Is there any connection between the distance from the sun and period of rotation?

Answer 1

Not 'rotation', but orbital 'revolution' around the sun.

The quantity

(square of the time to complete one orbital revolution) / (cube of the longest dimension across the orbit)

is the same number for every object in orbit around the sun.

Answer 2

Not rotation, but 'revolution' ... the time a body takes to travel all the way around

once in its orbit around the sun. There's a very definite connection between that

length of time and the body's distance from the sun.

Here's a way to describe the connection (although the numbers will be somewhat inconvenient).

For simplicity, let's consider only circular orbits, which is a pretty good approximation for all of

the planets and their moons, plus a large fraction of the asteroids.

-- Take the orbital period, in earth days. Square it.

-- Take the distance from the sun, in millions of miles. Cube it.

-- For bodies in our solar system, the first number divided by the second number

is always roughly 0.166 .

Examples:

-- Earth:

Orbital period = 365.26 days

Distance from sun = 92.956 million miles

(365)2 / (93)3 = 0.1656

-- Mars:

Orbital period = 686.97 earth days

Distance from sun = 141.63 million miles

(687)2 / (141.6)3 = 0.1662

-- Neptune:

Orbital period = 164.8 years = 60,190 earth days

Distance from sun = 2.79831 billion miles = 2,798 million miles

(60,190)2 / (2,798)3 = 0.1654

Is that cool or what !

This is actually one of Kepler's famous three laws.

I think it's #2.

The reason 'why' is: When you take Newton's simple formula for gravitational force,

and massage it sufficiently with lots of geometry and calculus, one of the things

that fall out of it, for a low-mass body in orbit around a high-mass body, is the

equation:

T2 / R3 = constant.