A couple questions about gravity

[fezmaster]

So I understand the equation f=g*m1m2/d^2 and I understand how to use it, but I'm unsure what my results actually mean. Once I have calculated the force, I don't know what the strength implies. How much force do I need for one object to orbit another? How much is so much that the objects become 'attached' to one another (like we are to the earth)? How much is too little?

Also, if we look at binary stars, they are both attracted to each other with a similar force due to their masses. What strength is required for this to happen? If I were to put two cars in space, they certainly wouldn't be massive enough to pull at each other. But how big/close together would two objects have to be in order for this to happen?

 

[Whovian]

So I understand the equation f=g*m1m2/d^2 and I understand how to use it, but I'm unsure what my results actually mean. Once I have calculated the force, I don't know what the strength implies. How much force do I need for one object to orbit another? How much is so much that the objects become 'attached' to one another (like we are to the earth)? How much is too little?

Do you have a basic knowledge of second-order partial differential equations? You should probably get some before attempting to solve this.

Also, if we look at binary stars, they are both attracted to each other with a similar force due to their masses. What strength is required for this to happen? If I were to put two cars in space, they certainly wouldn't be massive enough to pull at each other. But how big/close together would two objects have to be in order for this to happen?

Same, but two cars actually are massive enough to pull at each other, just rather weakly. There's also a good chance they'll be gravitationally bound (assuming that's what you mean.)

 

[fezmaster]

I believe that I understand it... Unless there's something fundamental that I'm missing, but I'm not sure what that would be. I just wondered how much force is required for one object to orbit another. I understand that there's no set answer to this question, but I was just hoping for some sort of ballpark estimate.

And I do understand that the cars would pull at each other with a little amount of force. I'm just unsure how much force would be enough that you could actually observe them being mutually attracted towards each other.

 

[mikelepore]

If I were to put two cars in space, they certainly wouldn't be massive enough to pull at each other.

That's not true. The equation which you already know tells you the force of attraction between them. Perhaps you mean that a person could spend a long time watching them and not notice their acceleration toward one another. That's just a matter of being able to notice movement. The hour hand of a clock is moving but it doesn't look like it.

 

[fezmaster]

That's not true. The equation which you already know tells you the force of attraction between them. Perhaps you mean that a person could spend a long time watching them and not notice their acceleration toward one another. That's just a matter of being able to notice movement. The hour hand of a clock is moving but it doesn't look like it.

Yes, I made an error when I wrote it out. I meant visibly pull at each other (just with our eyes)

 

[mikelepore]

As for what is noticably visible, maybe we can estimate that it's just barely visible if, during a period of time of one second, an object goes from being at rest to having a speed of 1 millimeter per second. If so, that would be an acceleration of a=0.001 m/s^2. Whatever "a" you want to use, solve F=ma to get the necessary values of force and mass.