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Newton's Law of Univ. Gravitation sans units

Over 300 years ago Newton figured out the Law of Universal Gravitation. The law is diagrammed below. The table describes the parts of the relationship. Note that 'G' is a very small number. Notice also that the gravitational force is a mutual force - felt equally by both objects.

Newton's Law of Universal Gravitation wikipedia illustration
Name Description Units
F1 Gravitational force felt by object 1 Newtons
F2 Gravitational force felt by object 2 Newtons
G Gravitational constant 6.674×10-11 N m2 kg-2
m1 Object 1 kilograms
m2 Object 2 kilograms
r radius meters

Directions

We will simplify our look at gravity to the point of error by removing all reference to the units and by deleting the gravitational constant 'G'. We will look at just the numbers, which is so very wrong! Please don't tell anyone. The formula is simplified to:     F = mass / r2.     For the problems below, find the gravitational force.

mass distance F = mass / r2 Effect on Gravitational Force
1 1 1 / 12 = 1 N With the beginning mass the gravitational force is 1 N
2 1 ______ times the mass = ______ times the gravitational force
3 1 ______ times the mass = ______ times the gravitational force
4 1 ______ times the mass = ______ times the gravitational force
16 1 16 / 12 = 16 N With the beginning distance the gravitational force is 16 N
16 2 _____ times the distance = ______ the gravitational force
16 3 _____ times the distance = ______ the gravitational force
16 4 _____ times the distance = ______ the gravitational force