The program was developed in an area which is not on the metric system but it does follow Newton's Law of Universal Gravitation - G comes out a little different as it will be expressed in English units. Read "A Closer Look" 5.3 to review this law.

Rewrite the equation using the following variables: planet mass mp, orbiting a sun ms at a distance r

?F=(4.82×10−10)r2mp?ms???

Step-by-step explanation

 Newton's law for gravity in SI system of units is given as,

?F=Gr2mp?ms???

Here the unit of mass is kg, the unit of distance is m, and the unit of Universal constant of gravitation (G) is m³/kg/s². Its value is found to be 6.67 X 10^-11 m³/kg/s².

In the English units system of measurements, the unit of force is pound-force (lbf). One pound-force is the gravitational force acting on one pound (lb) of a mass on the earth's surface.

One pound mass is 0.434 kg, and one foot (ft) is 0.3048 m.

From these relations, the right hand side of the law can be obtained as follows:

?Gr2mp?ms??=(6.67×10−11kg⋅sm3?)(r2mp?ms??m2kg2?)Gr2mp?ms??=(6.67×10−11s2kg⋅m?)(r2mp?ms??)Gr2mp?ms??=(6.67×10−11)(1kg0.454kg1lb?)(1m0.3048m1ft?)(r2mp?ms??)s21?Gr2mp?ms??=(6.67×10−11)(2.203lb)(3.281ft)(r2mp?ms??)s21?Gr2mp?ms??=4.82×10−10(r2mp?ms??)s2lb⋅ft??