Question

The square body of the orbital period of planet around is proportional to the cube of the planets orbital radius. this follows the____.
law of ellipses
law of harmonies
law of equal areas
law of kepler

Answer 1

law of kepler

It is said that Newton used this information to realise that the gravitational force was inverse square. That's pre relativity.

They were thinking solely in terms of space.

Einstein et al said that you had to consider time as well ... "space-time"

Answer 2

Answer:

Law of Kepler

Explanation:

As per kepler's law of planetary motion we know that

square of the time period of the planet around the sun is directly proportional to the cube of the radius of the orbit of the planet

So we will have

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

here we know that

$\frac{GMm}{r^2} = \frac{mv^2}{r}$

$v = \sqrt{\frac{GM}{r}}$

now time period is given as

$T = \frac{2\pi r}{v}$

$T = \frac{2\pi r}{\sqrt{\frac{GM}{r}}}$

$T = 2\pi\sqrt{\frac{r^3}{GM}}$