calculated using a formula that takes into account the masses and distances of the objects. The centre of mass can change over time, but the total mass of the system remains constant. In celestial mechanics, the centre of mass is important in understanding the motion of objects in space, as it determines their orbits. The centre of mass also affects the motion of two gravitating bodies, as the closer it is to one body, the stronger the gravitational force and the faster it will move towards the other body.
  • #1
Phillips101
33
0
Hi

How would I show that the centre of mass of two point particles, one of mass m1 and the other m2, when released from rest from infinite simultaneously, stays in the same place?

I feel this is a very simple question, I just can't seem to get it right. Everything I've tried still involves time in it...

Thanks for any help!
 
Physics news on Phys.org
  • #2
Have you tried conservation of (total) momentum?
 
  • #3
D'oh. I was right, it was very simple. Thanks for that!
 

1. What is the definition of centre of mass?

The centre of mass is a point that represents the average location of the mass of an object or system of objects. It is the point at which the mass of the object can be considered to be concentrated.

2. How is the centre of mass of two gravitating bodies calculated?

The centre of mass of two gravitating bodies can be calculated using the formula: r = (m1*r1 + m2*r2) / (m1 + m2), where r is the distance between the two bodies, m1 and m2 are the masses of the bodies, and r1 and r2 are the distances from the centre of mass to each body.

3. Can the centre of mass of two gravitating bodies change over time?

Yes, the centre of mass of two gravitating bodies can change over time if the distance between the bodies changes or if the masses of the bodies change. However, the total mass of the system will always remain constant.

4. What is the significance of the centre of mass in celestial mechanics?

The centre of mass is a crucial concept in celestial mechanics as it helps us understand the motion of objects in space. The orbit of a body around another body is determined by the position of their centre of mass, as the two bodies will rotate around this point.

5. How does the centre of mass affect the motion of two gravitating bodies?

The centre of mass plays a significant role in determining the motion of two gravitating bodies. If the centre of mass is located closer to one of the bodies, that body will experience a larger gravitational force and will move towards the other body faster. The motion of the two bodies will also be affected by the distance between them and their masses.

Similar threads

  • Classical Physics
3
Replies
84
Views
4K
  • Classical Physics
Replies
11
Views
1K
  • Classical Physics
Replies
24
Views
668
  • Classical Physics
2
Replies
67
Views
4K
Replies
6
Views
1K
Replies
31
Views
642
  • Introductory Physics Homework Help
Replies
16
Views
495
  • Classical Physics
Replies
8
Views
1K
  • Classical Physics
Replies
2
Views
1K
Replies
38
Views
2K
Back
Top