Name:

# 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 |
---|---|---|

F_{1} |
Gravitational force felt by object 1 | Newtons |

F_{2} |
Gravitational force felt by object 2 | Newtons |

G | Gravitational constant | 6.674×10^{-11} N m^{2} kg^{-2} |

M_{1} |
Object 1 | kilograms |

M_{2} |
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 m
_{1}= 5.94×10^{24}kg (Earth's Mass) - Let m
_{2}= 7.35×10^{22}kg (moon's Mass) - r= 3.84 ×10
^{5}m )distance from the Earth to the moon) - F = G (m
_{1}x m_{2}/ r^{2}) - F = 6.674×10
^{-11}N m^{2}kg^{-2}[5.94×10^{24}kg x 7.35×10^{22}kg / (3.84 ×10^{5}m)^{2}] - F = 1.98×10
^{26}N

- Let m

- m
_{1}=m_{2}= 2kg; r=1m. F = ? - m
_{1}=m_{2}= 2kg; r=1m. F = ? - m
_{1}=m_{2}= 3kg; r=1m. F = ? - m
_{1}=m_{2}= 4kg; r=1m. F = ? - m
_{1}=m_{2}= 4kg; r=2m. F = ? - m
_{1}=m_{2}= 4kg; r=3m. F = ? - m
_{1}=m_{2}= 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 _____________.