Janus58
Valued Senior Member
I agree. Janus58 just quoting the same equation isn't a sufficient explanation.
We all know how you feel about math, but my response was to CheskiChips, and they used math, so I responded with math.
I agree. Janus58 just quoting the same equation isn't a sufficient explanation.
We all know how you feel about math, but my response was to CheskiChips, and they used math, so I responded with math.
The laser reflector data analysis should be able to show whether the Moon's velocity is increasing or not. I'd rather trust that than your maths.
that tells the distance to the moon, to a few mm, I think, not its speed, which has an extremely low change as a percent /year. Also has the complexity of the changes due to moon not being in circular orbit. - Makes much greater speed changes than could be observed with lasers. To get the average speed from distance measurments you would need all the math I and Janus58 explained to you and more. You and some others active in this thread simply do not have the slightest knowledge of what you post about.*The laser reflector data analysis should be able to show whether the Moon's velocity is increasing or not. I'd rather trust that than your maths.
That's absolutely NOT true!!!Quite simply, The only difference between the graphics are the axial tilt of the satellite. The sidereal rotation and period of revolution is the same.
In the first graphic (Which BTW is the fourth graphic from a different viewpoint), you would say that the satellite tumbles around two axes, but in the 3rd, which closely resembles the orbit of the Moon, you would say that it doesn't rotate at all. Yet you have still failed to answer as where exactly between 90° and 0° axial tilt does the satellite stop all rotation, while to someone outside the system the rotation of the satellite doesn't change, just the angle at which it rotates.
Also, let's go back the the situation where you say the satellite is tumbling around two axes. This situation is very like that of Uranus. It too, essentially lays on its side as it orbits the Sun with its polar axis stationary with respect to the fixed stars. If you were to watch Uranus from the Sun, its apparent motion would be like that of graphic 4, with the exception that it would rotate around its polar axis more quickly.
A rotating body, however, does not naturally rotate around two axes, unless there is precession. Precession is caused by a torque applied to the axis of a rotating body. This torque acts at a right angle to the precession.
In this case it would have to act at a right angle to the orbital plane. However, there is nothing that can cause such a torque, and without a constant torque, there can be no precession.
Ergo, no matter what it looks like from the Sun, Uranus doesn't tumble around two axes (and neither does the satellite in the 4th graphic.) Instead, its polar axis stays fixed in one direction while it rotates around it.
And what holds for an axis of a planet of satellite holds to a face of a satellite. If a satellite keeps one face stationary with respect to the stars, it does not rotate, even though it presents all sides to the planet as it orbits.
The upshot is that, despite your earlier protest, there is a preferred frame for rotation. This is easily demonstrated. Take a bicycle wheel that is not rotating with respect to the fixed stars. You can grab it by the axle and easily turn it in any direction. Now spin it on its axle, and try to twist it, it will fight you.(and will precess as discussed above).
So even if the fixed stars are not the preferred frame for rotation, they are very close to it. And thus, rotation is properly judged with respect to the fixed stars in all instances.
You are arguing a tautology. Essentially, you are saying that since the moon doesn't rotate as it orbits it keeps the same face towards the Earth, and since it keeps the same face towards the Earth, it doesn't rotate.
You're assuming your conclusion as your initial premise.
The reverse argument is that because the Moon rotates once per orbit it keeps one face always towards the Earth.
Tidal locking locks the Moon's period of rotation to 1 rotation to one orbit. Though it doesn't keep the rotational speed matched to the orbital speed. The radians per sec swept out by the Moon's orbits speeds up and slows down from perigee to apogee, the radian per sec due to rotation however stays constant. This is what causes the libration of longitude, at different parts of the orbit the rotation speeds ahead of or lags behind the orbit. This indicates independence of rotation from orbit.
The Moon's orbital motion is slowing down not speeding up. Higher orbits are slower orbits and the Moon is receding from the Earth. It is gaining energy, it is just that the majority of that energy is gained as gravitational potential.
They are already posted one under the other, side by side would make no difference. I'm afraid that you are seeing what you want to see.That's absolutely NOT true!!!
Since I don't have full posting privileges yet and can't post your images side by side for easier comparison, why don't you do that for us all!
There is nothing to dispute, it is fact. These animations were done with a ray-tracer. Ray-tracing works like this: You place objects into a three dimensional area by defining their x,y and z coordinates. You also place a light source and "camera" in the area the same way. The computer then renders the image as it would appear from the "camera's" position. You can also translate and rotate objects in the scene by using a "clock" variable, causing the program to render successive frames of an animation. The only difference in scene language between the 1st and 4th graphic is the position and aiming of the Camera. The translation and rotation parameters of the satellite and its axis remain the same.I dispute that your 1st and 4th graphics are the same with their only differences the observer's viewpoints (i.e., center-point versus sidereal.)
http://www.apl.ucl.ac.uk/iopw/uworkshop_060905.pdfUranus' polar axis is essentially on its side, but its polar axis is NOT "stationary with respect to the fixed stars!"
Can you provide a citation?
if the force were applied parallel to the axis it will not precess. A toy top will only precess if its axis is tilted from vertical, in which case the force of gravity is not parallel to the axis, and there is no torque. No torque, no precession.The force causing torque can also be parallel to the spin axis, as is the case with a toy top's procession caused by the Earth's gravity.
There is both torque-free precession as well as procession caused by torque.
Wow, you can quote Wikipedia.Not so - since our Earth rotates on its polar axis and has constant torque being applied by the sun and moon at right angles:
The fixed stars. And yes, Uranus probably undergoes a small precession, but since its moons all orbit in or nearly in the plane of its equator, and any torque on its equatorial bulges caused by the Sun would be extremely small (Such a torque is caused by tidal forces, and tidal forces fall of by the cube of the distance), it would have an extremely long period.Stays fixed in relation to what?
which has absolutely nothing to do with the principles of the discussion at hand. You do seem to have a habit of flooding a post with irrelevant data.That simply is not true! Venus nearly does keep one face pointed towards the stars as it rotates clockwise (retrograde) on its polar axis nearly one time per orbit.
(NOTE: Venus completes one counter-clockwise orbit every 224.65 days and Venus rotates once clockwise every 243 days.)
Once again, you are simply imposing your personal perception of "rotation of an astronomical body. What you "plainly see" in that graphic is not what everyone else plainly sees. We plainly see a moon that does not rotate in the top graphic, and one that rotates counter-clockwise once per orbit in the bottom graphic.In any event, I've already covered that topic well, and an astronomical body that *appears* from the sidereal perspective to not be rotating, actually does have one polar axial spin (in a clockwise direction) per each complete orbit, as can plainly be seen in the top graphic here (don't add www):
community-2.webtv.net/kdine5/Lunacy/index.html
Once again, some pasted material that does not add anything to the discussion. The ability to paste does not infer understanding.That's an informal explanation of precession often demonstrated in high school classes:
"In a classic beginning physics demonstration, the instructor stands on a swiveling platform and holds a spinning bicycle wheel at arm's length. The wheel is vertical and the instructor is standing still. The instructor then tilts the wheel toward horizontal. This causes the instructor to start spinning slowly on the platform. Bringing the wheel back to vertical and tilting it the other way makes the instructor spin the other way.
"Since the forces on opposite sides are in opposite directions, the result is torque. Each pair of opposite particles on the wheel contributes to the torque that causes the instructor to turn on the platform. Tilting the wheel the other direction produces torque in the opposite direction, slowing the instructor's spin and eventually reversing it."
That is a silly argument. If enough time were to pass that the Earth becomes tidally locked to the Moon such that its tidal bulges remained fixed on its surface, would you then claim that the Earth had stopped rotating?As for a sidereal perspective being a "preferred" perspective (it obviously has its uses in astronomy), that doesn't turn its perspective into an absolute reality.
Absolutely not true!!! I have pointed out that a large astronomical body rotating around its polar axis assumes the shape of an oblate sphere (as the Earth is shaped.) WHEREAS, our non-polar-rotating moon has solidified into the shape of a football as it cooled over 3 billion years ago freezing its two tidal bulges in place.
When the moon still had axial rotation its tidal bulges wouldn't have been fixed in one location on its surface. When the moon lost its polar rotation over 3 billion years ago, it wound down to ZERO polar axial rotations per orbit, NOT one (1) polar axial rotation per orbit!
Again, it seems like you are using your own peculiar notion of rotation here. It can rotate around its own axis and revolve around a orbital axis while constantly facing the axis of revolution. In fact, it must rotate once per orbit to do so.Today the moon ONLY revolves around an exterior axis, the Earth-moon barycenter!
Models prove that an orbiting astronomical body CANNOT spin on two axes at the same time and still keep one of its faces constantly pointed towards the center point!
No it isn't because you are assuming that your notion of "rotation on an axis" is true to "prove" that it is correct.That's all quite a bit more than mere tautology!!!
It rotates around it own polar axis and revolves around the Earth-moon barycenter Oh, and by the way, the Moon's polar axis is tilted 6.5° to that of its orbit. Because of this, as seen from the Earth, the Moon's axis traces out a cone as with a period of once per orbit. This is what causes the libration of latitudesRotates around WHAT?? If the axis for that claimed rotation is the Earth-moon barycenter, which is the same axis of the moon's orbit, then that's classic tautology!!!
Learn to read. I never said it was your argument, I said it was the reverse of your argument, And as just as strong as your argument on their own merits.That's your apparent argument, not mine!
I say that one complete moon orbit is one (1) 360 degree revolution around the Earth. The moon's ONLY axis for that orbit is the Earth-moon barycenter located within the Earth.
Libration is interesting, but it doesn't account for any 360 degree rotations of the moon. What is at issue here is the location of the moon's axis as it orbits 360 degrees around the Earth.
What is at issue here is that that moon's path as it orbits the Earth-Moon barycenter is a separate and independent motion from its rotation about its own polar axis, just as much as if the moon traveled in a straight line rather than an ellipse. And both the librations of longitude and latitude demonstrate this independence of motion.
If you claim the moon has two separate 360 degree spin axes and it still keeps one face pointed towards us, then I dispute that!
Ken
Thus the Sun’s gravity is 1.30 x 6.50 = 8.45 times stronger force on the moon than the Earth’s gravity is. This is why the moon orbits the sun, not the Earth. All the Earth does is make the moon’s basically elliptical orbit about the sun have some small “wobble.”
Even those who dig themselves in deep embarrassing holes are right sometimes. This is one of those times. Any non-spherical body will undergo torque-free precession if its angular velocity vector is not aligned with one of the body's principal axes of rotation. Wikipedia discusses this briefly here. The Earth undergoes a torque-free nutation called the Chandler wobble. It is very tiny compared to the torque-induced lunisolar precession.There is both torque-free precession as well as procession caused by torque.No torque, no precession.
To get the average speed from distance measurments you would need all the math I and Janus58 explained to you and more. You and some others active in this thread simply do not have the slightest knowledge of what you post about.*
Or it might be that Billy is right and that you "simply do not have the slightest knowledge of what you post about." The math is very cut and dried, and has been since Newton's time. Read post #137, for instance, which contains the equation for the velocity of a small body in a circular orbit.I'm glad I started the thread though. From what I've seen above it might be that the maths isn't quite as cut and dried as you may like to think.
Even those who dig themselves in deep embarrassing holes are right sometimes. This is one of those times. Any non-spherical body will undergo torque-free precession if its angular velocity vector is not aligned with one of the body's principal axes of rotation. Wikipedia discusses this briefly here. The Earth undergoes a torque-free nutation called the Chandler wobble. It is very tiny compared to the torque-induced lunisolar precession.
Or it might be that Billy is right and that you "simply do not have the slightest knowledge of what you post about." The math is very cut and dried, and has been since Newton's time. Read post #137, for instance, which contains the equation for the velocity of a small body in a circular orbit.
More generally, the vis-viva equation describes the magnitude of the velocity vector for the orbit of one point mass about another (or two bodies with spherical mass distribution):
$$v^2 = G\,(m_1+m_2)\,\left(\frac 2 r - \frac 1 a\right)$$
Back to the circular orbital velocity equation presented by Janus,
$$v=\sqrt{\frac{GM}r}$$
The circumference of a circle is $$c = 2\pi r$$. The time taken to complete one revolution at a constant speed $$v$$ is
$$P = \frac c v = \frac{2\pi r}{v} = 2\pi \sqrt{\frac {r^3}{GM}}$$
or
$$\frac{P^2}{r^3} = \frac{4 \pi^2}{GM}$$
which is Kepler's third law. In other words, this is not just cut-and-dried mathematics, it is 400 year-old cut-and-dried mathematics.
I think you misunderstood why I mentioned that the sun's gravity was ~8.45 times stronger at the moon than the Earth's is. There were two reasons:... You are using the wrong metric, Billy. The Moon's velocity relative to the Earth is well below Earth escape velocity, and the Moon's orbit about the Earth lies well within the Earth's gravitational sphere of influence with respect to the Sun. ...
Ken: Another way to show how silly your POV is follows:
For convenience assume the moon & Earth are in “deep space” far from any other masses but all else is unchanged. I.e. the moon turns around once in exactly one orbit period, which is 28 days. Everyone but you and Dwayne describes this as “spinning” on its polar axis with period of 28 days, but you two say: “No that is not it is not spinning, it is tide-locked orbiting the barycenter without any spin.”
Now suppose a third body rapidly passed by, making a gravitational impulse (acting on the moon’s center of mass of course and applying no net torque* to the moon) which throws the moon into a new, much more elliptic, orbit about the barycenter with a period of 50 MONTHS. Now at apogee the moon is no longer keeping the same face turned towards the Earth, but turns 360 around MANY times so we see all side of the moon. (We already can see more than half of the moon as it is not now in a purely circular orbit.)
Do you at least agree it is “spinning” in its new orbit, even though it angular momentum about it polar axis is exactly what it was before the third body approached? If you do, why do you say it is NOT now spinning about its polar axis when the rotation about that axis (rate = 360degrees / 28 days) is exactly the same before as after the third body passed? ...
To Ken Dine:
You have a strong bias that drives you to claim the moon rotates about the Earth moon barycenter without spin.
(1) Treating as an absolute property of rotation the term "clockwise" and not realizing that "clockwise" switches to "counter -clockwise" as the observer changes from one side to the plane of rotation to the other. (Associated with your second "shooting of self in the foot" with a false "proof" that you were correct.)
(2) Not realizing the Foucault Pendulum operating above either pole of the moon does make a 360 circle in about 28 days - you offered the fact that it would not as if it did that would indicate moon was spinning about the polar axis. (Associated with your first "shooting of self in the foot" with a false "proof" that you were correct.)
(3) Not realizing that the sun's gravity is stronger force at the moon than the earth's gravity is. (I worked it out for you to show sun is 8.45 times stronger, but received no thanks or even an acknowledgement that you were wrong. - So I assume you still hold that false POV.)
(4) Not realizing that the tides are made by the gradient of gravity, not by the force of gravity. Or that your argument based on moon making stronger tides than the sun does not show the moon has stronger gravity at the moon.
(5) Not realizing the moon only appears to orbit the Earth for a small set of reference frames, but all others in the universe, for example for a frame based on any planet or asteroid, or the sun etc. see it is in orbit about the sun with about a 1/4 of one percent wobble. I illustrated this 1 part in 400 radial variation with 8 inch diameter circular drawn by a line only 0.01 inches wide. Something approximately this width| forming a circle filling your laptop computer screen and told you the wobble stayed inside the line's width. –I.e. was not even noticeable in that scale drawing!)
Hey, you do know what the barycenter is and most do not; but as they say: "A little knowledge is a dangerous thing", especially for one lacking the grace to admit their errors.
--------------
*Except Martians, of course.
...the moon merely turns around its polar axis, which is NOT the same thing as a true polar rotation...
Explain lunar libration with this model. Hint: You can't. Lunar libration results precisely because the moon's rotation rate (and rotational axis) is not exactly equal to the moon's orbital rate (and orbital axis). The moon's rotational rate is nearly constant; it's orbital rate is not because the moon's orbit is slightly elliptical.NO, I am instead saying that the moon ONLY revolves around an exterior axis once each 27.3 day orbit, and that axis the moon is revolving around is the common mass of the Earth & moon, which is called a barycenter, which is a foci located within the Earth.
Umm, turning about a polar axis is precisely the definition of rotation.In orbiting around that barycenter the moon merely turns around its polar axis, which is NOT the same thing as a true polar rotation.
We do have 366.24 sidereal days per year. What constitutes a "day" depends on one's frame of reference. You are assuming one and one only frame of reference is "true", and that viewpoint is simply wrong. All reference frames are equally valid, including the geocentric frame in which the Moon's motion appears to go a rather complex longitudinal and latitudinal libration and an inertial frame in which the Moon appears to undergoing nearly uniform rotation about an axis passing through its center of mass.E.g. the Earth has 365.25 true polar rotations per year, but from a sidereal perspective, the Earth *appears* to rotate 366.25 times per year. If the Earth has 366.25 sidereal rotations per year, then why do we only have 365 days per year?
(My graphics) are already posted one under the other, side by side would make no difference.
Ken said:(NOTE: Venus completes one counter-clockwise orbit every 224.65 days and Venus rotates once clockwise every 243 days.)
which has absolutely nothing to do with the principles of the discussion at hand. You do seem to have a habit of flooding a post with irrelevant data.
Besides which, the period. IOW, the time it takes for Venus to rotate once relative to the fixed stars.
Why would you think that the very astronomers that you claim are wrong about the rotation of the Moon would list a rotational period for Venus based on your perception of planetary rotation?
Ken said:In any event, I've already covered that topic well, and an astronomical body that *appears* from the sidereal perspective to not be rotating, actually does have one polar axial spin (in a clockwise direction) per each complete orbit, as can plainly be seen in the top graphic here (don't add www):
community-2.webtv.net/kdine5/Lunacy/index.html
Once again, you are simply imposing your personal perception of "rotation of an astronomical body. What you "plainly see" in that graphic is not what everyone else plainly sees. We plainly see a moon that does not rotate in the top graphic, and one that rotates counter-clockwise once per orbit in the bottom graphic.
Once again, some pasted material that does not add anything to the discussion. The ability to paste does not infer understanding.That is a silly argument. If enough time were to pass that the Earth becomes tidally locked to the Moon such that its tidal bulges remained fixed on its surface, would you then claim that the Earth had stopped rotating?
The fact that the moon is oblong is simple due to the fact that because of its slow rate of rotation, the tidal forces of the Earth had a greater effect on its shape. It is also related to the fact that the moon likely had a much more eccentric orbit when it cooled into its present shape.
Again, it seems like you are using your own peculiar notion of rotation here. It can rotate around its own axis and revolve around a orbital axis while constantly facing the axis of revolution. In fact, it must rotate once per orbit to do so.
No it isn't because you are assuming that your notion of "rotation on an axis" is true to "prove" that it is correct. It rotates around it own polar axis and revolves around the Earth-moon barycenter Oh, and by the way, the Moon's polar axis is tilted 6.5° to that of its orbit. Because of this, as seen from the Earth, the Moon's axis traces out a cone as with a period of once per orbit. This is what causes the libration of latitudesLearn to read. I never said it was your argument, I said it was the reverse of your argument, And as just as strong as your argument on their own merits.
And in doing so you are making yourself look foolish.
Yes, the orange spun once on its axis for each turn of me. If it hadn't, it would have appeared to rotate as I did, but it showed no apparent rotation (this is logical since it was stationary wrt my hand), therefore it must have rotated about its own axis.Ken Dine said:Spin 360 around with an orange in your out-stretched hand, and as you spin around looking at the orange (which isn't rotating around its own center of gravity), and then tell me the orange was spinning on its internal axis, or not?