Dear Greg,

Two of the distances in the formulas are distances between masses. The other distance is actually a change in the distance, not an actual distance. In addition there are two different masses. The mass that gets canceled out is the one being accelerated. So what you have shown is that the mass providing the force of acceleration is proportional to the acceleration times the distance between the masses squared. Newton knew that

The constant of proportionality also has units. When doing dimensional analysis, which is the name of what you have done, you have to include all units, even when they are in the constants.

Your dimensional analysis result is that the unit of mass is equal to the unit of volume, as you have said. However, that is not mathematically correct as you must always have the same units on both sides of an equation. Otherwise you cannot use the equal sign. You will learn this when you get to college.

yanniru

• One Distance Cubed - m3pers2 - January 25, 2003 - 17:32 UTC
  • Of course the distance that is changing is the distance between - yaniru - January 25, 2003 - 19:21 UTC
    • I expect an apology - m3pers2 - January 25, 2003 - 22:03 UTC
      • You contradicted your self - yaniru - January 26, 2003 - 04:27 UTC
        • Yanniru should apologize - quiet - January 28, 2003 - 16:56 UTC
        • It does stand up. - m3pers2 - February 1, 2003 - 05:35 UTC
          • Greater detail - yaniru - February 2, 2003 - 00:23 UTC
            • Details - m3pers2 - February 11, 2003 - 05:54 UTC
              • That volume is not the volume of mass a or b. - yaniru - February 11, 2003 - 13:26 UTC