My New Laws of Planetary Motion and Newton - How They are Related

How are the new laws I published yesterday related to Issac Newtons laws of gravity ? Newton discovered the inverse square law for distance in terms of the force of gravity. He deduced the inverse square law from Kepler's third law and the formula for a force in a circular orbit :

F    𝞪    V sq / R

We can now try a different route to Newton by replacing V squared with my second law :

• Velocity = √ Distance / Distance

F    𝞪    (√ R / R) ^2 / R

F    𝞪      (R / R^2) / R   = (1/R)  /  R = 1/R^2

F     𝞪    1 / R sq

We have arrived at Newton's inverse square law.

We can then combine Newton's inverse square law and my first law :

• Distance squared = Time / Velocity

F 𝞪 1 / (T / V)

F 𝞪 V / T

So the force of gravity is proportional to the velocity divided by the orbital period.

In the last article, I mentioned about doubling the distance and it's impact on velocity and the orbital period for mars relative to venus. This time let's work it out exactly :


• V = √ D / D

V = √2 / 2

V = 0.707

• D sq = T / V

4 = T / 0.707

T = 4 x 0.70 = 2.828.

So when the distance from the Sun is doubled the velocity of the more distant planet reduces by 30% and the orbital period increases by a factor of 2.82. Now lets put this into the formula above :

F 𝞪 V / T

F 𝞪 0.707 / 2.828

F 𝞪 0.25

This once again leads us to Newton's inverse square law for gravity which shows that when you double the distance from the Sun, the force of gravity is reduced to a quarter or 25% of its original strength.