This is not a difficult calculation for students who understand a few fundamental principles of physics and mathematics.

The Law of Conservation of Energy states that energy is neither created nor destroyed, that energy simply changes form. Since this law was written down, we have discovered that energy can be made from matter (Einstein’s famous equation,

(1)

states that the amount of energy E made by changing matter of mass m into energy is given by multiplying the mass loss by the speed of light squared) but that involves a nuclear reaction, and meteorite impacts do not involve nuclear physics.

A chunk of rock in deep interplanetary space loses potential energy – and gains kinetic energy – as it falls toward Planet Earth. How much potential does it lose before striking the earth’s surface? If we can calculate the change in potential energy, we can calculate the change in kinetic energy and hence its velocity.

Some physical science textbooks define potential energy as equal to height times gravity times mass, or

(2)

This works well enough so long as g is a constant. However, Newton’s equation of gravitational attraction tells us that the force of gravity decreases as the inverse square of the distance separating the center of mass of two objects (in this case, the earth and the chunk of rock). In other words, when working with interplanetary distances, g is variable. How can this problem be solved without using calculus?

Let us consider a different equation for gravitational potential. Let

(3)

equal the gravitational potential due to a planet of mass M at a distance r from the planet’s center of mass. Note that U approaches a maximum value of 0 as r approaches infinity. G is the universal gravitational constant.

(4)

If you cannot figure out the way to proceed, think about the problem while you look up the mass and the radius of Planet Earth. Write these down because you will need them in order to arrive at a numerical result (how fast).

Give up? So soon? Ok, look at these clues.