# Rotation of Heavenly Bodies

1. Mar 9, 2014

### jtban

Why do celestial bodies follow different laws of physics than terrestrial bodies?

A non-rotating object has a point on its axis, or axle, continually aligned with a point on the object. An axis is virtual, or imaginary; an axle is real and we live in a real physical world. In a real physical world, there are two ways a non-rotating object can move in a circle:

1. A point on the axle is continually aligned with the direction of motion and a point on the object. This is similar to a horse on a merry-go-round (MGR). The horse is rotating about the center of the MGR, not about its pole. Observer at the center only sees one side of the horse. Distant observer sees all sides of the horse once/orbit.

2. A point on the axle continually faces the same direction and is always aligned with a point on the object. This is similar to a non-rotating wheel on a vertical axle continually facing the same direction while moving in a circle. Observer at the center sees all sides of the wheel once/orbit. Distant observer only sees one side of the wheel.

In both scenarios the object is orbiting the center of the circle; not rotating on its axle.

In both scenarios, if the object is rotating on its axle and orbiting the center of a circle, a point on the axle is aligned with a point on the object once per orbit.

Rotating Object moving in a circle:

1. With the axle moving in the direction of motion and the object rotating once per orbit, the observer at the center sees all sides of the object once. A distant observer sees all sides twice.

2. With the axle continually facing the same direction and the object rotating once per orbit, the observer at the center only sees one side of the object. A distant observer sees all sides once.

Now compare tidally locked celestial bodies with a plane flying in a circle, a train moving on a circular track, and a horse on a MGR. Every object's axis is imaginary. None have a real axle about which to rotate. All are orbiting the center of a circle. When the forward motion of the plane, train, or MGR is stopped, the objects are not rotating. Why do tidally locked bodies continue to rotate?

Also, in the real world, it's impossible to fit the non-rotating plane, train, or horse into the scenario with an axis always facing the same direction. This can only be done virtually in your imagination.

2. Mar 9, 2014

### Bandersnatch

All bodies, be they celestial or not, follow the same physcial laws.

The short answer for the question stated in the penultimate paragraph is:

Friction

The situations are not equivalent for that reason. Without friction, a plane, a train, and anything else for that matter, with a non-zero angular velocity would keep on rotating with constant angular velocity unless a net torque is applied(Netwon's 1st law for rotational motion) - just like planets do.

This is actually no different than asking why planets keep on going on and on around the sun when objects on Earth(a train, a plane, a MGR) will come to a halt if you turn off the engine.

Last edited: Mar 9, 2014
3. Mar 9, 2014

### Staff: Mentor

Only if the object is rotating around the axle exactly once per orbit.

In order for this to happen the object would need to rotate around its own axis twice per orbit, not once.

Okay.

Because those objects require forward motion in order to rotate since they can't rotate freely around their own axes thanks to friction. Just like you can't go outside and spin your car around in a circle while its parked in the driveway. Celestrial objects are able to spin freely in space.

An axis is an imaginary line about which an object rotates, so I don't understand what you're saying. The axis always faces the same direction unless you tilt the object.

4. Mar 9, 2014

### jtban

Bandersnatch, To make sure I understand Netwon's law of rotational motion, if a plane's engine quits while traveling in a circle, it will continue to rotate while continuing in a straight line until friction brings it to a stop. Is this correct? Planets act accordingly.

Darkkith, Not so. An observer at the center of a merry-go-round only sees one side of the horse. The horse is rotating about the center, not about its pole. If rotating on its pole once per orbit, the observer would see all sides of the horse once.

I think I get it. A spinning object moving in a straight line continues to spin when its forward motion ceases. The same is true of an object moving in a circle. So, there is no difference between a MGR horse on a frictionless pole and a celestial body.

A MGR horse has a real axle (pole), but is not rotating about the pole. It is rotating about the center of the MGR. If given an axis, an imaginary pole, it would be considered to be rotating once per orbit, which we know is not true.

A tidally locked celestial body is rotating once per orbit, with a point on its axis always aligned in the same direction. The observer at the center only sees one side of the object. The only terrestrial object that fits the above scenario is one with a real axle. A plane, a train, a horse, or a celestial body does not have a real axle.

5. Mar 9, 2014

### Staff: Mentor

I'm having a difficult time understanding what's doing what. Could you clarify a little?

In order for a distant observer to see every side of the object twice, as you said in your example, the object MUST rotate around its axis twice.

Actually it is true. The horse will rotate once about its own axis as viewed from an observer on the ground. The horse revolves once about the MGR and rotates once about its rotational axis during that time. The rotation around its axis and revolution around the MGR are independent of each other and don't add.

6. Mar 10, 2014

### AlephZero

7. Mar 11, 2014

### jtban

If you swing a ball in a circle attached to a string and let go, the ball will travel in a straight line until stopped by some physical force. If the ball was rotating when you let go, it would continue to spin while traveling in a straight line until stopped by some physical force. If the sun suddenly disappeared, Earth would travel in a straight line and continue to rotate until stopped by some physical force.

Rotating horse on a MGR: The horse orbits its central axle (barry center) once and rotates about its pole (axis/axle) once. The distant observer would see all sides of the horse twice.

Imagine a horse on an oval race track. An observer at the center of the track only sees one side of the horse. An observer in the stands sees all sides of the horse once.

If at some point on the track the rider makes the horse go in a circle and then continues to the end of the track, the observer in the stands would see all sides of the horse twice; once orbiting the center of the track and once rotating in a circle. The observer at the center would now see all sides of the horse once; right side, head, left side, butt, and right side again.

If the rider made the horse go in 2 circles, the observer in the stands would see all sides of the horse 3 times: once orbiting the center of the track and twice rotating in a circle. The observer at the center would only see all sides of the horse when it was rotating.

From the perspective of a stationary sun, the observer would see all sides of Earth 365 ¼ times a year. From the perspective of a stationary distant observer: 366 ¼ times a year; once as a result of orbiting the sun and 365 ¼ times as a result of actual rotation. Earth in its orbit is not rotating. It is merely changing direction.

The illusion of rotation is a result of the horse changing direction. If you sit on a MGR horse and hold onto the pole (a point on the pole continually aligned with a point on the object: your hands), the horse is not rotating beneath you, it is merely changing direction orbiting the center of the MGR.

An axis could be real or imaginary. A real axis is called an axle. Celestial bodies are treated as though their axis is real. The MGR horse, plane flying in a circle, train on a circular track, and orbiting celestial body all have an imaginary axle (axis). The real axis (axle) is their barry center.

Sorry, however, a helicopter would have to travel forward 50% of the orbit and backward 50% of the orbit while always facing the same direction. I don't know if this is possible.

8. Mar 12, 2014

### Staff: Mentor

Your error here is that you are mixing and matching frames of reference inconsistently. You can say that with respect to you the horse is not rotating and with respect to the spectators it is and that isn't a contradiction. But is is an error to say the rotation is an "illusion". Neither is an illusion: they are direct observations. So if you want to hold a consistent frame of reference (and you should) based on the point of view of the spectators, then you should say the horse is rotating while revolving - and of course, the rider is also rotating with the horse.

Similarly, the moon is revolving about the earth and rotating about its axis (once a month for both) with respect to the fixed stars.

9. Mar 12, 2014

### Staff: Mentor

I'm not so sure about this. I'd be willing to bet that the ball is still spinning after you let go.

An axis and an axle are not the same thing. The horse rotates on its physical pole, its axle, once. Both the observer on the ground and the observer on the MGR would agree on this. But they won't agree on how many times it's rotated on its axis, as this is dependent on the observer's frame of reference.

Per wiki: A rotation is simply a progressive radial orientation to a common point. That common point lies within the axis of that motion. The axis is 90 degrees perpendicular to the plane of the motion. If the axis of the rotation lies external of the body in question then the body is said to orbit. There is no fundamental difference between a “rotation” and an “orbit” and or "spin". The key distinction is simply where the axis of the rotation lies, either within or without a body in question.

The Earth is rotating about an axis that passes through its center and it is also rotating around the Sun (its orbit).

In order to change direction the horse MUST rotate. In this case both you and the horse are rotating with respect to an observer on the ground.

An axle is not an axis. A plane flying in a circle is rotating around two axes (plural of axis?), one through the center of the plane, and one at the point which the plane is flying around.

It is entirely possible for a helicopter to fly around a point while facing the same direction.

10. Mar 13, 2014

### Bandersnatch

Aren't you both saying the same thing? Perhaps the zeal of correctitude(not a real word) took the better of you, eh?:tongue:

11. Mar 13, 2014

### Staff: Mentor

An actual problem might help:
You are on the edge of a 5 meter diameter merry-go-round, rotating at 120 rpm. You release a ball. What is its speed and rotation rate?

12. Mar 13, 2014

### jtban

Thanks for the correction about my use of the word illusion.

From the reference frame of the spectator, the horse is rotating once per orbit. But then, a non-rotating orbiting horse is impossible. The spectator would only see one side of the horse and the observer at the center would see all sides of the horse once: an impossibility.

Also, the observer at the center would not be able to distinguish between a non-rotating horse and one rotating twice per orbit: all sides of the object would be visible once in both instances. Again an impossibility.

Summary:
If we start with a non-rotating, orbiting object, center sees all sides once; spectator sees only one side.

1 rotation/orbit: center, only sees one side; spectator, all sides visible once.

2 rotations/orbit: center, sees all sides once; spectator, all sides visible twice.

~365 rotations/orbit: center, sees ~365 rotations; spectator, ~366 rotations. End

So, lets start again by considering orbiting objects continually facing the center as non-rotating. Observer at the center sees only one side; spectator sees all sides once.

1 rotation/orbit: center, sees all sides once; spectator, sees all sides twice.

2 rotations/orbit: center, sees all sides twice; spectator, sees all sides three times.

~365 rotations/orbit, center, sees all sides ~365 times; spectator sees all sides ~366 times.

However, with this scenario, there is no instance where the spectator would only see one side of an orbiting object. The object would have to be mounted on a real axle and bearing.

13. Mar 13, 2014

### Staff: Mentor

Why is this an impossibility?

If the observer had a way of measuring their own rotation they could determine whether the orbiting object is rotating around its own axis or not. Remember that a rotating frame is not an inertial frame and you can measure the fictitious forces.

Sure there is. If it rotates the opposite direction once per orbit.

14. Mar 14, 2014

### Staff: Mentor

It is not impossible, it just requires an agile horse!

Maybe you should try demonstrating this with objects on a table that you move with your hands.

15. Mar 14, 2014

### jtban

The horse would have to be running sideways and forward part of the way and sideways and backward part of the way. If mounted on an axle, no problem.

I can't think of one real world example where a non-rotating object moving in a circle could be mistaken for one rotating twice per orbit.

Only with an axle (real axis). There are two ways an object with an axis (virtual axle) can move in a circle: 1) axis aligned with the direction of motion, or 2) axis always facing the same direction. You have to be consistant. Objects mounted on axles and bearings are very versatile.

16. Mar 14, 2014

### Staff: Mentor

What? You're losing me. Why in the world would the horse have to do any running at all?

That's because in the real world it wouldn't happen. We have stationary external frames we can measure against.

In all of our examples the axis has been perpendicular to the direction of motion. Perhaps you're using the wrong terminology?

17. Mar 14, 2014

### jtban

Sorry if I wasn't clear. For the horse to move around the oval track and continually face the same direction, is a real problem. The horse is not stationary.

An example of an axis always facing the direction of circular motion would be a point on the pole of a MGR horse always facing the forward motion of the MGR.

An axis always facing the same direction would be a point on the MGR pole always pointing east.

18. Mar 14, 2014

### Staff: Mentor

On a Ferris Wheel, the cars revolve about the center axis without rorating.

Can I ask what the point of all of this is? Do you agree now that the first sentence of your first post was wrong?

19. Mar 14, 2014

### Staff: Mentor

Oh, I thought we were talking about the merry go round.

A point on the pole is not the axis itself. The axis remains perpendicular to the direction the object is moving in its orbit. Remember that the axis is a 1d line and cannot have a direction along any dimension but the 1 it is in. For example, a standard Y axis is aligned vertically and has no other facing in any other direction.

20. Mar 15, 2014

### jtban

Thanks for the example. I wish I thought of it.

Keep in mind that an axis is an imaginary axle.

The ferris wheel cars are mounted on axles (axis) that are physically attached (through bearings) to a central axle (axis). Each car is rotating about its axis once per orbit (thank God). All the cars are rotating about the central axis. Also, a point on each axle is continually facing the same direction; not the direction of motion.

Distant observer only sees one side of the cars; the observer at the center all sides once.

This scenario is only possible with the cars mounted on real axles.

Convention would classify the cars as non-rotating celestial bodies.