Where's the energy go for planets axis inclined from orbital plane?

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  • #1
Emu
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As we know from gyroscopes, the axis of a spinning object remains in the same orientation. For example, for a spinning object traveling in a straight line, the line of travel we could call a plane and the spin axis in the direction of travel could be perpendicular to the plane and the spin axis could be at a tilt or inclination relative to the plane. As the object travels, the inclination remains the same relative to the plane.

So let us look a non-spinning axis situation as it orbits; Let us view a platter on a Lazy Susan that has a cup with a straw near the edge of the platter. The straw is inclined with the plane of the platter. The one end of the straw is the highest and furthest from the center of the platter. We will say that the straw has a axis down its center. The straw axis changes direction as the platter turns. If the earth acted like the straw axis as it orbited the sun we would not have any seasons.

When the object is spinning as it orbits, the axis of spin remains oriented in the same direction regardless of the objects location in orbit, thus for earth, we have seasons in the hemispheres as we orbit earth.

When a gyroscope is forced, torque is generated on the axis. As a spinning object with its own axis of rotation orbits another object, torque is generated. So the questions is, where does the energy go in a stable system?
 

Answers and Replies

  • #2
Drakkith
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I would say it goes into resisting any gravitational influences on the rotating object.
 
  • #3
Emu
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You may be correct Mercury has highest eccentricity which may show that external gravitational influences are least hampered with the almost zero tilt of Mercury's rotation.
 
  • #4
When a gyroscope is forced, torque is generated on the axis. As a spinning object with its own axis of rotation orbits another object, torque is generated. So the questions is, where does the energy go in a stable system?
I am not sure I understand the question. Earlier in your post you write:
When the object is spinning as it orbits, the axis of spin remains oriented in the same direction regardless of the objects location in orbit, thus for earth, we have seasons in the hemispheres as we orbit earth.
This statement would seem to contradict your assertion that torque is generated. Technically, there is a very small amount of torque on the Earth due to the fact that continents prevent the tidal bulge from being exactly in line with the Earth and Sun. However, this does not seem to be the type of effect about which you are asking.
 
  • #5
Emu
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The question is in the contradiction between the observation of a orbiting planet with a tilted axis and the physics of a gyroscope being forced into a curved path i.e an orbit. From gyroscope physics, the force causing the curved path should induce a torque in the gyroscope. Since we observe tilted planets in orbits I would like to understand where and how the resulting torque is manifest. Does the torque cause the planet to shift in its orbit or is the internal structure of the planet affected? Is an effect of the torque a shift in rotation of internal fluid material (magma) as compared to the external rotation? Or as previously stated; where does the energy go?
 
  • #6
The question is in the contradiction between the observation of a orbiting planet with a tilted axis and the physics of a gyroscope being forced into a curved path i.e an orbit. From gyroscope physics, the force causing the curved path should induce a torque in the gyroscope. Since we observe tilted planets in orbits I would like to understand where and how the resulting torque is manifest.
A force produces a torque only if it affects the direction or magnitude of the rotation of an object. If one considers a number of point masses that are rotating, but whose radii are insignificantly small, there is no way for a (non-magnetic type of) central force to act on different parts of the objects differently so as to change the orientation of the axes around which they spin or the speed of their rotation (assuming their angular momentum is non-intrinsic). This is because a central force acts along the line connecting the centers of mass of each pair of objects that feel it (as long as they are spheres).

So, to the extent that a force cannot act differently and asymmetrically on different parts of an object, said object will experience no torque as regards its rotational axis (i.e., it will continue to rotate at the same rate with its axis of rotation always pointing in the same direction). The reason why one feels (and thus, reciprocally, the gyroscope "feels") a torque when one moves a gyroscope around is that one usually is exerting a force on the gyroscope that is not directed towards its center of mass. This force causes the gyroscope to rotate, changing the direction of (and/or rate of rotation about) its rotational axis (and possibly the speed of its rotation) which, by definition, requires one to exert a torque on the gyroscope. That is, one is applying a torque to the object by exerting a force on it that is not directed towards its center of mass.
Does the torque cause the planet to shift in its orbit or is the internal structure of the planet affected? Is an effect of the torque a shift in rotation of internal fluid material (magma) as compared to the external rotation? Or as previously stated; where does the energy go?
If an object is non-spherical (such as the Earth as described in my previous post), then even central forces (such as the electrostatic (coulomb) force or newtonian gravity) can exert a torque on an object. In such cases, any of the things you mentioned can occur. For example, Io, a moon of Jupiter, has a tidal bulge in its crust, just like that in water on Earth. The friction due to the movement of rock caused by this bulge heats the interior of Io until it partially melts, fueling the large amount of volcanism seen on this moon. It is probably possible for the crust of an object to be affected differently than the deeper layers; so I suppose the crust could be made to spin at a slightly different rate than the other layers (if the friction between the crust and the deeper layers was low enough). The reaction of Earth's moon to the slowing of Earth's rotation by the frictional force of the tidal bulge (due to the Moon's gravity) is that the Moon is slowly moving farther away from the Earth (so the total angular momentum of the Earth-Moon system, if isolated, would be conserved). In short, any rotational energy that is "lost" can be accounted for either as heat or a change in the orbits/rotation of the bodies.
 
  • #7
Emu
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. . . change in the orbits/rotation of the bodies.
Do you know if this is accounted for in the current modeling of the solar system?
 
  • #8
. . . change in the orbits/rotation of the bodies.
Do you know if this is accounted for in the current modeling of the solar system?
It is a very small effect, the Moon only moves away an average of http://en.wikipedia.org/wiki/Lunar_Laser_Ranging_Experiment" [Broken] than this increase. So, while the effects are modelled for Lunar laser ranging (and presumably when determining the heating due to tidal friction in the moons of the outer planets), I doubt they would be included in a solar system simulation (since they are smaller than the error in the position predictions/measurements of most objects).
 
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