Why didn't Newton give credit to Kepler ?

On Page 108 of Newton's Principa, he introduces for the first time Kepler's Third Law, without actually naming it's originator :

COR. 6. If the periodic times are in the sesquiplicate ratio of the radii

The sesquiplicate is the square root of the cube, in this case, the Orbital Period is proportional to the square root of the distance cubed. Kepler's third law states that :

D^3 𝞪 T^2

Therefore,

T 𝞪 √ D^3



He then inputs this into a simple speed = distance over time formula :

V = D / T

V= D / √ D^3

V = √ 1 / D

Then, combining the centripetal force formula, V^2 / R, with the above, he arrives at the groundbreaking force equals the inverse of the distance squared formula :

the centripetal forces will be in the duplicate ratio of the radii inversely :

At this point, Newton stops to give credit to other english physicists for the famous formula :

as Sir Christopher Wren, Dr. Hooke, and Dr. Halley have severally observed

But he has omitted the origin of his starting point, Johannes Kepler, a giant whose shoulders Newton was standing on more than anyone else. 

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.