Question concerning two bodies in space

In summary, the two spheres will move closer together until they come into contact, at which point the gravitational force will cause the spheres to crash together.
  • #1
Simon316
7
0
Two indentical spheres with radius 15cm and mass 100kg are 6mm apart from echother in space. My problem is to find how long it will take before gravitational attraction will cause the two spheres to come together?

What I have found out so far is:
I have the gravitational force Fg= 7,12*10^-6 N,
and used Newtons 2. law to find the spheres acceleration a=7,12*10^-8 m/s^2

I know the acceleration is not constant, because the gravitational forces increase as the spheres move towards each other. But I think I will neglect this, and treat it as constant.

If I do so, could I use the equation:
X = x0 + v0x +1/2*ax*t^2
t = sqrt((2*x)/ax)= 84269sek ,
x = 0,003m, v0x = 0 m/s, x0= 0 m

I don't know if I can treat v0x as being 0, should it be v0x = a?

Is this way of, or am I on the right track?

all kind of help would be apprciated, thx
 
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  • #2
Simon316 said:
Two indentical spheres with radius 15cm and mass 100kg are 6mm apart from echother in space. My problem is to find how long it will take before gravitational attraction will cause the two spheres to come together?

What I have found out so far is:
I have the gravitational force Fg= 7,12*10^-6 N,
and used Newtons 2. law to find the spheres acceleration a=7,12*10^-8 m/s^2

I know the acceleration is not constant, because the gravitational forces increase as the spheres move towards each other. But I think I will neglect this, and treat it as constant...

IMO wshful thinking: this needs to be done with calculus. You have already said so in so many words--ie acceleration is not constant.
 
  • #3
denverdoc said:
IMO wshful thinking: this needs to be done with calculus. You have already said so in so many words--ie acceleration is not constant.


That's true, but the error for this problem will be fairly small. The distance between the centres of the spheres only changes from 306mm to 300mm.

I don't know if I can treat v0x as being 0, should it be v0x = a?

The question doesn't say what v0x was and you have to assume it was something. But assuming "v0x = a" says "a velocity equals an accleration" which doesn't make any sense because they have different units.

I would assume it was 0.
 
  • #4
Yea I know about calculus, but the question says you get 90%/points for a reasonable answer, and 100% for a correct. I will settle with 90%, and use
X = x0 + v0x +1/2*ax*t^2 (although I'm not sure this is the right way), and use V0x = 0.

Thanks
 

1. What is the difference between a binary star system and a double star system?

A binary star system consists of two stars that orbit around each other, while a double star system is made up of two stars that appear close together in the sky, but may not be physically bound to each other.

2. How do scientists determine the mass of two bodies in space?

Scientists can determine the mass of two bodies in space by observing their orbital patterns and using mathematical equations, such as Newton's laws of motion and Kepler's laws of planetary motion.

3. Can two bodies in space collide?

Yes, two bodies in space can collide if their orbits intersect or if they are affected by external forces, such as gravitational pull from other bodies or changes in their own orbits.

4. What is the difference between a stable and unstable binary star system?

A stable binary star system is one in which the two stars maintain a consistent orbit around each other, while an unstable binary star system is one in which the two stars may eventually collide or be ejected from each other's orbit.

5. How do two bodies in space affect each other's gravitational pull?

The gravitational pull between two bodies in space is directly proportional to their masses and inversely proportional to the square of the distance between them. This means that as the distance between the bodies decreases, the gravitational pull increases, and vice versa.

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