Radial fall in a Newtonian gravitational field
This is how Wikipedia defines Newton's law of Gravitation:
Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:
- F is the force between the masses,
- G is the gravitational constant,
- m1 is the first mass,
- m2 is the second mass, and
- r is the distance between the centers of the masses.
Now, say 2 spheres, one the size of the earth and the other the size of a ping pong ball are placed say 10 km apart. There are no other forces acting on the system other than gravitation. If I've understood rightly, then both the ball & the earth sized sphere will be pulled towards each other with the same huge force.
My question is- how can we calculate when the 2 spheres will meet? And while calculating that shouldn't we consider the fact that the force is changing every moment because the distance between them $r$ changes every moment? How can I include this factor into my calculations?
Further, since the force is changing every moment, are the spheres undergoing acceleration or accelerated acceleration?? (Forgive me if my terminology is improper. I'm a beginner.) Is there any name for such forces & accelerations which change at a predictable rate as in this question?