How does newton's universal law of gravitation work?

Question

say there are 2 bodies A and B. suppose A and B are in contact. Then the distance between them becomes zero.

let the mass of one body be m1 and the other m2, the distance between them r = 0

then, according to the universal law of gravitation,

F(force of attraction) = G X m1 X m2 / r^2

= G X m1 X m2 / 0^2

= G X m1 X m2 / 0

= infinity (because (any number not equal to 0) / 0 = infinity)

so does this mean A attracts B with infinite force? but how is this possible?

Answer 1

BS Alert*

The law itself only refers to the force between point masses of infinitesimal extent. This is only an idealization, though. Since nothing is infinitesimal, the force is always finite in practice.

Contrary to what you are being told, the formula is *not* generally valid if you take R to be the distance between the centers of mass of extended objects. Using calculus, the formula can shown to be applicable only for nonoverlapping *spherically symmetric* mass distributions, where R is the distance between centers.

If you were interior to a large spherically symmetric mass distribution of uniform density (where you are small compared to the body, so can be treated as a point), your weight would increase in proportion to your distance from the center until you reached the surface. Only then would then fall off as 1/R^2 as you went higher.

* A BS alert is issued when the majority of other respondents are giving answers which are wrong or, worse yet, not even wrong.

Answer 2

First, the distance r is from center of mass to center of mass.  When the two bodies are in contact at their surfaces, there is still a distance r = r1 + r2 > 0 between them

Second, Newt's law assumes the bodies m1 and m2 do not lie wholly or partially within each other.  As you point out, when r = 0 (the CM's are coincident) the law breaks down.  The attraction does not go to infinity, but the equation is no longer valid in such circumstances.

Answer 3

It is the centre of mass that is considered (it is the point in the body where the entire mass of the body can be assumed to be situated) from which the distance is calculated.

Now if the distance between the two centre of masses (A and B) is say r' then in the equation r = r'.

Now if you say that what if the distance between the two centre of masses is made zero...well then all I could say is that it is impractical as r under no circumstances can be made zero.Also to be noted that centre of mass is an imaginary point (only in theory),its does not exist in practical.

Answer 4

If r=0, then that means the distance between the center of the 2 bodies is 0, which means they have no radius at all.  So, physically, r cannot equal 0 (there has to exist some distance between their centers to account for each of their radii).

Answer 5

It is not the distance between the surface of the objects that matters, but the distance between the objects center of mass. If your bodies A and B had an overall dimension of zero (i.e. black hole like singularities) then your reasoning would be valid. But in reality, the distance between the two bodies, even when they are touching, is radius of A plus radius of B (assuming they are both homogeneous spheres).

To figure out how much you weight right now, you are to assume that you are 6370 km from the center of the Earth, that is the "r" of the equation.