Comments on: The Renaissance Man Uniform Gravitational Acceleration SMACKDOWN

By: Mark Eichenlaub

Mark Eichenlaub — Mon, 10 Dec 2012 22:20:13 +0000

Kepler would also have been unable to tell you the acceleration of the planets in their orbits.

By: Mark Eichenlaub

Mark Eichenlaub — Sat, 08 Dec 2012 21:27:39 +0000

Peter, you are going to have to study calculus, differential equations, and then mechanics before you can understand the Kepler problem clearly. Ad-hoc algebraic manipulations will not teach you what you want to know.

By: Mark Eichenlaub

Mark Eichenlaub — Sat, 08 Dec 2012 07:11:14 +0000

No, that is not correct. The acceleration of a planet in a Keplerian orbit is always changing, since it points towards the sun and is proportional to 1/r^2.

By: Peter L. Griffiths

Peter L. Griffiths — Tue, 10 May 2011 16:03:45 +0000

Further to my comment of 25 April 2011, I hope your readers can tolerate a little bit of algebraic notation, let L equal a small change. From
v^2=d=1/r which is the usual velocity measure, we have
v^2+Lv^2=d+Ld=1/(r-Ld). For the reciprocal velocity measure we have v^2=r=1/d which after the small change will be
v^2+Lv^2=r+Lr=1/(d-Lr). This reflects the two ways of measuring velocity, distance per unit time and time per unit distance, one of which is the reciprocal of the other. Any change of d is equal to the opposite change of r.

By: Peter L. Griffiths

Peter L. Griffiths — Mon, 25 Apr 2011 15:42:28 +0000

One important aspect of Galileo’s law of falling bodies is that this discovery was also made by Kepler in a reciprocal form v^2=1/r where d+r equal the major axis of the elliptical orbit.

By: Shawn

Shawn — Sun, 29 Nov 2009 05:24:07 +0000

Maybe da Vinci was talking about position and triangular numbers rather than velocity. Suppose your position is given by: 0, 5, 20, 45, 80

Triangular Numbers (And Zero)
0, 1, 3, 6, 10, 15, 21, 28…
Average of successive terms
.5, 2, 4.5, 8, 12.5, 18, 24.5
If g=10, multiply by 10 to get the free fall positions
5, 20, 45, 80, 125, …

By: | Quiche Moraine

| Quiche Moraine — Fri, 16 Oct 2009 15:13:35 +0000

[...] Steel Cage Death Match: da Vinci vs. Galileo in The Renaissance Man Uniform Gravitational Acceleration SMACKDOWN [...]

By: Mark Eichenlaub

Mark Eichenlaub — Tue, 13 Oct 2009 10:43:43 +0000

According to what I’ve read elsewhere, he was referring to triangular numbers when he mentioned pyramids. But it does seem like there’s a little room for interpretation, based on the tiny bit of text I have.

By: Paul Murray

Paul Murray — Tue, 13 Oct 2009 06:29:13 +0000

Pehaps Da Vinci was right? Maybe by “the degree of its descent” he meant the distance, rather than the time? Obviously, that makes his velocity wrong … unless he meant total average velocity rather than instantaneous velocity?

And a pyramid is three-dimensional, anyway. The pyramidal numbers increase with the cube of n. Was LdV aware that kinetic energy is proportional to the square of the velocity? Is that what he meant by “the power of it’s motion”?