Teachers, please use this site if you wish for your students to be able to calculate the force of gravity on whatever moon or planet they put their colony.

In order to do this, the students must know the radius and the mass of the planet or moon they wish to build their colony on.

For a background to the theory and mathematics of gravity, please go to Ron Hipschman's excellent site Your Weight on Other Worlds.

According to the formula for universal gravitation, F(o) is proportional to M(o) times m(p) divided by R(o) squared or

(Note: in the following formula ^ is the symbol for "raised to the power of" - for example 10^8 is 10 to the power of 8 or 100,000,000. Also, please forgive me, but the equal sign is really supposed to be a sign for proportionality, but I can't insert a proportional sign in there so I'm using an equal sign.)

                       M (o) X m (p)     

  F (o)       =       _____________              

                                 R (o) ^ 2          

where F(o) is the force of gravity on the other moon or planet, M(o) is the mass of the other moon or planet, m(p) is the mass of the person, and R(o) is the radius of the other moon or planet.

To compare this with Earth's gravity, make a ratio of the force of gravity on the other moon or planet to the force of gravity on the Earth where F(e) is the force of gravity on the Earth, M(e) is the mass of the Earth and R (e) is the Earth's radius.

Since

                       M (o) X m (p)                                                    M (e) X m (p) 

  F (o)       =       _____________              and       F (e)     =    _____________

                                 R (o) ^ 2                                                          R (e) ^2

Then the ratio of the gravity of another moon or planet to the gravity of the Earth is

                                                 M (o) X m (p)

                                                          _____________

  F (o)                                                      R (o) ^ 2

______                =             __________________________

  F (e)                                                     M (e) X m (p)

                                                        ________________

                                                                R (e) ^ 2

For example, the mass of the earth's moon is 0.73483 X 10^23 kg and its' radius is 1738 km. The mass of the earth is 59.74 X 10^23 kg and its' radius is 6371 km. Since the mass of the person [ m (p)] is the same in both the numerator and the denominator of the equation, they "cancel" each other off.

                                                                 M (o)

                                                          _____________

  F (o)                                                      R (o) ^ 2

______                =             __________________________

  F (e)                                                     M (e)

                                                        ________________

                                                                R (e) ^ 2

When we put in the values for our moon and the Earth, they become

                                                           0.73483 X 10^23 kg

                                                          _____________

  F (o)                                                     ( 1738 km) ^ 2

______                =             __________________________

  F (e)                                                  59.74 X 10^23 kg

                                                        ________________

                                                                 (6371 km) ^ 2

When we continue the equation

 F (o)                                            0.73483 X 10^23 kg                               (6371 km) ^ 2          

______                =             ______________________        X      ________________

  F (e)                                          59.74 X 10^23 kg                                     ( 1738 km) ^ 2

And now

 F (o)                                       0.73483    kg                            40589641    km squared

______                =          _____________        X         ________________

  F (e)                                          59.74   kg                              3020644     km squared

After the multiplication and division, then the ratio of gravity on the moon to the gravity on earth is

F (o)                                               

______                =        0.165       

  F (e)                                              

 In other words, if a student weighed 100 pounds on earth, he or she would weigh 16.5 pounds on our moon. By substituting in the mass and the radius of whatever moon or planet (they can find this in the links provided) the students wish to build a colony on, they can calculate the gravity.

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