Science Forums 2

modest · 08-29-2009

Quote:

Originally Posted by Erasmus00

Also, while the above is a reasonable assertion of evidence that could lead to an inverse square law, the evidence that Newton and Hook actually followed to get inverse square was that an inverse square law produces conic section orbits (like Kepler's ellipses).

Apparently there was some question as to whether Newton or some fella named Christiaan Huygens first found the inverse square law. To make his case, Newton showed his early work preceding the well-known proofs in the Principia by some 20 years where he found the centripetal force and apparently used Kepler's 3rd law from that. I get from:

The birth of a new physics - Google Books

My question, which I know betrays the novice I am, how would you combine Kepler's third and v^2/r to get 1/r^2?

~modest

EDIT: Sorry

I got it. I had Kepler's velocity relationship wrong

$F = \frac{v^2}{r}$

$v = C \sqrt{\frac{1}{r}}$ (from Kepler's third)

$v^2 = C^2 \frac{1}{r}$

$F= \frac{C^2(1/r)}{r}$

$F \propto \frac{1}{r^2}$

Science Forums 2

Hypography?

Share the love!

Sponsors

Friends