Calculate the force of gravity on a 1–kilogram box located at a point 1.3 × 107 meters from the center of earth if the force on a 2.5–kilogram box at the same point is 6.1 newtons.

Since you already gave us the weight of the 2.5-kg box,
we don't even need to know what the distance is, just
as long as it doesn't change.

Look at the formula for the gravitational force:

                           F = G  m₁ m₂ / R² .

If 'G', 'm₁' (mass of the Earth), and 'R' (distance from the Earth's center)
don't change, then the Force is proportional to  m₂ ... mass of the box,
and you can write a simple proportion:

                       (6.1 N) / (2.5 kg)  =  (F) / (1 kg)

Cross-multiply:  (6.1 N) (1 kg)  =  (F) (2.5 kg)

Divide each side by (2.5 kg):  F = (6.1N) x (1 kg) / (2.5 kg)  =  2.44 N .

An  atom  (ours, not carroll's) consists of a positively charged  nucleus, surrounded by one or more negatively charged particles called  electrons. the positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. most of an atom's mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. although the nucleus is heavy, it is quite small compared with the overall size of an atom. the radius of a typical atom is around 0.1 to 0.25 nanometres (nm), whereas the radius of a nucleus is about 10-6  nm.  *  if an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily rest inside a small football stadium.read more on -