Planetary motions: translation, rotation, or both?

  • #1
nonequilibrium
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Hello,

Imagine two stars orbiting in circles around their center of mass. Is this movement generally called a translation, a rotation, or both? The concept of "revolution" is bothering me; is this always nothing but a rotation? Is a revolution a certain part of a rotation? A specific case?

Let me ask this concrete question:

Imagine we're in the center of mass (for the double star) and we stop the rotations -if present- of the stars, and by rotations I here mean like the rotation of the earth, so we leave the revolution intact (i.e. the sidereal day for a star has become zero). Can't we then call the movement of a star a translation? The star itself has all the characteristics the definition of translation asks.

Or is it perhaps the following: in this case, each star is translating (by definition?), but the whole system (the two stars) is seen as a rotation (because their center of mass is a fixed point?).
 

Answers and Replies

  • #2
tiny-tim
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hello mr. vodka! :smile:

if the Moon kept the same face towards a particular star (instead of towards the Earth), then that would still be rotation, not translation …

the rotation is about a point in the Earth


however, the (special relativity) Lorentz transformation for an observer on the Moon would be the ordinary "translation" equation, not the combination of translation and rotation that would be necessary if the Moon was spinning …

in that sense (only), i suppose you could say that it was a translation
 
  • #3
nonequilibrium
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Hm I'm only familiar with an introduction to special relativity, so my knowledge on Lorentz transformations is limited.

Anyway, thanks for the reply, but I'm a bit confused by it: in my example there is no Earth. I suppose we could just as well take Sun-Earth as our example though! So let's: now say I stop the spinning of the earth in the sense that the sidereal day of the earth is zero days, and such that one solar day now takes a year. Now you say this is still a rotation of the earth. Why is that? Isn't this movement the definition of a translation? (all points move the same relatively to one another, no fixed point)
 
  • #4
tiny-tim
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i see what you mean, but it obviously is rotating about the sun

why does it matter? … i mean, what's the application? :confused:
 
  • #5
nonequilibrium
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but it obviously is rotating about the sun

Why? I don't understand how the earth is then obviously rotating.

why does it matter? … i mean, what's the application?

Understanding the meanings of translation and rotation and how they apply to solar systems? (and by induction to other systems):)

PS: an interesting side-Q might be: is it even possible for a planet to orbit its sun like that, or will gravitational coupling always tend to rotate the earth around its axis, meaning that the steady-state revolution of an earth around a sun is one where the solar day is zero, i.e. one where the earth always faces the same side toward the sun?
 
  • #6
K^2
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Tidal forces acting on the planet will tend to force it towards a tidal lock. So if the planet happens to have exactly zero rotation at one point in time, it won't last. You're right about that. It is still possible as a temporary situation, though. Suppose you start out with a planet that's rotating in retrograde. That does not happen in a natural formation, but if the planet is an extrasolar capture, it can be rotating the "wrong" way. Then, due to tidal lock, it will be slowing down more and more until it passes a point where it does not rotate at all.
 
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  • #7
nonequilibrium
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Hm, seems very understandable, thank you!

And in THAT moment of time that the planet is not rotating, then it's translating, right?
Subtler question: is the whole system (sun-earth) still rotating at that moment? (I would think so because their common center of mass is a fixed point, and a movement with a fixed point is a rotation?) Or is this question meaningless?
 
  • #8
K^2
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Rotation always needs a center specified. Rotation around what? A planet may rotate around a star without rotating around own axis. So yeah, you can say that the star-planet system is rotating, while the planet is not, keeping in mind that centers of rotation for the two systems are different.
 
  • #9
klimatos
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Hello,

Imagine two stars orbiting in circles around their center of mass. Is this movement generally called a translation, a rotation, or both? The concept of "revolution" is bothering me; is this always nothing but a rotation? Is a revolution a certain part of a rotation? A specific case?

Let me ask this concrete question:

Imagine we're in the center of mass (for the double star) and we stop the rotations -if present- of the stars, and by rotations I here mean like the rotation of the earth, so we leave the revolution intact (i.e. the sidereal day for a star has become zero). Can't we then call the movement of a star a translation? The star itself has all the characteristics the definition of translation asks.

Or is it perhaps the following: in this case, each star is translating (by definition?), but the whole system (the two stars) is seen as a rotation (because their center of mass is a fixed point?).

I cannot speak to your general question since I believe the problem is one of a chosen frame of reference.

However, in terms of general earth-sun relationships, we speak of the Earth as "rotating" on its axis while "revolving" around the Sun.
 

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