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**this is not a homework question**, it is an example of a problem I thought up to illustrate what I have trouble with:

*Two spheres, each with a mass of 1 kg and a radius of 1 meter, lie in space. Their centers are 10 meters apart. When will they make contact?*

Now obviously the initial force acting on each sphere is easily calculable from the gravity equation. But an infinitesmall period of time after they have moved towards each other, their distance apart will have changed, and the force acting on each sphere will increase. Not only are they accelerating towards each other because of gravity, but they are also increasing their acceleration as they get closer to each other.

I am sure calculus will be involved and that's fine. What's the simplest method that you would use to solve a problem where force changes with distance/time?

Thanks!