# Calculate the equatorial rotation velocity

1. Mar 4, 2013

### Vetmora

(If this is in the wrong section, please feel free to move it.)

Hi all,

How would one calculate the equatorial rotation velocity or rotation period without the other?

Is this possible using the values; diameter, circumference, mass and revolutionary/orbital period?

Thank you.

2. Mar 4, 2013

### Staff: Mentor

If you know diameter or circumference (those are related via geometry), you can find a relation between equatorial rotation velocity and rotation period. That is simple geometry.

3. Mar 4, 2013

### Vetmora

Thanks I do realise this. Should have been more elaborate.

I am making fictional planets and wonder if there is a formula for making rough rotation velocities without actually using the velocity or period. Whether this uses the mass or radius to get a rough figure.

Doesn't need to be super realistic, just a guide, as this is all fictional.

4. Mar 4, 2013

### Mordred

Stars and planets form in the collapse of huge clouds of interstellar gas and dust. The material in these clouds is in constant motion. As the planet forms it conserves that angular momentum unless otherwise influenced. Much like a skater as the planet shrinks in diameter the planet will spin faster. If the planet somehow increases in diameter the spin will slow down. Other factors such as tidal influences, near misses and collisions affect the rotation.
Beyond that the rotational velocity is described as MFB described.

So essentially you can make up any value you like as its not mass dependant rather its dependant on its conservation of angular momentum at the time the planet was forming.

Last edited: Mar 4, 2013
5. Mar 5, 2013

### Staff: Mentor

Exactly.

Just consider our solar system as example: We have one planet with 1 earth-mass and a day of 1 earth-day (Earth), and another planet with roughly the same mass and a day of ~250 earth-days (Venus).

Small objects too close to the star will have synchronous rotation (so they do not have a day/night cycle at all).

6. Mar 5, 2013

### Vetmora

Found some good formulas here: http://arxiv.org/pdf/1301.4720.pdf

In particular Eq. (13) and S ∝ Gm2/v

Not sure if they would be exactly what I'm looking for. Can't seem to find the definition of all the symbols though. It also seems there is a relation between the rotation period, mass and radius.

7. Mar 5, 2013

### Mordred

Best I can say on that paper is sort of. To explain further this paper is describing other influenced that affect the spin of a planet.
However it attempts to do so using their interpretation of a relation of orbital angular momentum to a combination of electrmagnetism and gravity.
Its an interesting paper I am definitely going to study it further. However for your estimates you describe not really suitable.
In classical Einstein models. As mfb mentioned planets are tidally locked and spin slower. Part of this paper describes this in their model.
The introduction described
Conservation of energy and Keplers laws this is the part that applies mostly to yhose estimates. The rest of the paprr describes other factors that later influence that conservation of energy.
mass is involved mass/momentum describes The amount of energy/force involved in its current spin and how those other influences affects it.

8. Mar 5, 2013

### Mordred

This site here has an excellent explanation of what Myself and mfb are describing.
Certainly better than I can do from my phone lol.

http://passion4science.wordpress.com/2012/08/02/why-do-planets-rotate/ [Broken]

The second site is better. However the first is still decent.

Last edited by a moderator: May 6, 2017
9. Mar 6, 2013

### Vetmora

Thanks for helping me out further and finding those interesting articles. I'll take your advice and give each planet it's own value and look at our own planets for reference.

Thanks again.