Re: Why are the concepts of universal law of gravity and coulombs law different

Dear Chavez,

First let me recap both force laws for the benefit of our readers.
Newton's Law of Universal Gravitation is:

          F = G m M / r^2

where F is the magnitude of the force acting on one of the two masses
m and M, r is the distance between their centers, and G is a
fundamental property of the universe called Newton's constant which
describes the strength of the gravitational interaction.  If the
masses are measured in kilograms and the distance is measured in
meters, then G = 6.673 x 10^-11 m^3 kg^-1 s^-2.

Coulomb's Law for electrostatics is:

          F = k q Q / r^2

where F is the magnitude of the force acting on one of the two charges
q and Q, r is the distance between their centers, and k is a
fundamental property of the universe called Coulomb's constant which
describes the strength of the electric interaction.  If the charges
are measured in coulombs and the distance is measured in meters, then
k = 8.987 x 10^9 kg m^3 C^-2 s^-2.

As you say, there are many similarities in the form of the two laws.
There are also restrictions that apply to both laws: the masses or
charges must be either mathematical points or spherically symmetric
distributions of mass or charge.  Finally, both forces are "central"
meaning that the direction of the force is along the line joining
their centers.

Now to your question.
> ... in chemistry, the bigger the atom (or bigger ionic radii), the
> less attractive force it has with it's bonded partner. Why not the
> bigger the atom, the higher the force of attraction?

The force in Coulomb's Law depends on the CHARGES of the ions, not
their MASSES.  The charges of the ions depend on the number of
electrons exchanged to form the bond, and have nothing to do with
the size of the atom.

Remember that atoms are electrically neutral; the positive charge
of the protons in the nucleus is cancelled exactly by the negative
charge of the electrons surrounding the nucleus.  When two neutral
atoms form an ionic bond, one atom loses some electrons and the
other atom acquires the same number of electrons.  This determines
the charges q and Q that appear in the numerator of Coulomb's Law.

As an example, consider two salts: sodium chloride and cesium iodide.
Both sodium and cesium have one electron in their outermost shells;
both chlorine and iodine need one electron to complete their outermost
shells.  When sodium and chlorine bond ionically, the sodium atom
donates one electron to the chlorine atom.  The sodium atom (now an
ion) has a charge of +1e and the chlorine ion has a charge of -1e,
where e is the absolute value of the charge of one electron,
e = 1.602176 x 10^-19 coulomb.  These are the charges q and Q to be
used in Coulomb's law.  The distance r is the sum of the radii of
the sodium and chlorine ions.

When cesium and iodine form an ionic bond, the charges are +1e and
-1e respectively, the SAME q and Q as in sodium chloride because in
both cases one electron is exchanged to make the bond.  The distance
r is different this time; it is the sum of the radii of the cesium
and iodine ions.  This new r for cesium iodide is larger than the
r for sodium chloride because the cesium ion is larger than the
sodium ion, and the iodine ion is larger than the chlorine ion.
Coulomb's Law predicts correctly that sodium chloride is more tightly
bound than cesium iodide.

> Lastly, if the size of Earth increases, does that mean the force of
> gravity acting on me would increase? If so, why?

The answer depends on which values you change and which values you
hold fixed.

If the radius of the Earth increased while the mass of the Earth remained
fixed, then the force of gravity acting on you as you stood on the
Earth's surface would decrease.  Why?  Consider Newton's Law of
Universal Gravitation; leave the masses m and M alone and increase the
radius r.  Clearly the force F would decrease.

However, if both the mass and the radius of the Earth increased while
the density (mass per volume) remained fixed, then the force of gravity
acting on you at the surface would increase.

--Randall J. Scalise    http://www.phys.psu.edu/~scalise/