The time take to two balls (gravitationally attract), to reach each other

[Mad_Eye]

two balls with known mass, radios, and distance between each other, are attract, due to gravitational force. how much time will it take them to reach each other?

this is NOT homework... just something i thought about, and have no idea how to solve.

(pay attention the mass and radios of each ball is not necessarily identical)

 

[mgb_phys]

Have you done calculus?

If not you can solve this with a computer program or a spreadsheet.
the tricky thing is that the force depends on the distance and is constantly changing
So you could work out for each second what the separation is, then what the force is an then the accelration which would give the speed an the change in distance for that second.
You keep doing this until the separation is zero.

Remember the distance in the gravity equation is the distance between centres, while the processes ends when the spheres touch - the distance will never got to zero.

 

[sganesh88]

Mgb_phys,
How can we solve this using calculus and get precise values for distance between the two spheres at a particular instant?
I haven't mastered calculus but can follow the steps with some difficulty..

 

[Identity]

Hmm yeah I've tried to solve this problem but it's a catch-22
You need to know the distance to find the acceleration at time t,
But you need to know the acceleration to find the distance at time t.

 

[Mad_Eye]

Mgb_phys,
How can we solve this using calculus and get precise values for distance between the two spheres at a particular instant?
I haven't mastered calculus but can follow the steps with some difficulty..

+1 exact same with me

 

[DocZaius]

I asked this question a little bit ago. In the thread is the answer, with calculus!:

https://www.physicsforums.com/showthread.php?t=306442

 

[Identity]

Thanks DocZaius,

with that answer, I'm confused why arildno multiplies both sides of

$$\frac{d^2D}{dt^2} = \frac{-2G}{D^2}$$

by $$\frac{dD}{dt}$$

$$\Rightarrow \frac{d^2D}{dt^2}\frac{dD}{dt} = \frac{-2G}{D^2}\frac{dD}{dt}$$

And also how you're supposed to integrate that

 

[Mad_Eye]

wow. i didn't understand anything... where can i learn this stuff from the very basic?