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Newton's Law of Universal Gravitation

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.

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

For the first group of problems below, find the gravitational force.
Write out all the steps as shown in this example for each problem!
Example Problem:
- Let m₁= 5.94×10²⁴ kg (Earth's Mass)
- Let m₂= 7.35×10²² kg (moon's Mass)
- r= 3.84 ×10⁵ m )distance from the Earth to the moon)
- F = G (m₁ x m₂ / r²)
- F = 6.674×10^-11 N m² kg^-2 [5.94×10²⁴ kg x 7.35×10²²kg / (3.84 ×10⁵m)²]
- F = 1.98×10²⁶ N

m₁=m₂= 2kg; r=1m. F = ?
m₁=m₂= 2kg; r=1m. F = ?
m₁=m₂= 3kg; r=1m. F = ?
m₁=m₂= 4kg; r=1m. F = ?
m₁=m₂= 4kg; r=2m. F = ?
m₁=m₂= 4kg; r=3m. F = ?
m₁=m₂= 4kg; r=4m. F = ?

If the mass is doubled the gravitational force is _____________.
If the mass is tripled the gravitational force is _____________.
If the mass is quadrupled the gravitational force is _____________.
If the distance is doubled the gravitational force is _____________.
If the distance is tripled the gravitational force is _____________.
If the distance is quadrupled the gravitational force is _____________.