Sun's rotation vs planets velocity

[DeepThought]

Is there a mathematical/physical theory which links the rotational velocity of the sun with the orbital velocity of the planets?

Ta.

[D H]

No. For one thing, different planets orbit at different velocities. See Kepler's laws (http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion) for details.

[DeepThought]

No. For one thing, different planets orbit at different velocities. See Kepler's laws (http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion) for details.

D H,

That's over my head at the present time.

I found this diagram which suggests there is some connection between a planets orbital velocity and its distance from the sun:

http://www.enchantedlearning.com/pgifs/Planetvelocity.GIF

[Montec]

Hello Deepthought, et al.

The simplest explanation is that there is a balance of forces at work. These are gravity and centrifugal force. A more complicated approach could use both general relativity (GR) and special relativity (SR).

:)

[D H]

I found this diagram which suggests there is some connection between a planets orbital velocity and its distance from the sun:
There most certainly is a connection between orbital velocity and distance from the Sun. That is exactly what Kepler's Laws say. There is, on the other hand, no connection between orbital velocity and the rotational rate of the Sun.

[Dinosaur]

I wish people would stop talking about centrifugal force: There is no such animal. It is an illusion.

[Montec]

Hello Dinosaur, et al.
I wish people would stop talking about centrifugal force: There is no such animal. It is an illusion.
So true, both gravity and centrifugal forces are classified as "pseudo" forces. However they are both the result of "time gradients". Atomic clocks that "tick" at the same rate at sea level everywhere on the Earth is an example for these "time gradients" and "time rates".

:)

[Dinosaur]

Montec: When you classify both gravity & centrifugal force as pseudo forces, you indicate that you do not understand at least one of them.

Consider an amusemant park ride which spins rapidly. Your mind tells you there is a force trying to make you flee from the center of the rotating cage.

If the cage were to disappear, you would move tangential to the circular path of your rotation. You would not move radially away from the center. What your body feels is a reaction to a force directed toward the center of rotation.

Both gravity & the rotating amusemsnt park ride create a force directed toward the center of rotation of a planet or a person on the ride. There is no force directed radially away from the center of rotation. There is inertia, the tendency of a moving body to stay still or move in a straight line.

[Montec]

Hello Dinosaur, et al.

Hmm, according to this article (http://en.wikipedia.org/wiki/Fictitious_force) from wiki both gravity and centrifugal force are classified as pseudo of fictional forces.

How do you explain the fact that at "sea level" atomic clocks "tick" at the same rate everywhere on the Earth?

We have both gravity and centrifugal force affecting "time rates".

I would love to see a Pound-Rebka experiment (http://en.wikipedia.org/wiki/Pound-Rebka_experiment) performed in a centrifuge.

:)

[DeepThought]

There most certainly is a connection between orbital velocity and distance from the Sun. That is exactly what Kepler's Laws say. There is, on the other hand, no connection between orbital velocity and the rotational rate of the Sun.


Thanks.

My next question is why not?

If the whole Solar System coalesced out of a spinning cloud of plasma with the Sun at the center, why doesn't the Sun's core have a rotational velocity faster than the orbital velocity of Mercury?

[D H]

My next question is why not?

If the whole Solar System coalesced out of a spinning cloud of plasma with the Sun at the center, why doesn't the Sun's core have a rotational velocity faster than the orbital velocity of Mercury?

Better, but still not the right question. Don't look at velocity. Angular momentum is what you want to investigate because angular momentum is a conserved quantity in a closed system. So, I'll ask the "right question" for you:

The whole solar system coalesced out of a spinning interstellar gas cloud. Since the Sun has 99.9% of the total mass of the solar system, why does the Sun have less than 0.5% of the total angular momentum of the solar system?

The answer is twofold (at least). The planets cannot fall into the Sun because they have too much angular momentum. The same applied during the initial formation of the Sun: Only particles with relatively little angular momentum fell to the center of the gas cloud. The nascent Sun was born with less than its share of angular momentum.

The second part of the answer is that once the Sun lit up it lost angular momentum. Infant stars produce a lot more stellar wind than do mature stars. The solar wind interacts with the Sun's magnetic field and carries angular momentum away from the Sun.

Other factors contribute to the discrepancy. For example, the planets steal angular momentum from the Sun through tidal interactions in much the same manner that the Moon is slowing the Earth's rotation rate. These other factors are likely much smaller contributors to the angular momentum problem than are the first two.

[James R]

On the centifugal force issue...

I wish people would stop talking about centrifugal force: There is no such animal. It is an illusion.

Try telling the astronauts who train in a centrifuge that centrifugal force is an illusion. Or fighter pilots pulling out of a dive. Or people riding the Gravitron.

If you're in a rotating frame of reference, then centrifugal force is very very real - for you. But for somebody watching you rotate from a non-rotating frame of reference, there is no centrifugal force. This is why centrifugal force is sometimes called a "pseudoforce" - it is a force that exists or doesn't exist depending on your frame of reference, unlike other kinds of forces which exist in all reference frames.

When you classify both gravity & centrifugal force as pseudo forces, you indicate that you do not understand at least one of them.

No. You can make gravity disappear by jumping out of a window. Since you can go to a reference frame where there is no force of gravity, that tells us that gravity is a pseudoforce, just like centrifugal force.

Consider an amusemant park ride which spins rapidly. Your mind tells you there is a force trying to make you flee from the center of the rotating cage.

If the cage were to disappear, you would move tangential to the circular path of your rotation. You would not move radially away from the center. What your body feels is a reaction to a force directed toward the center of rotation.

It depends on your frame of reference.

Both gravity & the rotating amusemsnt park ride create a force directed toward the center of rotation of a planet or a person on the ride. There is no force directed radially away from the center of rotation. There is inertia, the tendency of a moving body to stay still or move in a straight line.

In the rotating reference frame, there really is a force directed away from the centre of rotation. This is the only way you can explain why objects don't accelerate towards the centre of rotation in that frame.

[D H]

On the centifugal force issue...
Minor correction: On the centrifugal force hijack ...

The simplest explanation is that there is a balance of forces at work. These are gravity and centrifugal force.
There is no reason to invoke a rotating frame. Without a rotating frame there is no centrifugal force. The simplest explanation of orbits is inverse square central force motion in an inertial frame.

Montec: When you classify both gravity & centrifugal force as pseudo forces, you indicate that you do not understand at least one of them.
That gravity is a pseudo force was one of the key insights that led Einstein to the development of general relativity. The force on some object due to any pseudo force is proportional to the object's mass. The force on some object due to gravity is proportional to the object's mass. This led Einstein to question whether gravity was a physical force or a pseudo force.

Another way to look at it is with accelerometers. From a Newtonian point of view, an accelerometer measures the acceleration due to all physical forces except gravity. Accelerometers due not sense the acceleration due to gravity. Nothing can directly sense the acceleration due to gravity. From a general relativistic point of view, an accelerometer measures the acceleration due to all physical forces, period. Gravitation is not a physical force. It is yet another pseudo force that accelerometers cannot sense.

Yet another way to look at it is the xkcd point of view (http://xkcd.com/123/).

[Dinosaur]

James R: I find it hard to believe that you posted the following.Try telling the astronauts who train in a centrifuge that centrifugal force is an illusion.First, let me state that I never said that astronauts in a centrifuge or people on an amusement park ride are not subject to a force.

The force on a person rotating is directed toward the center of rotation. Your body feels the center directed force and the mind has an illusion of a force directed away from the center of rotation. There is no outward directed force.

Oddly enough an analogous situation does not fool the mind. If a force pushes you against a wall, the sensory input from your back is the same as that of an astronaut in a centrifuge, but you do not interpret it as a force trying to make you flee from the wall. Even without the wall, your mind correctly interprets a force pushing against your back as just that: A force pushing against your back. Your mind does not give you the illusion of a force directed in the direction opposite to that of the forcing pushing against your back.

When in free fall, your sensory input correctly tells you that there are no forces acting on you. It is when you hit the ground that you are aware of forces. However that does not make gravitational force an illusion. When standing on the surface of the Earth or accelerating in a rocket ship, there are forces acting on your body. They are not an illusion. If you call gravity in this case an illusion, you must also declare that the force felt due to acceleration is an illusion. The GR argument that the two forces are equivalent does not make either of them an illusion: It only claims that there is a problem deciding what is the cause of the force.

[James R]

The force on a person rotating is directed toward the center of rotation. Your body feels the center directed force and the mind has an illusion of a force directed away from the center of rotation. There is no outward directed force.

There's no illusion about it.

From your point of view, in the rotating reference frame, you feel the force pushing towards the centre. But, you're not accelerating towards the centre in this frame of reference - you're stationary with an acceleration of zero. Therefore, there must be an equal and opposite force pushing outwards on you.

Oddly enough an analogous situation does not fool the mind. If a force pushes you against a wall, the sensory input from your back is the same as that of an astronaut in a centrifuge, but you do not interpret it as a force trying to make you flee from the wall. Even without the wall, your mind correctly interprets a force pushing against your back as just that: A force pushing against your back. Your mind does not give you the illusion of a force directed in the direction opposite to that of the forcing pushing against your back.

Wrong. In both examples, there are two forces that you experience - the force pushing on your back and the one pushing on your front.

When in free fall, your sensory input correctly tells you that there are no forces acting on you. It is when you hit the ground that you are aware of forces. However that does not make gravitational force an illusion.

As viewed in your free-falling reference frame, you are not accelerating. Therefore, the net force on you must be zero. If you want to argue that there is a gravitational force pulling down on you, then you must also agree that there is an equal and opposite force pushing up on you (and that force is another example of what is called a pseudoforce). Alternatively, you can take Einstein's position that in free-fall there is no gravitational force, which obviates the need for a counteracting upwards force to prevent your acceleration in the freefall frame.

When standing on the surface of the Earth or accelerating in a rocket ship, there are forces acting on your body. They are not an illusion. If you call gravity in this case an illusion, you must also declare that the force felt due to acceleration is an illusion.

So, we agree! Neither force is an illusion, in the accelerating reference frame.