# Rotation of heavenly bodies

• PalashD

#### PalashD

I have had this question for a very long time. Never got a convincing answer

Every Heavenly body rotates about its axis.
The sun, the planets, the galaxies, every heavenly body
why is it so?
what makes the rotate?

ps:It is very likely that this question would be a repetition. If it is then please direct me to the earlier thread.

From my understanding conservation of angular momentum is responsible for this. I may be wrong though I am not yet an expert.

where does the initial angular momentum come from?
is it that the creation of every heavenly object is such that it imparts angular momentum to every object?

This is simplly a matter of the absence of perfection in real life. There are an infinite number of numbers, but only one zero. The odds of a cloud of gas being so perfectly uniform that it has zero radial density variations and zero angular momentum is essentially...well...zero. A cloud of gas is composed of individual, randomly moving particles and the sum of their relative motions is the resulting anguar velocity of the cloud.

Start with circular orbits. A tiny particle with negligible mass in a circular orbit around a star of mass Ms at a distance r from the star has an orbital velocity of
$$v_{\text{particle}} = \sqrt{GM_s/r}$$

A planetesimal with mass mp at the same orbital radius will have a slightly high orbital velocity:
$$v_{\text{planetesimal}} = \sqrt{G(M_s+m_p)/r}$$

The planetesimal will thus collide with all the little stuff in its way. This clears a path along the planetesimal's orbit. These collisions will also make the planetesimal's orbital radius decrease over time. The planetesimal gobbles up the stuff in front of and beneath the planetesimal. There isn't much stuff in front of and above the planetesimal; it has already gobbled that stuff. The collisions are one-sided, and these one-sided collisions impart a prograde rotation to the planetesimal.

This is a bit over-simplistic; things get a lot hairier when the planetesimal and the stuff in its neighborhood have eccentric orbits.

So this is just a case of probability. The rotation period of a heavenly object depends upon the velocity and orientation of the cloud of gas or the asteroids it encounters in the period of its creation?

So this is just a case of probability. The rotation period of a heavenly object depends upon the velocity and orientation of the cloud of gas or the asteroids it encounters in the period of its creation?
Think of a figure skater starting a slow spin and then retracting his or her arms. The skater's spin speeds up. Now think of a cloud of gas and dust that condenses under gravitational self-attraction (look up the M-42 nebula for a nice example of a stellar nursery) and consider what will happen when the materials condense to form stars or protostars. Unless the net angular momentum of that cloud of gas is exactly zero (which as Russ pointed out is not possible) bodies condensing out of it will spin up to conserve angular momentum.

I'm not sure if this is the case, but I think that it is probably safe to assume than any over-or-under-density in the cloud in which the proto-star is condensing will contribute to unbalanced in-flows of material and the imbalance can result in even more spin for the condensing body. The proto-star will continue to grow and spin up until its fusion processes light up and it develops enough radiation pressure to push away the materials from which it is forming.

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Think of a figure skater starting a slow spin and then retracting his or her arms. The skater's spin speeds up. Now think of a cloud of gas and dust that condenses under gravitational self-attraction (look up the M-42 nebula for a nice example of a stellar nursery) and consider what will happen when the materials condense to form stars or protostars. Unless the net angular momentum of that cloud of gas is exactly zero (which as Russ pointed out is not possible) bodies condensing out of it will spin up to conserve angular momentum.
That model only explains the angular momentum of the central body and the orbits of the planets. It does not explain why planets have a rotation as well as an orbit.

In fact, this model is at odds with the observed angular momenta of stars. For example, almost all of the mass in our solar system is concentrated in the Sun, but the vast majority of the total angular momentum arises from the planets orbiting the Sun. The Sun has a marked angular momentum deficit. The solution is to think of figure skaters spinning with their arms enfolded. When the skaters extend their arms their spin slows down. The Sun has been extended its arms for a long, long time -- in the form of solar wind.

That model only explains the angular momentum of the central body and the orbits of the planets. It does not explain why planets have a rotation as well as an orbit.

In fact, this model is at odds with the observed angular momenta of stars. For example, almost all of the mass in our solar system is concentrated in the Sun, but the vast majority of the total angular momentum arises from the planets orbiting the Sun. The Sun has a marked angular momentum deficit. The solution is to think of figure skaters spinning with their arms enfolded. When the skaters extend their arms their spin slows down. The Sun has been extended its arms for a long, long time -- in the form of solar wind.
The point is that during the condensation/accretion stages, the accreting body spins up. Yes, the Sun is throwing off mass, and has been doing so for billions of years, but it was not always that way. Baby steps.

That model only explains the angular momentum of the central body and the orbits of the planets. It does not explain why planets have a rotation as well as an orbit.

In fact, this model is at odds with the observed angular momenta of stars. For example, almost all of the mass in our solar system is concentrated in the Sun, but the vast majority of the total angular momentum arises from the planets orbiting the Sun. The Sun has a marked angular momentum deficit. The solution is to think of figure skaters spinning with their arms enfolded. When the skaters extend their arms their spin slows down. The Sun has been extended its arms for a long, long time -- in the form of solar wind.

You're presuming that stars start with a lot of angular momentum that they must then lose. This isn't necessarily so. However young stars are regularly observed with a high rotation rate, so some means of shedding angular momentum probably exists. A favourite mechanism is via magnetic braking.

Alternatively the planets have more angular momentum than the Sun because they were captured from a passing protostar in the Sun's birth-nebula. Michael Woolfson has modeled this particular process extensively with results much like the observed planets.

OTOH Andrew Prentice's Modern Laplacian Theory turns a perceived problem into a virtue by the planets themselves - or rather the rings of gas and dust they formed from - being the means by which the proto-Sun shed excess momentum.

So there's a few options.