Wrong, Wrong, Wrong!

A certain incident has been nibbling away at my consciousness for ages like a kind of psychic termite. It happened in my freshman physics class when the teacher was introducing Newton's law of gravitation. In order to protect the reputation of said teacher, I shall refer to him here as Professor X.

Professor X presented the equation for finding the force exerted on an object by the earth's gravity. It's a classic, lovely little equation...

M_e = the mass of the earth, about 1.3 x 10²⁵ lbs or 5.97 x 10²⁴ kilograms. (Do we remember our metric conversions and our scientific notation?)

m = the mass, in kilograms, of some object.

r = how far that object is from the center of the earth.

G = the universal gravitation constant, a sort of cosmic fudge factor, equal to

6.673 x 10^-11 N•m²/kg² 

(the "N" stands for "Newtons", the unit of measure for force; read as "Newton meters squared per kilograms squared").

A student asked a question: "So, if r = 0, the force is infinite?"

Knowing that we had been taught in our math classes that anytime you divide a number by 0 the answer is ∞, Professor X said, "Yes, if r is 0, F_g is infinitely large."

There are a few reasons why the professor might have responded to the student's question with such an incredibly wrong answer: