# How would I calculate the length of the day of this planet?

Take the following planet:

• Same distance from the main star as Earth
• Main star is the same size as the sun
• Planet is the size of Venus

• The piece of information you need is pretty much "the length of the day". It is independent of your variables. (Though if the planet is really close to the star, it would tend to be tidally locked.) – SE - stop firing the good guys Sep 9 '16 at 14:54

It's almost completely unconstrained. There's a limit to how fast a planet can spin before it starts to break up, which is $p = 2 \pi / \sqrt{m G / r^{3}}$ (where $m$ is the planet's mass and $r$ is its radius). For something like the Earth (and Venus is pretty similar), this corresponds to about 1.4 hours. So the day has to be longer than that.
You can use Kepler's third law to get the length of a year $$\frac{P^2}{a^3} = \frac{4 \pi^2}{G(M+m)},$$ where $P$ is the period of rotation, $a$ is the distance between the planet and the star, $M$ is the mass of the star, $m$ is the mass of the planet and $G$ is the universal gravity constant. As the mass of Venus is roughly the same as the Earth's ($M_V = 0.815M_\oplus$), you will get something close but a bit larger than 365 days.