# Where does the kinetic energy of infalling bodies come from?

* Imagine two planet-sized bodies in deep space. Placed 'near' to each
other (by which I mean not in orbit around each other) they will
accelerate towards each other under mutual gravitational attraction,
and eventually collide.*

To be concrete about this, let's assume that we are placing the objects sufficiently close together that they will collide on a timescale much shorter than that of the Universe's expansion, so that for all intents and purposes the Universe is static. If the bodies have no relative velocities or angular momentum to start, then they will collide.

*
In the classical sense, 'work' is being done to move them, and thus energy is being expended.
*

Work is the integral of the (dot) product of a force (here, gravity) and
a distance; so work is, indeed, being done here. Be careful about stating
that energy is expended, however. If we assume that the system is closed
in the sense that heat doesn't escape the pair (a very good assumption up
until the bodies actually collide), then the total energy of the system is
*conserved*. I am guessing that by "energy expended", you mean that the
bodies lose gravitational potential energy and gain kinetic energy during
the infall. There is therefore an "exchange" of energy, if you will,
between the potential energy of the system and the net kinetic energy,
but energy is not lost.

*
What is the source of this energy?
*

In light of the above, the "source" of energy is gravitational potential
energy. In fact, you impart this energy to the system by placing the
bodies in space at the chosen distance. The situation is analogous to
placing two styrofoam balls on either end of a spring, stretching it out,
and letting the balls "spring" together. When you stretch out the string,
you are doing work to store potential energy in the spring. When you let
go and the balls are pulled together by the string, the potential energy
stored in the string is in converted into kinetic energy in the attached
balls (we ignore any heat dissipated in the string here). Where did the
energy in the moving balls come from? From *you*, when you did work to
place the balls a certain distance apart by stretching the string. The
same is true for gravity in the example you mention: someone (or
something) does work to place the balls a distance apart (think about how
much work you would do to carry a bowling ball to the top floor of a
skyscraper using the stairs; you do indeed do work to separate the bowling
ball (object 1) from the Earth (object 2)!). The gravitational potential
energy in the system is then converted into kinetic energy as the force of
gravity pulls the objects towards each other.

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