Question

he force of gravity between two objects is given by  Fg = −Gm1m2 r2 , where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the objects' centers. Find the vertical asymptote of the graph of the function and explain its meaning in context.

Answer 1

Examine the denominator and find that

r^2 = 0 when r = 0.

Determine that there is a vertical asymptote at r = 0.

Conclude that as the distance between the objects approaches 0, the gravitational force between them approaches infinity.

Answer 2

By definition, the gravitational force is given by:

`Fg = -Gm1m2 / r ^ 2`
Where,
m1 and m2: are the masses of the objects
G: is the gravitational constant
r is the distance between the objects' centers
The vertical asymptote of the function occurs when the denominator is equal to zero.
We have then:

`r ^ 2 = 0 r = 0`
In this context, it means that physically, the distance between the center of the objects can not be equal to zero (which is logical).