1. Take the equation F=[G(m(adsbygoogle = window.adsbygoogle || []).push({}); _{1})(m_{2})]/r^{2}

2. Assume a single mass of 20 (units don't matter), which will be divided in the following ways:

2.1. System 1: m_{1}=20, m_{2}=0

2.2. System 2: m_{1}=19, m_{2}=1

2.3. System 3: m_{1}=18, m_{2}=2

2.4. System 4: m_{1}=17, m_{2}=3

.

.

.

2.11.System 11: m_{1}=10, m_{2}=10

Now...

3. If we keep both G and r constant, then the force is going to depend on the allocation of mass by the factor(m_{1})(m_{2})

4. The factors for the systems would then be:

4.1. System 1:(m=20 (or zero?)_{1})(m_{2})

4.2. System 2:(m=19_{1})(m_{2})

4.3. System 3:(m=36_{1})(m_{2})

4.4. System 4:(m=51_{1})(m_{2})

4.5. System 5:(m=64_{1})(m_{2})

.

.

.

4.11.System 11:(m=100_{1})(m_{2})

5. My question is this: why does the force of gravity change when the distribution of mass of the overall system doesn't change? This might seem obvious to someone else, it may be mathematically obvious why, but I still don't understand intuitively why this happens. I would have thought that if you have 20 units of mass in one system and 20 units of mass in another, all else being equal, the force in the two systems would be the same.

What am I missing here, conceptually?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Qualitative query regarding Newton's Law of Universal Gravitation

**Physics Forums | Science Articles, Homework Help, Discussion**