Common Formulas Dealing with Motion

This equation is used to calculate the gravitational force between two masses m1 and m2, separated by a distance d (measured from the center of the objects).

G represents the Gravitational constant, which is  6.67x10-11  m3/kg/s2.  (see Physical Constants)

Note that sometimes this equation is written without the negative sign. The negative sign indicates that the gravitational force is attractive and is included here for completeness. 

Other versions of the equation replace the terms m1 and m2, with m, M, however both are correct and represent the masses of the two objects experiencing the gravitational force. 

Another modification is to use the letter r instead of d. 

Again, both are correct and both represent the distance between the two masses.   

In both of these equations P and a represent the same quantities.

P represents the period or the time an object takes to complete one orbit (in years for Kepler's Third Law).

a represents the semimajor axis distance (in AU for Kepler's Third Law). 

In Newton's version of Kepler's Third Law, if the period is given in years, the mass in solar masses, and the distance in AU, then the factor of 4π2 / G can be removed.

The escape velocity is the velocity needed for an object to escape the gravitational force of another object. The distance between the two objects is R. The mass in the equation R is the mass of the object being "escaped from."

G represents the Gravitational constant, which is  6.67x10-11  m3/kg/s2.  (see Physical Constants)