# What determines how long a day is on a planet?

A quick Google search shows that the day is about 116 (Earth) days for Venus, 1 day for Mars, 10 hours for Jupiter. I can't find an obvious connection between how long a day is with anything. Is it just random?

I can't find an obvious connection between how long a day is with anything. Is it just random, a mystery?

Mainly it is conservation of angular momentum, and in a sense, random.

The blobs of the primordial cloud that became our solar system, sun in the center and planets rotating in stable orbits around it, at the center of mass of the system have an angular momentum, which, when the system separated to what we see now as a solar system, had to be conserved.

How much of it went to the rotational angular momentum of the planets would depend on the process of formation of thei indiviual planets, and in that sense random. Once a rotating mass was formed conservation of angular momentum keeps it turning, unless tidal forces reduce the angular momentum and the planets become tidally locked, as surmised for the Trappist planets. .

It is not random at all :

In the Solar System the equation that governs the period of rotation of the planets, from Earth to Neptune,is (in hours)

$rot = 25.513757010 + 6.355661671*10^{-9}*diam*mass - 0.000116821*diam - 0.000814341*dist$

( the precision better than 0.18% rules out any randomness )
data is from the Nasa - Planetary Fact Sheet

and
dist is the distance to the Sun
diam is the diameter of the planet
mass is mass of the planet
It is easy to justify that Mercury, Venus and Pluto do not fit the equation

The above equation afaik was first written down by myself.